Problem 1 :
Evaluate using distributive property :
7(10 + 2)
Problem 2 :
Evaluate using distributive property :
6(x + y)
Problem 3 :
Evaluate using distributive property :
m(n + p)
Problem 4 :
Evaluate using distributive property :
5(x2 + y2 + z2)
Problem 5 :
Evaluate using distributive property :
m(m2 + m + 5)
Problem 6 :
Write the given verbal phrase into algebraic expression
"3 times the sum of two different numbers"
Problem 7 :
If 4 times the sum of a number and 5 is 32, find the number.
Problem 8 :
Write the given verbal phrase into algebraic expression :
"6 times the sum of three different numbers"
Problem 9 :
If 7 times the sum of 3 times of a number and 6 is 147, find the number.
Problem 10 :
If 9 times the sum of 7 and 4 times of a number is 135, find the number.
Problem 1 :
Evaluate using distributive property :
7(10 + 2)
Solution :
Use distributive property.
7(10 + 2) = 7(10) + 7(2)
7(10 + 2) = 70 + 14
7(10 + 2) = 84
Problem 2 :
Evaluate using distributive property :
6(x + y)
Solution :
Use distributive property.
6(x + y) = 6x + 6y
Problem 3 :
Evaluate using distributive property :
m(n + p)
Solution :
Use distributive property.
m(n + p) = mn + mp
Problem 4 :
Evaluate using distributive property :
5(x2 + y2 + z2)
Solution :
Use distributive property.
5(x2 + y2 + z2) = 5x2 + 5y2 + 5z2
Problem 5 :
Evaluate using distributive property :
m(m2 + m + 5)
Solution :
Use distributive property.
m(m2 + m + 5) = m ⋅ m2 + m ⋅ m + 5m
m(m2 + m + 5) = m3 + m2 + 5m
Problem 6 :
Write the given verbal phrase into algebraic expression
"3 times the sum of two different numbers"
Solution :
Let x and y be the two different numbers.
Then, 3 times the sum of two different numbers is
= 3(x + y)
Use distributive property.
= 3x + 3y
Problem 7 :
If 4 times the sum of a number and 5 is 32, find the number.
Solution :
Let x be the number.
Then,
4(x + 5) = 32
Use distributive property.
4x + 20 = 32
Subtract 20 from each side.
4x = 12
Divide each side by 4.
x = 3
So, the number is 3.
Problem 8 :
Write the given verbal phrase into algebraic expression :
"6 times the sum of three different numbers"
Solution :
Let x, y and z be the three different numbers.
Then, 6 times the um of three different numbers is
= 6(x + y + z)
Use distributive property.
= 6x + 6y + 6z
Problem 9 :
If 7 times the sum of 3 times of a number and 6 is 147, find the number.
Solution :
Let x be the number.
Then,
7(3x + 6) = 147
Use distributive property.
21x + 42 = 147
Subtract 42 from each side.
21x = 105
Divide each side by 21.
x = 5
So, the number is 5.
Problem 10 :
If 9 times the sum of 7 and 4 times of a number is 135, find the number.
Solution :
Let x be the number.
Then,
9(7 + 4x) = 135
Use distributive property.
63 + 36x = 135
Subtract 63 from each side.
36x = 72
Divide each side by 36.
x = 2
So, the number is 2.
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