head 1.1; access; symbols; locks; strict; comment @# @; 1.1 date 2018.03.14.16.01.29; author root; state Exp; branches; next ; desc @This document (U3_L2_A1_Find the Real distance) is re-created by black-butterfly-cc on 07 May 2017 @ 1.1 log @Initial revision @ text @{ "_id": { "$oid": "59425fcc4975ac013d976b85" }, "_type": "GSystem", "access_policy": "PUBLIC", "altnames": "2.1 \u0905\u0938\u0932 \u0926\u0942\u0930\u0940 \u0928\u093f\u0915\u093e\u0932\u0947\u0902", "annotations": [], "attribute_set": [], "author_set": [], "collection_set": [], "comment_enabled": null, "content": "
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Proportional reasoning\r\n

\u0905\u0938\u0932 \u0926\u0942\u0930\u0940 \u0928\u093f\u0915\u093e\u0932\u0947\u0902

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\u091c\u093e\u092e\u0941\u0928\u0940 \u0915\u094b \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u092a\u095d\u0928\u0947 \u092e\u0947\u0902 \u092e\u095b\u093e \u0906\u0924\u093e \u0939\u0948 \u0914\u0930 \u0935\u0939 \u092c\u095c\u0940 \u0909\u0924\u094d\u0938\u0941\u0915\u0924\u093e \u0938\u0947 \u0926\u094b \u091c\u0917\u0939\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940 \u0905\u0932\u0917-\u0905\u0932\u0917 \u0930\u093e\u0938\u094d\u0924\u094b\u0902 \u0938\u0947 \u0928\u093f\u0915\u093e\u0932\u0924\u0940 \u0939\u0948| \u0909\u0938\u0947 \u0935\u093f\u0936\u094d\u0935 \u0915\u093e \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u092a\u095d\u0928\u093e \u0905\u091a\u094d\u091b\u093e \u0932\u0917\u0924\u093e \u0939\u0948 \u0914\u0930 \u092a\u0948\u092e\u093e\u0928\u0947 \u0915\u0940 \u092e\u0926\u0926 \u0938\u0947 \u0926\u094b \u091c\u0917\u0939\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940 \u0928\u093f\u0915\u093e\u0932 \u092a\u093e\u0924\u0940 \u0939\u0948|

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\r\n\u0915\u093e\u0930\u094d\u092f 1

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\u0926\u093f\u092f\u0947 \u0917\u092f\u0947 \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u092e\u0947\u0902 \u092a\u0948\u092e\u093e\u0928\u0947 \u0915\u094b \u0927\u094d\u092f\u093e\u0928 \u0938\u0947 \u0926\u0947\u0916\u0947\u0902| \u0906\u092a \u0915\u094d\u092f\u093e \u0926\u0947\u0916\u0924\u0947 \u0939\u0948\u0902? \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u0915\u0947 \u092a\u0948\u092e\u093e\u0928\u0947 \u092e\u0947\u0902 \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u0940 \u0917\u0908 \u0926\u0942\u0930\u0940 (\u0907\u0915\u093e\u0908) \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u0905\u092a\u0928\u0947 \u0938\u094d\u0915\u0947\u0932 \u092a\u0930 \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u0940 \u0917\u0908 \u0907\u0915\u093e\u0908 \u0938\u0947 \u0915\u0930\u0947\u0902| \u0907\u0938 \u0924\u093e\u0932\u093f\u0915\u093e \u0915\u094b \u092a\u0942\u0930\u093e \u0915\u0930\u0947\u0902 \u0914\u0930 \u0938\u0939\u0940 \u0907\u0915\u093e\u0908 \u0932\u093f\u0916\u0947\u0902|
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\"map\"

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\r\n\r\n\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\r\n\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\r\n\t\r\n
 \r\n\t\t\t

\u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930-\u0938\u094d\u0915\u0947\u0932 

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\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0926\u0942\u0930\u0940

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1 \u092e\u093e\u0924\u094d\u0930\u0915 

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_____________

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__________________

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\u0905\u092a\u0928\u0947 \u0905\u0935\u0932\u094b\u0915\u0928 \u0932\u093f\u0916\u0947\u0902| \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u0915\u0947 \u092a\u0948\u092e\u093e\u0928\u0947 \u0915\u0940 \u0907\u0915\u093e\u0908 \u0905\u0938\u0932\u0940 \u0926\u0942\u0930\u0940 \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u093e \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948?

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____________________________________________________________________________________________
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\u0909\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930, \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u0915\u0947 \u092a\u0948\u092e\u093e\u0928\u0947 \u0915\u0940 2 \u0907\u0915\u093e\u0907\u092f\u093e\u0902 \u0905\u0938\u0932\u0940 \u0926\u0942\u0930\u0940 \u092e\u0947\u0902 \u0915\u093f\u0924\u0928\u093e \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948\u0902?

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_________________________________________________________________________________________

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\r\n(\u0932\u093f\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u092f\u0947 \u092f\u0939\u093e\u0901 \u0915\u094d\u0932\u093f\u0915 \u0915\u0930\u0947\u0902)

\r\n\"note\"  
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\r\n\u0915\u093e\u0930\u094d\u092f 2

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\u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u092a\u0948\u092e\u093e\u0928\u093e \u0914\u0930 \u0905\u0938\u0932\u0940 \u0926\u0942\u0930\u0940 \u0915\u0947 \u092c\u0940\u091a \u0915\u0947 \u0905\u0928\u0941\u092a\u093e\u0924 \u0915\u094b \u0939\u092e ___ : ___ \u0932\u093f\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902| \u0915\u093f\u0938\u0940 \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u0915\u0947 \u0932\u093f\u092f\u0947 \u092f\u0939 \u0905\u0928\u0941\u092a\u093e\u0924 \u092a\u0948\u092e\u093e\u0928\u0947 \u0915\u093e \u0917\u0941\u0923\u0915 (scale factor) \u0915\u0939\u0932\u093e\u0924\u093e \u0939\u0948|  \u092f\u0939 \u0938\u0941\u0935\u093f\u0927\u093e \u0915\u093f \u092c\u093e\u0924 \u0939\u0948 \u0915\u093f \u0939\u092e \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0928\u0947 \u092f\u093e \u0909\u0938\u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u092f\u0947 \u0915\u093f\u0938 \u0917\u0941\u0923\u0915 \u0915\u093e \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902|

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\u0905\u092c \u090a\u092a\u0930 \u0926\u093f\u092f\u0947 \u0917\u092f\u0947 \u092a\u0948\u092e\u093e\u0928\u0947 \u0915\u0947 \u0917\u0941\u0923\u0915 \u0915\u093e \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u0930 \u0928\u0958\u094d\u0936\u0947 \u092e\u0947\u0902 \u0915\u093f\u0938\u0940 \u092d\u0940 \u0926\u094b \u0938\u094d\u0925\u093e\u0928\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0926\u0942\u0930\u0940 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902| \u0907\u0938 \u0915\u093e\u0930\u094d\u092f \u0915\u094b \u0915\u0930\u0928\u0947 \u0915\u0947 \u0905\u0932\u0917-\u0905\u0932\u0917 \u0924\u0930\u0940\u0915\u0947 \u0938\u094b\u091a\u0947\u0902| \u0907\u0938 \u0924\u093e\u0932\u093f\u0915\u093e \u0915\u094b \u092d\u0930\u0947\u0902:

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(\u0938\u0902\u0915\u0947\u0924: \u0927\u093e\u0917\u0947 \u0915\u093e \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0915\u0930 \u0918\u0941\u092e\u093e\u0935\u0926\u093e\u0930 \u0930\u093e\u0938\u094d\u0924\u0947 \u0915\u0940 \u0932\u092e\u094d\u092c\u093e\u0908 \u092a\u0924\u093e \u0915\u0930\u0947\u0902 \u0914\u0930 \u092b\u093f\u0930 \u092a\u091f\u0930\u0940 \u0914\u0930 \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u0915\u0947 \u0917\u0941\u0923\u0915 \u0915\u0947 \u0907\u0938\u094d\u0924\u0947\u092e\u093e\u0932 \u0938\u0947 \u0909\u0928 \u0936\u0939\u0930\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0915\u0940 \u0905\u0938\u0932\u0940 \u0926\u0942\u0930\u0940 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0947\u0902)
\r\n 

\r\n\r\n
\r\n\r\n\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\r\n\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\r\n\t\r\n
\r\n\t\t\t

 \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930-\u0938\u094d\u0915\u0947\u0932   

\r\n\t\t\t
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\u0909\u092a\u092f\u094b\u0917 \u092e\u0947\u0902 \u0932\u093f\u090f \u0917\u090f \u0927\u093e\u0917\u0947 \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 

\r\n\t\t\t
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\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0926\u0942\u0930\u0940

\r\n\t\t\t
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1 \u0938\u0947\u092e\u0940 = 12 \u0915\u093f\u092e\u0940

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_______________

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_______________

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1 \u0938\u0947\u092e\u0940 = 12 \u0915\u093f\u092e\u0940

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_______________

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_______________

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1 \u0938\u0947\u092e\u0940 = 12 \u0915\u093f\u092e\u0940

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_______________

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_______________

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\r\n
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\u0932\u093f\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u092f\u0947 \u092f\u0939\u093e\u0901 \u0915\u094d\u0932\u093f\u0915 \u0915\u0930\u0947\u0902)
\r\n\"note\"  

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\r\n\u0915\u093e\u0930\u094d\u092f 3

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\u090f\u0915 \u0926\u0942\u0938\u0930\u093e \u0924\u0930\u0940\u0915\u093e \u091c\u093f\u0938\u0938\u0947 \u0915\u093f\u0938\u0940 \u0928\u0958\u094d\u0936\u0947 \u092e\u0947\u0902 \u092a\u0948\u092e\u093e\u0928\u0947 \u0915\u0947 \u0917\u0941\u0923\u0915 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0947 \u0939\u0948\u0902, \u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930 \u0939\u0948 - \u090f\u0915 \u0907\u0915\u093e\u0908 \u0926\u0942\u0930\u0940 \u0915\u093e \u0905\u0938\u0932\u0940 \u0926\u0942\u0930\u0940 \u0915\u0947 \u0938\u093e\u0925 \u0938\u092e\u094d\u092c\u0928\u094d\u0927 \u0938\u094d\u0925\u093e\u092a\u093f\u0924 \u0915\u0930\u0915\u0947, \u091c\u0948\u0938\u0947 1 \u0938\u0947\u092e\u0940 = 50 \u0915\u093f\u092e\u0940| \u092f\u0939 \u0917\u0941\u0923\u0915 \u092c\u0924\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0928\u0958\u094d\u0936\u0947 \u092a\u0930 1 \u0938\u0947\u092e\u0940 \u0915\u0940 \u0926\u0942\u0930\u0940 \u0926\u0930\u0905\u0938\u0932 50 \u0915\u093f\u092e\u0940 \u0915\u0940 \u0905\u0938\u0932\u0940 \u0926\u0942\u0930\u0940 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u0940 \u0939\u0948|
\r\n\r\n
\u0928\u0940\u091a\u0947 \u0926\u0940 \u0917\u0908 \u0938\u093e\u0930\u0923\u0940 \u092e\u0947\u0902 (\u0935\u093f\u092d\u093f\u0928\u094d\u0928 \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930\u094b\u0902 \u0938\u0947) \u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0926\u0942\u0930\u0940 \u091c\u094d\u091e\u093e\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930-\u0938\u094d\u0915\u0947\u0932\u094b\u0902 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0917\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948\u0964 \r\n\r\n
 \r\n
\r\n\r\n\t\r\n\t\t\r\n\t\t\r\n\t\t\r\n\t\r\n\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\r\n\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\t\r\n\t\t\r\n\t\r\n
\r\n\t\t\t

\u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930-\u0938\u094d\u0915\u0947\u0932  

\r\n\t\t\t
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\u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u092a\u0930 \u0926\u0942\u0930\u0940 

\r\n\t\t\t
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\u0935\u093e\u0938\u094d\u0924\u0935\u093f\u0915 \u0926\u0942\u0930\u0940

\r\n\t\t\t
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1 \u0938\u0947\u092e\u0940 = 15 \u0915\u093f\u092e\u0940

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6 \u0938\u0947\u092e\u0940

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________________

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1 \u0938\u0947\u092e\u0940 = 12 \u0915\u093f\u092e\u0940

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10.5 \u0938\u0947\u092e\u0940

\r\n\t\t\t
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________________

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1 \u0938\u0947\u092e\u0940 = 20 \u0915\u093f\u092e\u0940

\r\n\t\t\t
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1/2 \u0938\u0947\u092e\u0940

\r\n\t\t\t
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________________

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\r\n\u092e\u093e\u0928\u091a\u093f\u0924\u094d\u0930 \u092a\u0930 \u0926\u0942\u0930\u0940 \u0914\u0930 \u0905\u0938\u0932\u0940 \u0926\u0942\u0930\u0940 \u0915\u0947 \u092c\u0940\u091a \u0915\u094d\u092f\u093e \u0938\u092e\u094d\u092c\u0928\u094d\u0927 \u0939\u0948?
\r\n(\u0932\u093f\u0916\u0928\u0947 \u0915\u0947 \u0932\u093f\u092f\u0947 \u092f\u0939\u093e\u0901 \u0915\u094d\u0932\u093f\u0915 \u0915\u0930\u0947\u0902)

\r\n\"note\"
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CLIx English\r\n

Activity 1

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Question 1:

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Jamuni loves to read maps. She is amazed by how the scale given in a small map can be used to represent great distances.

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Carefully look at the map-scale (scale given in the map here).  What do you see?

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\"map.jpeg\"

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    Compare 1 unit of the map-scale with 1 unit of the ruler (scale) you have.  

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    Now complete the following table, carefully enter the correct units.

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Map-scale

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Real distance

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1 unit

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__________________

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Question 2:

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The ratio between map-scale and real distance can be written as  ___:___.  

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This ratio is also called the \u201cscale factor\u201d of the map.

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Question 3:

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For convenience, we choose different scaling factors to show or calculate the distance between two places on a map.

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    Choose any two cities of your choice on the given map and using the scale factor find the distance between these cities in kilometres. Think about different ways of doing this task.

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    Then complete the following table.

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Hint: Use a thread to measure circuitous routes. Then, use a ruler and the given map-scale to calculate the actual distance between the two cities.

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Map-scale

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Length of thread used

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Real distance

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1 cm = 12 km

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1 cm = 12 km

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1 cm = 12 km

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_______________

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Question 4:

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The map-scale shown in the map indicates the unit distance and the real distance. For example, a map-scale of 1 cm = 50 km indicates that 1 cm on the map is equivalent to 50 km on the ground, that is, real distance.

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Use the given map-scales (from different maps) to find the real distance in the table below.  

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Map-scale

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Real distance

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1 cm = 15 km

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6 cm

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1 cm = 12 km

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10.5 cm

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1 cm = 20 km

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1/2 cm

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________________

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