Page 32 - ICSE Math 8

6. Verify that x × (y + z) = (x × y) + (x × z) for:
4 − 3 12 4 − 6 − 2
(a) x = , y = , z = (b) x = , y = , z =
7 8 − 13 5 7 3
−5 −1
7. Divide the sum of and by their difference.
4 3
−28 −5
8. By what number should be multiplied to get the multiplicative inverse of ?
15 7
9. Represent the following rational numbers on a number line.
−3 8 1 −7
(a) (b) (c) (d)
5 3 −1 1 3 2
10. Find five rational numbers between and .
2 2 5
11. Jack is doing some woodwork. He has a piece of wood 4 metres long. He cuts off a piece 2 m long.
8
3
Find the length of wood left with Jack. If he needs 5 more pieces that are each m long, find the total
length of wood with Jack now. 10

THINK SMART

2 2
–1
1. A bus is moving at the speed of 40 km h . How far will it travel in 6 hours? If the bus is still at a
2 5 3
distance of 10 km from the final destination, how far is the final destination from the starting point?
3
3 2
2. If of a number exceeds its by 44, find the number.
5 7
2
3. Which is longer and by how much—perimeter of a square of side 4 m or perimeter of a rectangle with
1 2 3
length 5 m and breadth 3 m?
5 5
Maths Lab Activity

Objective: To learn about rational numbers and its various operations pictorially
Material required: Art sheet, coloured papers, sketch pens, glue, protractor, compass, scissors
2 3
Step 1: Choose two rational numbers. For example, and
9 5
Step 2: Draw two circles on the art sheet.
Step 3: Represent the first rational number in the first circle. To do this, first
divide 360º by 9. What you get is 40º. From the centre of the circle draw C B
a radius, say OA. Using a protractor, draw ∠AOB = 40°. Then draw
∠BOC = 40°. In this manner, divide the circle into 9 equal sectors. A
Now paste coloured paper in two sectors. O
2
This is the representation of rational number .
9
Step 4: Repeat step 3 for the second rational number.
Step 5: Show the basic operation (+, –, ×, ÷) at the bottom of the art sheet.
2 3 3 2 2 3 2 3
+ , − , × , ÷
9 5 5 9 9 5 9 5
Step 6: Show the result of various operations pictorially as explained in steps 2 and 3.
Now do this activity yourself, choosing any two rational numbers and have fun.

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