Advertisements
Advertisements
Question
Give an example and verify the following statement.
Distributive property of multiplication over subtraction is true for rational numbers. That is, a(b – c) = ab – ac
Solution
Let a = `2/9`, b = `3/6`, c = `1/3` be three rational numbers.
To prove a × (b – c) = ab – bc
a × (b – c) = `2/9 xx (3/6 - 1/3)`
= `2/9 xx ((3 - (1 xx 2))/6)`
= `2/9 xx ((3 - 2))/6`
= `2/9 xx 1/6`
=`1/27` ....(1)
ab – ac = `(2/9 xx 3/6) - (2/9 xx 1/3)`
= `1/9 - 2/27`
= `((1 xx 3) - 2)/27`
= `(3 - 2)/27`
= `1/27` ....(2)
∴ From (1) and (2)
a × (b – c) = ab – bc
∴ Distributivity of multiplication over subtraction is true for rational numbers.
APPEARS IN
RELATED QUESTIONS
Verify the property: x × y = y × x by taking:
Verify the property: x × (y × z) = (x × y) × z by taking:
Verify the property: x × (y + z) = x × y + x × z by taking:
Name the property of multiplication of rational numbers illustrated by the following statements:
Name the property of multiplication of rational numbers illustrated by the following statements:
Find: `2/5 xx (-3)/7 - 1/14 - 3/7 xx 3/5`.
For every rational numbers x, y and z, x + (y × z) = (x + y) × (x + z).
Simplify the following by using suitable property. Also name the property.
`[1/2 xx 1/4] + [1/2 xx 6]`
Name the property used in the following.
`-2/3 xx [3/4 + (-1)/2] = [(-2)/3 xx 3/4] + [(-2)/3 xx (-1)/2]`
Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.
| Name | Distance covered (km) |
| Seema | `1/25` |
| Nancy | `1/32` |
| Megha | `1/40` |
| Soni | `1/20` |
Who walked farther, Nancy or Megha?
