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Proportional Reasoning–2 Try to find the distances between the same two pairs of cities with different maps that have different scales (ratios). Do they all give the same geographical distance, approximately? Note to the Teacher: Bring maps and atlases to the classroom and encourage students to observe the scale given as a ratio (usually in the lower right corner) on the map. Use the maps and atlases in the library and ask students to find the geographical distances between two locations on the map that are of local interest. Ask them to verify with each other if they get similar distances and to find the reasons if the distances are very different. Map Making Activity: Guide students to make a sketch of their classroom with an accurate scale (ratio of 1: 50). They should mark the location of various objects in the classroom like the teacher᾿s desk, blackboard, fans and lights, according to scale. Students can use appropriate symbols to represent different objects like fans, lights, tables, chairs, and so on. 3.3 Ratios with More than 2 Terms Viswanathisexperimentingwithaspice mix powder. He makes the powder by grinding 8 spoons of coriander seeds, 4 red chillies, 2 spoons of toor dal, and 1 spoon of fenugreek (methi) seeds. For his spice mix powder, the ratio of coriander seeds to red chillies to toor dal to fenugreek seeds is 8 : 4 : 2 : 1. Notice that the ratio has 4 terms. Ratios can have many terms if each of the quantities change by the same factor to maintain the proportional relationship. Puneet has only 2 red chillies in his kitchen. But he wants to make spice mix powder that tastes the same as Viswanath’s spice mix powder. How much of the other ingredients should Puneet use to make his spice mix powder? ForPuneet’sspicemixpowdertobesimilartoViswanath’s,theratioof all the ingredients should be the same as Viswanath’s spice mix powder. Puneet has only 2 red chillies. He has half the number of chillies that Viswanath used in his mixture. So, the quantity of the other ingredients should also be reduced to half. Thus, Puneet should add 4 spoons of coriander seeds, 2 red chillies, 1 spoon of toor dal, and half a spoon of fenugreek seeds. The ratio is 4 : 2 : 1 : 0.5. 57