Question

Use the distributive property to write an equivalent expression for 88 plus 55

Answer 1

We are asked to use the distributive property to write an equivalent expression for 88 plus 55​.

Let us first understand what is distributive property?

`a\cdot(b+c)=a\cdot b+a\cdot c`

The above property means that multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

But we have only two numbers 88 and 55 so how are we going to apply this property?

We need to break these numbers.

Let us find out the GCF (greatest common factor) of these two numbers.

11 is the greatest common factor of numbers 88 and 55

So, we can break the numbers as

`\begin{gathered} 88=11\cdot8 \\ 55=11\cdot5 \end{gathered}`

Now we have three numbers so let us apply the distributive property.

`\begin{gathered} a\cdot(b+c)=a\cdot b+a\cdot c \\ 11\cdot(8+5)=11\cdot8+11\cdot5 \end{gathered}`

Therefore, the equivalent expression for 88 plus 55​ is

`88+55=11\cdot(8+5)_{}`