Question

Use the distributive property and the GCF of the addends to rewrite each sum as an equivalent expression that has two factors.28 + 4240 + 25 30 + 5475 + 90

Answer 1

We need to find the greatest common factor GCF of the two numbers, then first list the prime factors of each number:

a. 28: 2*2*7

42: 2*3*7

28 and 42 share one 2 and one 7 in common.

Multiply it to get the GCF: 2*7=14.

The GCF of 28 and 42 is 14.

Now, to use the distributive property, write the sum in the form: GCF(a+b) then:

`28+42=14(2+3)`

b. 40+25

40: 2*2*2*5

25: 5*5

They share one 5 in common.

The GCF of 40 and 25 is 5.

By using the distributive property:

`40+25=5(8+5)`

c. 30+54

30: 2*3*5

54: 2*3*3*3

They have one 2 and one 3 in common. Then 2*3=6.

The GCF of 30 and 54 is 6.

By using the distributive property:

`30+54=6(5+9)`

d. 75+90

75: 3*5*5

90: 2*3*3*5

They have one 3 and one 5 in common. So 3*5=15.

The GCF of 75 and 90 is 15.

By using the distributive property:

`75+90=15(5+6)`