Let's look at a way to find the sum of or difference between two numbers that uses the greatest common factor (GCF) and the distributive property.
For example, let's say we wanted to evaluate $72-48$72−48.
First, we can find the greatest common factor (GCF) between the two numbers.
The factors of $48$48 are:
$1,2,3,4,6,8,12,16,24,48$1,2,3,4,6,8,12,16,24,48
The factors of $72$72 are:
$1,2,3,4,6,8,9,12,18,24,36,72$1,2,3,4,6,8,9,12,18,24,36,72
The numbers that appear in both factor lists are:
$1,2,3,4,6,8,12,24$1,2,3,4,6,8,12,24
The largest number in this list is the GCF, $24$24.
Now, we can rewrite the expression as an equivalent multiplication by using the distributive property.
$48=24\times2$48=24×2
$72=24\times3$72=24×3
$72-48=24\times\left(3-2\right)$72−48=24×(3−2)
Finally, we multiply the two integers to find our answer.
$24\times\left(3-2\right)=24\times1$24×(3−2)=24×1
$24\times1=24$24×1=24
So, $72-48=24$72−48=24.
And there you go! Another way to find the sum or difference between to numbers.
Consider the difference $88-20$88−20 :
Find the greatest common factor of $88$88 and $20$20.
Complete the gaps such that $88-20$88−20 is rewritten as an equivalent multiplication using the distributive property.
$88-20$88−20 |
$=$= |
$4\cdot\left(\editable{}-5\right)$4·(−5) |
$=$= |
$4\cdot\editable{}$4· |
Consider $11\left(8-3\right)$11(8−3).
Using the distributive property complete the gap so that $11\left(8-3\right)$11(8−3) is rewritten as the difference of two integers.
$11\left(8-3\right)=88-\editable{}$11(8−3)=88−
Hermione and Yuri both earn $\$11$$11 per hour in their casual job. In a day where one works for $7$7 hours and the other works for $2$2 hours, complete the number sentence that can be used to evaluate the difference in their wages (with the difference expressed as a positive quantity).
Difference in wages = $\editable{}\left(\editable{}-\editable{}\right)$(−)