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Proportional Reasoning-1

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Page 159: We can see that all the images are of different sizes. Which images look similar and which ones look different?
Page 160: Do images B and E look like the other three images?
Page 160: Why?
Page 160: What makes images A, C, and D appear similar, and B and E different?
Page 160: Can you check by what factors the width and height of image D change as compared to image A? Are the factors the same?
Page 161: By what factor should we multiply the ratio 60 : 40 (image A) to get 90 : 60 (image D)?
Page 161: What is the simplest form of the ratios of images B and E?
Page 162: Example 1: Are the ratios 3 : 4 and 72 : 96 proportional? What is the HCF of 72 and 96?
Page 162: Example 2: Kesang wanted to make lemonade for a celebration. She made 6 glasses of lemonade in a vessel and added 10…
Page 163: Example 3: Nitin and Hari were constructing a compound wall around their house. Nitin was building the longer side,…
Page 163: Example 4: In my school, there are 5 teachers and 170 students. The ratio of teachers to students in my school is 5…
Page 163: Example 5: Measure the width and height (to the nearest cm) of the blackboard in your classroom. What is the ratio…
Page 164: Example 6: When Neelima was 3 years old, her mother's age was 10 times her age. What is the ratio of Neelima's age…
Page 164: Example 7: Fill in the missing numbers for the following ratios that are proportional to 14 : 21.
Page 164: Why is this coffee stronger? Why is this coffee lighter?
Page 165: Table: is each cup of coffee stronger, lighter, or regular?
Page 165: Circle the following statements of proportion that are true. (i) 4 : 7 :: 12 : 21 (ii) 8 : 3 :: 24 : 6 (iii) 7 : 12…
Page 165: Give 3 ratios that are proportional to 4 : 9.
Page 165: Fill in the missing numbers for these ratios that are proportional to 18 : 24.
Page 166: Look at the following rectangles. Which rectangles are similar to each other? You can verify this by measuring the…
Page 166: Look at the following rectangle. Can you draw a smaller rectangle and a bigger rectangle with the same width to…
Page 166: The following figure shows a small portion of a long brick wall with patterns made using coloured bricks. Each wall…
Page 167: Let us draw some human figures. Measure your friend's body — the lengths of their head, torso, arms, and legs. Write…
Page 167: Example 8: For the mid-day meal in a school with 120 students, the cook usually makes 15 kg of rice. On a rainy day,…
Page 169: Example 9: A car travels 90 km in 150 minutes. If it continues at the same speed, what distance will it cover in 4…
Page 169: Example 10: A small farmer in Himachal Pradesh sells each 200 g packet of tea for ₹200. A large estate in Meghalaya…
Page 170: Activity 1: Take your favourite dish. Find out all the ingredients and their respective quantities needed to make…
Page 170: The Earth travels approximately 940 million kilometres around the Sun in a year. How many kilometres will it travel…
Page 170: A mason is building a house in the shape shown in the diagram. He needs to construct both the outer walls and the…
Page 171: Puneeth's father went from Lucknow to Kanpur in 2 hours by riding his motorcycle at a speed of 50 km/h. If he drives…
Page 171: Activity 2: Go to the market and collect the prices of different sizes of shampoo containers of the same shampoo and…
Page 172: Discuss the pros and cons of different size bottles for the company and for customers. For reducing ecological…
Page 172: Activity 3: Form a pair. Collect 12 countable objects or counters (it can be coins, seeds, or pebbles). Now, share…
Page 173: Now, if you want to share the counters in the ratio of 3 : 1 between the two of you, how many counters would each of…
Page 174: Example 11: Prashanti and Bhuvan started a food cart business near their school. Prashanti invested ₹75,000 and…
Page 174: Example 12: A mixture of 40 kg contains sand and cement in the ratio of 3 : 1. How much cement should be added to…
Page 175: Divide ₹4,500 into two parts in the ratio 2 : 3.
Page 175: In a science lab, acid and water are mixed in the ratio of 1 : 5 to make a solution. In a bottle that has 240 mL of…
Page 175: Blue and yellow paints are mixed in the ratio of 3 : 5 to produce green paint. To produce 40 mL of green paint, how…
Page 175: To make soft idlis, you need to mix rice and urad dal in the ratio of 2 : 1. If you need 6 cups of this mixture to…
Page 175: I have one bucket of orange paint that I made by mixing red and yellow paints in the ratio of 3 : 5. I added another…
Page 176: Anagh mixes 600 mL of orange juice with 900 mL of apple juice to make a fruit drink. Write the ratio of orange juice…
Page 176: Last year, we hired 3 buses for the school trip. We had a total of 162 students and teachers who went on that trip…
Page 176: The area of Delhi is 1,484 sq. km and the area of Mumbai is 550 sq. km. The population of Delhi is approximately 30…
Page 176: A crane of height 155 cm has its neck and the rest of its body in the ratio 4 : 6. For your height, if your neck and…
Page 176: Let us try an ancient problem from Līlāvatī. At that time weights were measured in a unit named palas and niskas was…
Page 177: Harmain is a 1-year-old girl. Her elder brother is 5 years old. What will be Harmain's age when the ratio of her age…
Page 177: The mass of equal volumes of gold and water are in the ratio 37 : 2. If 1 litre of water is 1 kg in mass, what is…
Page 177: It is good farming practice to apply 10 tonnes of cow manure for 1 acre of land. A farmer is planning to grow…
Page 177: A tap takes 15 seconds to fill a mug of water. The volume of the mug is 500 mL. How much time does the same tap take…
Page 177: One acre of land costs ₹15,00,000. What is the cost of 2,400 square feet of the same land?
Page 177: A tractor can plough the same area of a field 4 times faster than a pair of oxen. A farmer wants to plough his…
Page 177: The ₹10 coin is an alloy of copper and nickel called ‘cupro-nickel’. Copper and nickel are mixed in a 3 : 1 ratio to…

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