{"id":11821,"date":"2024-09-09T21:37:00","date_gmt":"2024-09-09T16:07:00","guid":{"rendered":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/%e0%a4%ad%e0%a4%bf%e0%a4%a8%e0%a5%8d%e0%a4%a8-%e0%a4%95%e0%a5%87-%e0%a4%b8%e0%a4%be%e0%a4%a5-%e0%a4%ae%e0%a4%9c%e0%a4%bc%e0%a4%be\/"},"modified":"2026-05-24T17:38:50","modified_gmt":"2026-05-24T12:08:50","slug":"%e0%a4%ad%e0%a4%bf%e0%a4%a8%e0%a5%8d%e0%a4%a8-%e0%a4%95%e0%a5%87-%e0%a4%b8%e0%a4%be%e0%a4%a5-%e0%a4%ae%e0%a4%9c%e0%a4%bc%e0%a4%be","status":"publish","type":"post","link":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/%e0%a4%ad%e0%a4%bf%e0%a4%a8%e0%a5%8d%e0%a4%a8-%e0%a4%95%e0%a5%87-%e0%a4%b8%e0%a4%be%e0%a4%a5-%e0%a4%ae%e0%a4%9c%e0%a4%bc%e0%a4%be\/","title":{"rendered":"\u092d\u093f\u0928\u094d\u0928 \u0915\u0947 \u0938\u093e\u0925 \u092e\u091c\u093c\u093e"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">\u0906\u0907\u090f \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0930\u0932 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u201c\u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928\u094b\u0902\u201d \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0947\u0902 :<\/p>\n\n<ul class=\"wp-block-list\">\n<li>\u0928\u093f\u092f\u092e-1 : \\(\\frac{1}{2}\\) \u090f\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u0928\u093f\u092f\u092e-2 : \u092f\u0926\u093f \\(\\frac{p}{q}\\) \u090f\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948, \u0924\u094b \\(\\frac{p}{q + p}\\) \u092d\u0940 \u090f\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u0928\u093f\u092f\u092e-3 : \u092f\u0926\u093f \\(\\frac{p}{q}\\) \u090f\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948, \u0924\u094b \\(\\frac{q}{q + p}\\) \u092d\u0940 \u090f\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964<\/li>\n<\/ul>\n\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0939\u092e \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \\(\\frac{1}{2}\\) \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0928\u093f\u092f\u092e-2 \u0914\u0930 \u0928\u093f\u092f\u092e-3 \u0915\u094b \u092c\u093e\u0930-\u092c\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0915\u0947 \u0905\u0928\u094d\u092f \u0938\u092d\u0940 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u091c\u092c \u0928\u093f\u092f\u092e-2 \u0932\u093e\u0917\u0942 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u094b \u090f\u0915 <span>\u0932\u093e\u0932 \u0924\u0940\u0930<\/span> \u0916\u0940\u0902\u091a\u0915\u0930 \u0914\u0930 \u091c\u092c \u0928\u093f\u092f\u092e-3 \u0932\u093e\u0917\u0942 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u094b \u090f\u0915 <span>\u0928\u0940\u0932\u093e \u0924\u0940\u0930<\/span> \u0916\u0940\u0902\u091a\u0915\u0930 \u0939\u092e \u0928\u093f\u092f\u092e-2 \u0914\u0930 3 \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0915\u0940 \u092a\u094d\u0930\u0915\u094d\u0930\u093f\u092f\u093e\u0913\u0902 \u0915\u094b \u0926\u0943\u0936\u094d\u092f \u0930\u0942\u092a \u0938\u0947 \u0926\u093f\u0916\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 <\/p>\n\n<p class=\"wp-block-paragraph\">\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \\(\\frac{p }{q}\\) \u090f\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964 \\(\\frac{p}{q}\\) \u092a\u0930 \u0928\u093f\u092f\u092e-2 \u0914\u0930 \u0928\u093f\u092f\u092e \\(3\\) \u0932\u093e\u0917\u0942 \u0915\u0930\u0915\u0947, \u0939\u092e\u0947\u0902 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u092e\u0940\u0915\u0930\u0923 \u092e\u093f\u0932\u0924\u093e \u0939\u0948 :  <\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"415\" height=\"205\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-1.jpg\" alt=\"fraction-fig-1\" class=\"wp-image-15255\" style=\"object-fit:cover\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-1.jpg 415w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-1-360x178.jpg 360w\" sizes=\"auto, (max-width: 415px) 100vw, 415px\" \/><\/figure>\n\n<p class=\"wp-block-paragraph\">\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \\(\\frac{1}{2}\\) \u092a\u0930 \u0928\u093f\u092f\u092e-2 \u0914\u0930 \u0928\u093f\u092f\u092e-3 \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u0915\u094b \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 :<\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"318\" height=\"200\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-2.jpg\" alt=\"fraction-fig-2\" class=\"wp-image-15263\" style=\"object-fit:cover\"\/><\/figure>\n\n<p class=\"wp-block-paragraph\">\u0907\u0938 \u0936\u093e\u0916\u093e \u0915\u094b \u090f\u0915 \u0914\u0930 \u0938\u094d\u0924\u0930 \u0924\u0915 \u092c\u0922\u093c\u093e\u0924\u0947 \u0939\u0941\u090f \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0926\u0947\u0916\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 :<\/p>\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-3.jpg\" alt=\"fraction-fig-3\" class=\"wp-image-15266\" style=\"object-fit:cover\"\/><\/figure>\n\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0938\u0947 \u092a\u0924\u093e \u091a\u0932\u0924\u093e \u0939\u0948 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0936\u093e\u0916\u093e\u0913\u0902 \u092e\u0947\u0902 \u092c\u0901\u091f\u0915\u0930 \u0926\u094b \u0928\u090f \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u092c\u0928\u093e \u0926\u0947\u0924\u0940 \u0939\u0948\u0964<\/p>\n\n<p class=\"wp-block-paragraph\"><em><span><strong>\u0917\u0924\u093f\u0935\u093f\u0927\u093f :<\/strong> \u0936\u093e\u0916\u093e\u0913\u0902 \u0915\u094b \u0905\u0917\u0932\u0947 \u0926\u094b \u0938\u094d\u0924\u0930\u094b\u0902 \u0924\u0915 \u0935\u093f\u0938\u094d\u0924\u093e\u0930 \u0926\u0947\u0902\u0964 \u0906\u092a\u0915\u0947 \u0905\u0935\u0932\u094b\u0915\u0928 \u0915\u094d\u092f\u093e \u0939\u0948\u0902? <\/span><\/em><\/p>\n\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0915\u0947 \u092c\u093e\u0926, \u0906\u0907\u090f \u0915\u0941\u091b \u0938\u094d\u0935\u093e\u092d\u093e\u0935\u093f\u0915 \u092a\u094d\u0930\u0936\u094d\u0928\u094b\u0902 \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u090f\u0901 \u091c\u093f\u0928\u0915\u093e \u0909\u0932\u094d\u0932\u0947\u0916 NRICH \u0935\u0947\u092c\u092a\u0947\u091c \u092a\u0930 \u092d\u0940 \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \u092a\u093e\u0920\u0915\u094b\u0902 \u0938\u0947 \u0906\u0917\u094d\u0930\u0939 \u0939\u0948 \u0915\u093f \u0938\u092e\u093e\u0927\u093e\u0928\u094b\u0902 \u0915\u0940 \u091c\u093e\u0901\u091a \u0915\u0930\u0928\u0947 \u0938\u0947 \u092a\u0939\u0932\u0947 \u0907\u0928\u094d\u0939\u0947\u0902 \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0947\u0902 : <\/p>\n\n<ol class=\"wp-block-list\">\n<li>\u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940\/ \u091b\u094b\u091f\u0940 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0915\u094c\u0928-\u0938\u0940 \u0939\u0948?<\/li>\n\n\n\n<li>\u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u093e\/ \u091b\u094b\u091f\u093e \u0905\u0902\u0936 \u0915\u094c\u0928-\u0938\u093e \u0939\u0948?<\/li>\n\n\n\n<li>\u0915\u094d\u092f\u093e \u092f\u0939 \u0938\u0939\u0940 \u0939\u0948 \u0915\u093f \u0905\u0902\u0936 \u0918\u091f\u0924\u0947 \u0915\u094d\u0930\u092e \u092e\u0947\u0902 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0947?<\/li>\n\n\n\n<li>\u0910\u0938\u093e \u0932\u0917\u0924\u093e \u0939\u0948 \u0915\u093f \u090f\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0915\u0947 \u0905\u0902\u0936 \u0914\u0930 \u0939\u0930 \u092e\u0947\u0902 1 \u0915\u094b \u091b\u094b\u0921\u093c\u0915\u0930 \u0915\u094b\u0908 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u092d\u093e\u091c\u0915 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0915\u094d\u092f\u093e \u092f\u0939 \u0939\u092e\u0947\u0936\u093e \u0938\u0939\u0940 \u0939\u094b\u0924\u093e \u0939\u0948? <\/li>\n\n\n\n<li>\u0915\u094d\u092f\u093e \u092d\u093f\u0928\u094d\u0928\u094b\u0902 \u0915\u093e \u090f\u0915 \u092c\u0928\u094d\u0926 \u092b\u0928\u094d\u0926\u093e \u092c\u0928\u093e\u0928\u093e \u0938\u092e\u094d\u092d\u0935 \u0939\u0948, \u091c\u0939\u093e\u0901 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928\u094b\u0902 \u0915\u093e \u090f\u0915 \u0915\u094d\u0930\u092e \u0906\u092a\u0915\u094b \u092a\u094d\u0930\u093e\u0930\u092e\u094d\u092d\u093f\u0915 \u092c\u093f\u0928\u094d\u0926\u0941 \u092a\u0930 \u0935\u093e\u092a\u0938 \u0932\u0947 \u0906\u090f?<\/li>\n<\/ol>\n\n<p class=\"wp-block-paragraph\">\u0905\u092c, \u092e\u0948\u0902 \u092a\u093e\u0920\u0915\u094b\u0902 \u0915\u094b \u0909\u092a\u0930\u094b\u0915\u094d\u0924 \u0938\u092e\u0938\u094d\u092f\u093e\u0913\u0902 \u0915\u094b \u0939\u0932 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0905\u092a\u0928\u0940 \u092f\u093e\u0924\u094d\u0930\u093e \u092a\u0930 \u0932\u0947 \u091c\u093e\u0928\u093e \u091a\u093e\u0939\u0942\u0901\u0917\u093e\u0964 \u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947 \u0939\u092e \u090f\u0915 \u0938\u0902\u0915\u0947\u0924\u0928 \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902 : \u091a\u0942\u0901\u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091a\u0930\u0923 \u092e\u0947\u0902 \u0915\u0947\u0935\u0932 \u0926\u094b \u0938\u092e\u094d\u092d\u093e\u0935\u0928\u093e\u090f\u0901 \u0939\u0948\u0902, \u0907\u0938\u0932\u093f\u090f \u0939\u092e \u0928\u0940\u091a\u0947 \u0935\u0930\u094d\u0923\u093f\u0924 \u0938\u0902\u0915\u0947\u0924\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0915\u094b \u0926\u0930\u094d\u0936\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 <\/p>\n\n<ul class=\"wp-block-list\">\n<li>\u0928\u093f\u092f\u092e-1 \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0915\u094b \u092a\u094d\u0930\u0924\u0940\u0915 \\(A\\) \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u0928\u093f\u092f\u092e-2 \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u090f\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0915\u094b \u092a\u094d\u0930\u0924\u0940\u0915 \\(B\\) \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0914\u0930<\/li>\n\n\n\n<li>\u0928\u093f\u092f\u092e-3 \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u0924\u094d\u092a\u0928\u094d\u0928 \u090f\u0915 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0915\u094b \u092a\u094d\u0930\u0924\u0940\u0915 \\(C\\) \u0926\u094d\u0935\u093e\u0930\u093e \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964<\/li>\n<\/ul>\n\n<p class=\"wp-block-paragraph\">\u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \\(\\frac{1}{2}\\) \u0915\u094b \\(A\\) \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u0917\u092f\u093e \u0939\u0948 \u0914\u0930 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0905\u0928\u094d\u092f \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0915\u094b \\(A\\) \u0938\u0947 \u0936\u0941\u0930\u0942 \u0939\u094b\u0928\u0947 \u0935\u093e\u0932\u0940 \u0936\u0943\u0902\u0916\u0932\u093e \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0926\u0930\u094d\u0936\u093e\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0914\u0930 \u0909\u0938\u0915\u0947 \u092c\u093e\u0926 \\(Bs\\) \u0914\u0930\/ \u092f\u093e \\(Cs\\) \u0915\u093e \u0926\u094d\u0935\u093f\u0906\u0927\u093e\u0930\u0940 \u0938\u0902\u092f\u094b\u091c\u0928 \u0906 \u0938\u0915\u0924\u093e \u0939\u0948\u0964  .<br\/>\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \\(ABCB\\) \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u200d\u0928 \u0915\u094b \u092a\u094d\u0930\u0938\u094d\u0924\u0941\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \\(\\frac{3}{7}\\) , \u0915\u094d\u092f\u094b\u0902\u0915\u093f<\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"392\" height=\"164\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-4-2.jpg\" alt=\"&#x92D;&#x93F;&#x928;&#x94D;&#x928; &#x91A;&#x93F;&#x924;&#x94D;&#x930;-4\" class=\"wp-image-15269\" style=\"object-fit:cover\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-4-2.jpg 392w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-4-2-360x151.jpg 360w\" sizes=\"auto, (max-width: 392px) 100vw, 392px\" \/><\/figure>\n\n<h1 class=\"wp-block-heading\">\u0938\u092e\u093e\u0927\u093e\u0928<\/h1>\n\n<ol class=\"wp-block-list\">\n<li>\u091a\u0942\u0901\u0915\u093f \\(\\frac{1}{2}\\) \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u0939\u0930 \u0926\u0942\u0938\u0930\u0940 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0927\u0928\u093e\u0924\u094d\u092e\u0915 \u0939\u094b\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964 \u0938\u093e\u0925 \u0939\u0940, \u091a\u0942\u0901\u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0915\u093e \u0939\u0930, \u0905\u0902\u0936 \u0938\u0947 \u092c\u0921\u093c\u093e \u0939\u094b\u0924\u093e \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \\(1\\) \u0938\u0947 \u091b\u094b\u091f\u093e \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u0905\u092c \u0906\u0907\u090f \\(A\\), \\(AB\\), \\(ABB\\), \\(ABBB\\), \\(ABBBB\\), \u0907\u0924\u094d\u092f\u093e\u0926\u093f \u0915\u0947 \u0930\u0942\u092a \u0915\u0947 \u092e\u095b\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928\u094b\u0902 \u0915\u094b \u0926\u0947\u0916\u0947\u0902\u0964 \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \u0915\u093f \u0939\u092e \u0928\u093f\u092f\u092e-2 \u0915\u094b \\(\\frac{1}{2}\\) \u092a\u0930 \u092c\u093e\u0930-\u092c\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930 \u0930\u0939\u0947 \u0939\u0948\u0902\u0964 \u0926\u0943\u0936\u094d\u092f \u0930\u0942\u092a \u092e\u0947\u0902 \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0938\u092c\u0938\u0947 \u092c\u093e\u0908\u0902 \u0936\u093e\u0916\u093e \u0939\u0948 :<\/li>\n<\/ol>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"518\" height=\"493\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-5.jpg\" alt=\"&#x92D;&#x93F;&#x928;&#x94D;&#x928; &#x91A;&#x93F;&#x924;&#x94D;&#x930;-5\" class=\"wp-image-15273\" style=\"object-fit:cover\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-5.jpg 518w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-5-378x360.jpg 378w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-5-212x202.jpg 212w\" sizes=\"auto, (max-width: 518px) 100vw, 518px\" \/><\/figure>\n\n<p class=\"wp-block-paragraph\">\u0915\u093f\u0938\u0940 \u092d\u0940 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \\(n\\) \u0915\u093e \u0935\u094d\u092f\u0941\u0924\u0915\u094d\u0930\u092e \\(\\frac{1}{n}\\) \u0907\u0938 \u0936\u093e\u0916\u093e \u092e\u0947\u0902 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0907\u0938 \u0936\u093e\u0916\u093e \u092e\u0947\u0902 \u092a\u094d\u0930\u0935\u093f\u0937\u094d\u091f\u093f\u092f\u093e\u0901 \u091b\u094b\u091f\u0940 \u0939\u094b\u0924\u0940 \u0930\u0939\u0924\u0940 \u0939\u0948\u0902 \u0914\u0930 \u0915\u092d\u0940 \u0938\u092e\u093e\u092a\u094d\u0924 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902\u0964 \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \u0915\u093f \u0915\u094b\u0908 \u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u0940 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0938\u092e\u094d\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964<\/p>\n\n<p class=\"wp-block-paragraph\">\u0906\u0907\u090f \u0905\u092c \u0939\u092e \\(AC\\), \\(ABC\\), \\(ABBC\\), \\(ABBBC\\), \\(ABBBBC \\)\u0907\u0924\u094d\u092f\u093e\u0926\u093f \u0930\u0942\u092a\u094b\u0902 \u0915\u0940 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928\u094b\u0902 \u0915\u094b \u0926\u0947\u0916\u0947\u0902\u0964 \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \\(\\frac{1}{2}\\) \u092a\u0930 \u0928\u093f\u092f\u092e-2 \u0915\u094b \u092c\u093e\u0930-\u092c\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u093e \u0914\u0930 \u092b\u093f\u0930 \u0905\u0928\u094d\u0924 \u092e\u0947\u0902 \u090f\u0915 \u092c\u093e\u0930 \u0928\u093f\u092f\u092e-3 \u0915\u094b \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u093e\u0964 \u0926\u0943\u0936\u094d\u092f \u0930\u0942\u092a \u0938\u0947, \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \u2018\u0926\u0942\u0938\u0930\u0940\u2019 \u0938\u092c\u0938\u0947 \u092c\u093e\u0908\u0902 \u0936\u093e\u0916\u093e :<\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"577\" height=\"561\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-6.jpg\" alt=\"&#x92D;&#x93F;&#x928;&#x94D;&#x928; &#x91A;&#x93F;&#x924;&#x94D;&#x930;-6\" class=\"wp-image-15276\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-6.jpg 577w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-6-370x360.jpg 370w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-6-208x202.jpg 208w\" sizes=\"auto, (max-width: 577px) 100vw, 577px\" \/><\/figure>\n\n<p class=\"wp-block-paragraph\">\u0907\u0938 \u0936\u093e\u0916\u093e \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \\(n &gt; 1\\) \u0915\u0947 \u0932\u093f\u090f \\(\\frac{n }{n + 1}\\) \u0915\u0947 \u0930\u0942\u092a \u0915\u0947 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0902\u0964 \u0907\u0938\u0932\u093f\u090f \u092f\u0939 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928\u094b\u0902 \u0915\u093e \u090f\u0915 \u092c\u0922\u093c\u0924\u093e \u0939\u0941\u0906 \u0915\u094d\u0930\u092e \u0939\u0948 \u091c\u094b \u0915\u092d\u0940 \u0938\u092e\u093e\u092a\u094d\u0924 \u0928\u0939\u0940\u0902 \u0939\u094b\u0924\u093e\u0964 \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \u0915\u093f \u0915\u094b\u0908 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u0940 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0938\u092e\u094d\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964  <\/p>\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li>\u0938\u092c\u0938\u0947 \u091b\u094b\u091f\u093e \u0905\u0902\u0936 \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947 \\(1\\) \u0939\u0948, \u091c\u094b \\(\\frac{1 }{2}\\) \u0915\u093e \u0905\u0902\u0936 \u0939\u0948\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u091c\u0948\u0938\u093e \u0915\u093f \u0939\u092e\u0928\u0947 \u0938\u092e\u093e\u0927\u093e\u0928-\\(1\\) \u092e\u0947\u0902 \u0926\u0947\u0916\u093e, \\(\\frac{n}{n + 1}\\) \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \\(n\\) \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f \u0915\u094b\u0908 \u092d\u0940 \u0938\u092c\u0938\u0947 \u092c\u0921\u093c\u093e \u0905\u0902\u0936 \u0938\u092e\u094d\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e \u0939\u0948\u0964<\/li>\n\n\n\n<li>\u0939\u093e\u0901, \u091a\u0942\u0901\u0915\u093f \u0928\u093f\u092f\u092e-2 \u0905\u0902\u0936\u094b\u0902 \u0915\u094b \u092c\u0928\u093e\u090f \u0930\u0916\u0924\u093e \u0939\u0948 \u0914\u0930 \u0928\u093f\u092f\u092e-3 \u0905\u0902\u0936\u094b\u0902 \u0915\u094b \u092c\u0922\u093c\u093e\u0924\u093e \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u0905\u0902\u0936 \u0915\u092d\u0940 \u0918\u091f \u0928\u0939\u0940\u0902 \u0938\u0915\u0924\u0947\u0964 \u0932\u0947\u0915\u093f\u0928 \u0915\u094d\u092f\u093e \u0939\u094b\u0917\u093e \u092f\u0926\u093f \u0939\u092e \u0915\u093f\u0938\u0940 \u0938\u094d\u0924\u0930 \u092a\u0930 \u0905\u0902\u0936 \u0914\u0930 \u0939\u0930 \u0915\u0947 \u092c\u0940\u091a \u090f\u0915 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0917\u0941\u0923\u0928\u0916\u0923\u094d\u0921 \u0915\u094b \u0928\u093f\u0930\u0938\u094d\u0924 \u0915\u0930 \u0938\u0915\u0947\u0902? \u0905\u0917\u0932\u093e \u0938\u092e\u093e\u0927\u093e\u0928 \u0915\u0939\u0924\u093e \u0939\u0948 \u0915\u093f \u092f\u0939 \u0938\u092e\u094d\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964   <\/li>\n\n\n\n<li>\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \\(\\frac{p}{q}\\) \u090f\u0915 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0964 \u0928\u093f\u092f\u092e-\\(2\\) \u092f\u093e \u0928\u093f\u092f\u092e-\\(3\\) \u0932\u093e\u0917\u0942 \u0915\u0930\u0928\u0947 \u092a\u0930, \u0939\u092e\u0947\u0902 \u0915\u094d\u0930\u092e\u0936\u0903 \u092d\u093f\u0928\u094d\u0928 \\(\\frac{p}{q}\\) \u092f\u093e   \u092f\u093e \\(\\frac{p}{p + q}\\) \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u0947 \u0939\u0948\u0902\u0964 \u0906\u0907\u090f \u0939\u092e \u0907\u0928 \u0924\u0940\u0928 \u092d\u093f\u0928\u094d\u0928\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0905\u0902\u0936\u094b\u0902 \u0914\u0930 \u0939\u0930\u094b\u0902 \u0915\u0947 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0917\u0941\u0923\u0928\u0916\u0923\u094d\u0921\u094b\u0902 \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930\u0947\u0902\u0964 <br\/><br\/>\u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f \\(d\\), \\(p\\) \u0914\u0930 \\(q\\) \u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u090f\u0915 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0917\u0941\u0923\u0928\u0916\u0923\u094d\u0921 \u0939\u0948\u0964 \u0924\u092c \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947 \\(d\\) \u0915\u094b \\(p + q\\) \u0915\u094b \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930, \u092e\u093e\u0928 \u0932\u0940\u091c\u093f\u090f \u0915\u093f d, p \u0914\u0930 \\(p + q\\) \u0926\u094b\u0928\u094b\u0902 \u0915\u093e \u090f\u0915 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0917\u0941\u0923\u0928\u0916\u0923\u094d\u0921 \u0939\u0948, \u0924\u094b d \u0915\u094b \\(q = (p + q) &#8211; p\\) \u0915\u094b \u092d\u0940 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \u0915\u093f \\(p\\), \\(q\\) \u0914\u0930 \\(p + q\\) \u0915\u0947 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0917\u0941\u0923\u0928\u0916\u0923\u094d\u0921\u094b\u0902 \u0915\u0940 \u0938\u0942\u091a\u0940 \u092c\u093f\u0932\u094d\u0915\u0941\u0932 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964   <br\/><br\/>\u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947, \u092a\u0939\u0932\u0940 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \\(\\frac{1}{2}\\) \u0915\u0947 \u0932\u093f\u090f, \u0905\u0902\u0936 \u0914\u0930 \u0939\u0930 \u0915\u0947 \u092c\u0940\u091a \u0915\u0947\u0935\u0932 \u090f\u0915 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0917\u0941\u0923\u0928\u0916\u0923\u094d\u0921 \u0939\u0948, \u0905\u0930\u094d\u0925\u093e\u0924 \\(1\\)\u0964 \u0907\u0938\u0932\u093f\u090f \u0939\u0930 \u0926\u0942\u0938\u0930\u0940 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \\(\\frac{p}{q}\\) \u0915\u0947 \u0932\u093f\u090f, \u0905\u0902\u0936 \\(p\\) \u0914\u0930 \u0939\u0930 \\(q\\) \u0915\u093e \u090f\u0915\u092e\u093e\u0924\u094d\u0930 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0917\u0941\u0923\u0928\u0916\u0923\u094d\u0921 1 \u0939\u0940 \u0939\u0948\u0964 <\/li>\n<\/ol>\n\n<ol start=\"5\" class=\"wp-block-list\">\n<li>\u0928\u093f\u092f\u092e-2 \u0914\u0930 3 \u0926\u094b\u0928\u094b\u0902 \u0939\u0940 \u0939\u0930\u094b\u0902 \u0915\u094b \u092c\u0922\u093c\u093e\u0924\u0947 \u0939\u0948\u0902\u0964 \u0907\u0938\u0932\u093f\u090f \u092c\u0928\u094d\u0926 \u092b\u0928\u094d\u0926\u093e \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u090f\u0915\u092e\u093e\u0924\u094d\u0930 \u0924\u0930\u0940\u0958\u093e \u091b\u094b\u091f\u0947 \u0905\u0902\u0936 \u0914\u0930 \u0939\u0930 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u092e\u0947\u0902 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0917\u0941\u0923\u0928\u0916\u0923\u094d\u0921\u094b\u0902 \u0915\u094b \u0928\u093f\u0930\u0938\u094d\u0924 \u0915\u0930\u0928\u093e \u0939\u0948\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f, \u0938\u092e\u093e\u0927\u093e\u0928-\\(4\\) \u0915\u0947 \u0905\u0928\u0941\u0938\u093e\u0930, \u092f\u0939 \u0938\u092e\u094d\u092d\u0935 \u0928\u0939\u0940\u0902 \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f \u0915\u094b\u0908 \u092b\u0928\u094d\u0926\u093e \u0928\u0939\u0940\u0902 \u092c\u0928\u0924\u093e\u0964   <\/li>\n<\/ol>\n\n<p class=\"wp-block-paragraph\">\u092e\u0948\u0902\u0928\u0947 \u090f\u0915 \u0914\u0930 \u0926\u093f\u0932\u091a\u0938\u094d\u092a \u092c\u093e\u0924 \u0926\u0947\u0916\u0940\u0964 \u0906\u0907\u090f \u0938\u092c\u0938\u0947 \u0926\u093e\u0908\u0902 \u0936\u093e\u0916\u093e \u0915\u094b \u0926\u0947\u0916\u0947\u0902, \u091c\u093f\u0938\u0915\u0940 \u092a\u094d\u0930\u0935\u093f\u0937\u094d\u091f\u093f\u092f\u093e\u0901 \\(A\\), \\(AC\\), \\(ACC\\), \\(ACCC\\), \\(ACCCC \\)\u0907\u0924\u094d\u092f\u093e\u0926\u093f \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \u0939\u0948\u0902\u0964 <\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"585\" height=\"447\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-7.jpg\" alt=\"&#x92D;&#x93F;&#x928;&#x94D;&#x928; &#x91A;&#x93F;&#x924;&#x94D;&#x930;-7\" class=\"wp-image-15279\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-7.jpg 585w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-7-471x360.jpg 471w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-7-264x202.jpg 264w\" sizes=\"auto, (max-width: 585px) 100vw, 585px\" \/><\/figure>\n\n<p class=\"wp-block-paragraph\">\u0927\u094d\u092f\u093e\u0928 \u0926\u0947\u0902 \u0915\u093f \u0907\u0928 \u092d\u093f\u0928\u094d\u0928\u094b\u0902 \u0915\u094b \u0928\u093f\u092e\u094d\u0928\u093e\u0928\u0941\u0938\u093e\u0930 \u092a\u0941\u0928\u0930\u093e\u0935\u0930\u094d\u0924\u0940 \u0930\u0942\u092a \u0938\u0947 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e \u0938\u0915\u0924\u093e \u0939\u0948 \u0914\u0930 \u0939\u092e\u0947\u0902 \u095e\u093f\u092c\u094b\u0928\u093e\u091a\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0940 \u092f\u093e\u0926 \u0906\u0928\u0940 \u091a\u093e\u0939\u093f\u090f\u0964 \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u092a\u094d\u0930\u093e\u0915\u0943\u0924\u093f\u0915 \u0938\u0902\u0916\u094d\u092f\u093e \\(m\\) \u0915\u0947 \u0932\u093f\u090f <\/p>\n\n<p class=\"has-text-align-left wp-block-paragraph\">\\(F_1 = 1\\)<br\/>\\(F_2 = 2\\)<br\/>\\(F_{m + 2} = F_{m + 1} + F_{m}\\)<\/p>\n\n<p class=\"wp-block-paragraph\"> \u0938\u094d\u092a\u0937\u094d\u091f \u0930\u0942\u092a \u0938\u0947, \\(ACCC\\)\u2026\\(CCC \\)\u0915\u0947 \u0930\u0942\u092a \u0915\u093e \u0915\u094b\u0908 \u092d\u0940 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \\(\\frac{F_{m + 1}} {F_{m + 2}}\\) \u0915\u0947 \u0905\u0932\u093e\u0935\u093e \u0915\u0941\u091b \u0928\u0939\u0940\u0902 \u0939\u094b \u0938\u0915\u0924\u093e, \u091c\u0939\u093e\u0901 m \u0905\u0928\u094d\u0924 \u092e\u0947\u0902 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0928\u0947 \u0935\u093e\u0932\u0947 \\(C\\) \u0915\u0940 \u0938\u0902\u0916\u094d\u092f\u093e \u0939\u0948\u0964 \u091c\u0948\u0938\u093e \u0915\u093f \u0939\u092e \u092a\u0939\u0932\u0947 \u0939\u0940 \u0926\u093f\u0916\u093e \u091a\u0941\u0915\u0947 \u0939\u0948\u0902, \u0907\u0938\u0915\u093e \u092e\u0924\u0932\u092c \u0939\u0948 \u0915\u093f \u0915\u094d\u0930\u092e\u093e\u0928\u0941\u0917\u0924 \u095e\u093f\u092c\u094b\u0928\u093e\u091a\u0940 \u0938\u0902\u0916\u094d\u092f\u093e\u0913\u0902 \u0915\u0947 \u092c\u0940\u091a \\(1\\) \u0915\u0947 \u0905\u0932\u093e\u0935\u093e \u0915\u094b\u0908 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0917\u0941\u0923\u0928\u0916\u0923\u094d\u0921 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902\u0964<\/p>\n\n<p class=\"wp-block-paragraph\">\u092e\u0948\u0902\u0928\u0947 \u092f\u0939 \u092d\u0940 \u0926\u0947\u0916\u093e \u0915\u093f \u092f\u0926\u093f \u0939\u092e \u0939\u0930 \\(F_{m + 2}\\) \u0915\u094b \u0905\u0902\u0936 \\(F_{m + 1}\\) \u0938\u0947 \u092d\u093e\u0917 \u0926\u0947\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 \u0939\u092e\u0947\u0936\u093e \u0936\u0947\u0937 \\(F_{m}\\) \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964 \u0910\u0938\u093e \u0907\u0938\u0932\u093f\u090f \u0939\u0948 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \\(F_{m + 2} = F_{m + 1} + F_{m}\\)\u0964 \u092b\u093f\u0930 \u092e\u0948\u0902\u0928\u0947 \u0915\u0941\u091b \u0914\u0930 \u0926\u093f\u0932\u091a\u0938\u094d\u092a \u092c\u093e\u0924 \u0926\u0947\u0916\u0940\u0902\u0964 \u092f\u0939 \\(ACCC\\)\u2026\\(CCCBBB\\)\u2026\\(BBB \\)\u0915\u0947 \u0930\u0942\u092a \u0935\u093e\u0932\u0947 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u092d\u0940 \u0938\u0939\u0940 \u0939\u0948, \u091c\u0939\u093e\u0901 \\(C\\) \u092c\u0940\u091a \u092e\u0947\u0902 m \u092c\u093e\u0930 \u0914\u0930 \\(B\\) \u0905\u0928\u094d\u0924 \u092e\u0947\u0902 <em>k<\/em> \u092c\u093e\u0930 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u093e \u0939\u0948\u0964   <\/p>\n\n<p class=\"wp-block-paragraph\">\u0909\u0926\u093e\u0939\u0930\u0923 \u0915\u0947 \u0932\u093f\u090f, \\(AB\\), \\(ACB\\), \\(ACCB\\), \\(ACCCB\\), \\(ACCCCB \\)\u0907\u0924\u094d\u092f\u093e\u0926\u093f \u0915\u0947 \u0930\u0942\u092a \u0935\u093e\u0932\u0940 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u0940 \u0939\u0948\u0902 :<\/p>\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"651\" height=\"643\" src=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-8.jpg\" alt=\"&#x92D;&#x93F;&#x928;&#x94D;&#x928; &#x91A;&#x93F;&#x924;&#x94D;&#x930;-8\" class=\"wp-image-15285\" srcset=\"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-8.jpg 651w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-8-364x360.jpg 364w, https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/fraction-fig-8-205x202.jpg 205w\" sizes=\"auto, (max-width: 651px) 100vw, 651px\" \/><\/figure>\n\n<p class=\"has-text-align-left wp-block-paragraph\">\u0906\u0907\u090f \u0926\u0947\u0916\u0947\u0902 \u0915\u093f \u092f\u0939 \u0915\u094d\u092f\u094b\u0902 \u0938\u0924\u094d\u092f \u0939\u0948\u0964  \\( \\frac{p}{q}\\) \u0930\u0942\u092a \u0915\u0940 \u090f\u0915 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948, \\(ACCC\\)\u2026\\(CCCBBB\\)\u2026\\(BBB \\) \u091c\u0939\u093e\u0901 \u092c\u0940\u091a \u092e\u0947\u0902 \\(C\\), m \u092c\u093e\u0930 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u093e \u0939\u0948 \u0914\u0930 \\(B\\) \u0905\u0928\u094d\u0924 \u092e\u0947\u0902 \\(k\\) \u092c\u093e\u0930 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u093e \u0939\u0948\u0964 \u0926\u0942\u0938\u0930\u0947 \u0936\u092c\u094d\u0926\u094b\u0902 \u092e\u0947\u0902, \u092a\u0939\u0932\u0947, \u0928\u093f\u092f\u092e-3 \u0915\u094b \u0932\u0917\u093e\u0924\u093e\u0930 \\(m\\) \u092c\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0915\u0947 \u0914\u0930 \u092b\u093f\u0930 \u0928\u093f\u092f\u092e-2 \u0915\u094b \u092c\u093e\u0930-\u092c\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0915\u0947 \\(\\frac{p}{q}\\)\u0938\u0947 \\(\\frac{p }{q}\\) \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948\u0964 \u0907\u0938\u0932\u093f\u090f \\(\\frac{p}{q}\\) \u0915\u094b \u0928\u093f\u092f\u092e-2 \u0915\u094b \\(k\\) \u092c\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0915\u0947 \\(\\frac{F_{m + 1}}{F_{m + 2}}\\) \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u090f\u0917\u093e\u0964 \u0907\u0938\u0932\u093f\u090f \u0939\u092e\u093e\u0930\u0947 \u092a\u093e\u0938 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f           <\/p>\n\n<p class=\"has-text-align-left text-center wp-block-paragraph\">\\(\\frac{p}{q}= \\frac{F_{m + 1}}{F_{m + 2} + k(F_{m + 1})}\\)<\/p>\n\n<p class=\"has-text-align-left wp-block-paragraph\">\u0907\u0938\u0932\u093f\u090f \u092f\u0926\u093f \u0939\u092e \u0939\u0930 \\(q\\) \u0915\u094b \u0905\u0902\u0936 \\(p\\) \u0938\u0947 \u092d\u093e\u0917 \u0926\u0947\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 \u092d\u093e\u0917\u092b\u0932 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \\(k + 1\\) \u0924\u0925\u093e \u0936\u0947\u0937 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 \\(F_m\\) \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0928\u093e \u091a\u093e\u0939\u093f\u090f\u0964 \u0907\u0938\u0932\u093f\u090f \u0939\u092e\u0928\u0947 \u091c\u094b \u0938\u093f\u0926\u094d\u0927 \u0915\u093f\u092f\u093e \u0939\u0948 \u0935\u0939 \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u092a\u094d\u0930\u092e\u0947\u092f \u0939\u0948\u0964<\/p>\n\n<p class=\"wp-block-paragraph\"><strong>\u092a\u094d\u0930\u092e\u0947\u092f:<\/strong> \u092e\u093e\u0928 \u0932\u0947\u0902 \u0915\u093f \\(\\frac{p }{q}\\) \u090f\u0915 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948 \\(\\frac{1}{2}\\) \u091c\u093f\u0938\u0947 \u0928\u093f\u092f\u092e-3 \u0915\u094b \\(m\\) \u092c\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0915\u0947 \u0914\u0930 \u092b\u093f\u0930 \u0928\u093f\u092f\u092e-2 \u0915\u094b \\(k\\) \u092c\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0915\u0947 \u0938\u0947 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948, \u092b\u093f\u0930 \u092f\u0926\u093f \u0939\u092e \\(q\\) \u0915\u094b \\(p\\)\u0938\u0947 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0936\u0947\u0937 \u0939\u092e\u0947\u0936\u093e \\(F_m\\) \u0939\u094b\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u0947 \u0928\u093f\u092e\u094d\u0928 \u0930\u0942\u092a \u092e\u0947\u0902 \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 :<\/p>\n\n<p class=\"has-text-align-left wp-block-paragraph\">\\(F_1 = 1\\)<br\/>\\(F_2 = 2\\)<br\/>\\(F_{m + 2} = F_{m} + F_{m+1}\\)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u0906\u0907\u090f \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0938\u0930\u0932 \u0928\u093f\u092f\u092e\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u201c\u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928\u094b\u0902\u201d \u0915\u094b \u092a\u0930\u093f\u092d\u093e\u0937\u093f\u0924 \u0915\u0930\u0947\u0902 : \u0907\u0938\u0915\u093e \u0905\u0930\u094d\u0925 \u092f\u0939 \u0939\u0948 \u0915\u093f \u0939\u092e \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u0938\u0947 \u0936\u0941\u0930\u0942 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0928\u093f\u092f\u092e-2 \u0914\u0930 \u0928\u093f\u092f\u092e-3 \u0915\u094b \u092c\u093e\u0930-\u092c\u093e\u0930 \u0932\u093e\u0917\u0942 \u0915\u0930\u0915\u0947 \u0905\u0928\u094d\u092f \u0938\u092d\u0940 \u092e\u091c\u093c\u0947\u0926\u093e\u0930 \u092d\u093f\u0928\u094d\u0928 \u092c\u0928\u093e \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964 \u091c\u092c \u0928\u093f\u092f\u092e-2 \u0932\u093e\u0917\u0942 \u0915\u093f\u092f\u093e \u091c\u093e\u0924\u093e \u0939\u0948 \u0924\u094b \u090f\u0915 \u0932\u093e\u0932 \u0924\u0940\u0930 \u0916\u0940\u0902\u091a\u0915\u0930 \u0914\u0930 \u091c\u092c [&hellip;]<\/p>\n","protected":false},"author":17,"featured_media":28274,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_wpcom_ai_launchpad_first_post":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[242],"tags":[379,509,559,560],"stage-class":[1008],"magazine_category":[287],"class_list":["post-11821","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category----hi","tag-379","tag-509","tag-559","tag-560","stage-class-middle-class-6-8-hi","magazine_category--20--2024"],"acf":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/wp-content\/uploads\/2024\/09\/Fun-with-Fractions-thumbnail.png","_links":{"self":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/11821","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/users\/17"}],"replies":[{"embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/comments?post=11821"}],"version-history":[{"count":2,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/11821\/revisions"}],"predecessor-version":[{"id":24326,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/posts\/11821\/revisions\/24326"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/media\/28274"}],"wp:attachment":[{"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/media?parent=11821"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/categories?post=11821"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/tags?post=11821"},{"taxonomy":"stage-class","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/stage-class?post=11821"},{"taxonomy":"magazine_category","embeddable":true,"href":"https:\/\/atrightangles.azimpremjiuniversity.edu.in\/hi\/wp-json\/wp\/v2\/magazine_category?post=11821"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}