Multiplication of whole numbers
The Distributive Property
1. Which of the following option is true? Use the distributive property to
break apart the multiplication expression.
(4 × 4)
(A) (4 × 4) = (2 + 4) × 4
(B) (4 × 4) = (2 – 2) × 4
(C) (4 × 4) = (2 + 2) ÷ 4
(D) (4 × 4) = (2 + 2) × 4
Solution:
(4 × 4) = (2 + 2) × 4
Since (4 = 2 + 2)
2. Which of the following option is true? Use the distributive property to
break apart the multiplication expression.
(50 × 24)
(A) (50 × 24) = 50(50) ÷ 50(24)
(B) (50 × 24) = 50(20) – 50(4)
(C) (50 × 24) = 50(20) + 50(4)
(D) (50 × 24) = 50(50) + 50(4)
Solution:
(50 × 24) = 50(20) + 50(4)
Since (24 = 20 + 4)
3. Which of the following option is true? Use the distributive property to
break apart the multiplication expression.
n · 67
(A) n · 67 = n · 60 × n · 7
(B) n · 67 = n · 60 + n ·7
(C) n · 67 = n · 60 – n · 7
(D) n · 67 = n · 60 ÷ n · 3
Solution:
n · 67 = n(60 + 7) = n × 60 + n × 7 = n · 60 + n · 7
4. Which of the following option is true? Use the distributive property of
multiplication.
(100m + 50m + 6m) =?
(A) 156 · m
(B) 156m · m
(C) 156 · m × (100 + 50 + 6)
(D) 156 · (100 + 50 + 6) × m
Solution:
(100m + 50m + 6m) = 156 · m
5. Which of the following options is true? Use the distributive property to
break apart the multiplication expression.
25x =?
(A) 20x + 5x
(B) 25 · x
(C) 25 + x
(D) 25 × x
Solution:
25x = 20x + 5x because the distributive property has to be used to break apart
the multiplication expression
6. Which of the following expression is not true?
(A) 12p = (10 + 2)p
(B) 12p = (10p + 2p)p
(C) 12p = 10 · p + 2 · p
(D) 12p = (10 + 2) × p
Solution:
12p = (10 + 2)p = (10 + 2) × p = 10 · p + 2 · p
12p ≠ (10p + 2p)p
7. Fill in blank using the distributive property of multiplication expression.
9 × 103 = ______ × (100 + 3)
(A) 3
(B) 100
(C) 9
(D) 90
Solution:
9 × 103 = 9 × (100 + 3)
8. Fill in blank using the distributive property of multiplication expression.
p × 96 = (p ·____) + (p · 6)
(A) 6
(B) 60
(C) p
(D) 90
Solution:
p × 96 = (p · 90) + (p · 6)
9. Fill in blank using the distributive property of multiplication expression.
5 × 63 = 5 × (60 + 3) and (5 ×___) + (5 × 3)
(A) 3
(B) 60
(C) 20
(D) 5
Solution:
5 × 63 = 5 × (60 + 3) and (5 × 60 ) + (5 × 3)
10. Multiply using distributive property. Choose the correct option.
525 × 10
(A) (500 ÷ 25) ÷ 10
(B) (500 × 25) × 10
(C) (500 – 25) × 10
(D) (500 + 25) × 10
Solution:
525 × 10 = (500 + 25) × 10
11. Multiply using distributive property. Choose the correct option.
25 × 4
(A) (20 × 5)4
(B) (20 + 5)4
(C) (20 ÷ 5)4
(D) (20 – 5)4
Solution:
25 × 4 = (20 + 5)4
12. Multiply using distributive property. Choose the correct option.
150 × 700
(A) (15 ÷ 10)700
(B) (15 – 10)700
(C) (100 + 50)700
(D) (15 + 10) ÷ 700
Solution:
150 × 700 = (100 + 50)700
13. Multiply using distributive property. Choose the correct option.
656 × 6
(A) (600 + 50 + 6)6
(B) (600 × 50 + 6)6
(C) (600 + 50 + 6) ÷ 6
(D) (600 × 50 × 6)6
Solution:
656 × 6 = (600 + 50 + 6)6
14. A group of girls paid n × $25 for bags and n × $35 for books. Which is the
correct expression for the total expense?
(A) n (25 + 35)
(B) n (25 × 35)
(C) (n × 25 × 35)
(D) 25(n + 35)
Solution:
The total expense for bags and books = n × 25 + n × 35 = n(25 + 35)
15. In a restaurant each table holds 6 seats. How many people can occupy the
seats at the same time if there are 20 tables? State which option is not true?
(A) 20 × 6
(B) (20 + 6)1
(C) (20 × 6)1
(D) 20 × 6 × 1
Solution:
Number of seats per table = 6
Number of seats for 20 tables = 6 × 20 = (20 × 6)1= 20 × 6 × 1