Question

Using the distributive property, show how to decompose 8 * 78WRITER1

Answer 1

The distributive property states the following:

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

So in order to decompose the expression 8 * 78, we can decompose the number 78 in any two numbers that when added are equal 78:

`\begin{gathered} 8\cdot(40+38) \\ 8\cdot(1+77) \\ 8\cdot(39+39) \end{gathered}`

For each case, let's show using the distributive property that the result is the same:

`\begin{gathered} 8\cdot78=624 \\ \\ 8\cdot(40+38)=8\cdot40+8\cdot38=320+304=624 \\ 8\cdot(1+77)=8\cdot1+8\cdot77=8+616=624 \\ 8\cdot(39+39)=8\cdot39+8\cdot39=312+312=624 \end{gathered}`