Distributive property of multiplication over subtraction worksheets are much useful to the kids who would like practice problems on distributive property of multiplication
Distributive property of multiplication over subtraction is a very useful property that lets us simplify expressions in which we are multiplying a number by the difference of two other numbers.
The property states that the product of a number and the difference of two other numbers is equal to the difference of the products.
More clearly,
1. Evaluate using distributive property : 7(10 - 2)
2. Evaluate using distributive property : 6(x - y)
3. Evaluate using distributive property : m(n - p)
4. Evaluate using distributive property : 5(x² - y²)
5. Evaluate using distributive property : m(m² - m)
6. Write the given verbal phrase into algebraic expression
"3 times the difference of two different numbers"
7. If 4 times the difference of a number and 5 is 32, find the number.
8. Write the given verbal phrase into algebraic expression
"6 times 3 less than 4 times of a number"
9. If 7 times 6 less than 3 times of a number is 147, find the number.
10. If 9 times the difference of 7 and 4 times of a number is 27, find the number.
Problem 1 :
Evaluate using distributive property : 7(10 - 2)
Solution :
7(10 - 2) = 7(10) - 7(2)
7(10 - 2) = 70 - 14
7(10 - 2) = 56
Problem 2 :
Evaluate using distributive property : 6(x - y)
Solution :
6(x - y) = 6x - 6y
Problem 3 :
Evaluate using distributive property : m(n - p)
Solution :
m(n - p) = mn - mp
Problem 4 :
Evaluate using distributive property : 5(x² - y²)
Solution :
5(x² - y²) = 5x² - 5y²
Problem 5 :
Evaluate using distributive property : m(m² - m)
Solution :
m(m² - m) = m.m² - m.m
m(m² - m) = m³ - m²
Problem 6 :
Write the given verbal phrase into algebraic expression
"3 times the difference of two different numbers"
Solution :
Let "x" and "y" be the two different numbers.
Then,
The difference of two different numbers = x - y
3 times the sum of two different numbers = 3(x - y)
Problem 7 :
If 4 times the difference of a number and 5 is 32, find the number.
Solution :
Let "x" be the required number.
According to the question, we have
4(x - 5) = 32
4x - 20 = 32
4x = 52
x = 13
Hence the required number is 13.
Problem 8 :
Write the given verbal phrase into algebraic expression
"6 times 3 less than 4 times of a number"
Solution :
Let "x" be the number.
Then,
4 times of number = 4x
3 less than 4 times of number = 4x - 3
6 times 3 less than 4 times of a number = 6(4x - 3)
6 times 3 less than 4 times of a number = 24x - 18
Problem 9 :
If 7 times 6 less than 3 times of a number is 147, find the number.
Solution :
Let "x" be the required number.
According to the question, we have
7(3x - 6) = 147
21x - 42 = 147
21x = 189
x = 9
Hence the required number is 9.
Problem 10 :
If 9 times the difference of 7 and 4 times of a number is 27, find the number.
Solution :
Let "x" be the required number.
According to the question, we have
9(7 - 4x) = 27
63 - 36x = 27
36 = 36x
1 = x
Hence the required number is 1.
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