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 $$72−48.
First, we can find the greatest common factor (GCF) between the two numbers.
The factors of $$48 are:
$$1,2,3,4,6,8,12,16,24,48
The factors of $$72 are:
$$1,2,3,4,6,8,9,12,18,24,36,72
The numbers that appear in both factor lists are:
$$1,2,3,4,6,8,12,24
The largest number in this list is the GCF, $$24.
Now, we can rewrite the expression as an equivalent multiplication by using the distributive property.
$$48=24×2
$$72=24×3
$$72−48=24×(3−2)
Finally, we multiply the two integers to find our answer.
$$24×(3−2)=24×1
$$24×1=24
So, $$72−48=24.
And there you go! Another way to find the sum or difference between to numbers.
Consider the difference $$88−20 :
Find the greatest common factor of $$88 and $$20.
Complete the gaps such that $$88−20 is rewritten as an equivalent multiplication using the distributive property.
$$88−20 |
$$= |
$$4·(−5) |
$$= |
$$4· |
Consider $$11(8−3).
Using the distributive property complete the gap so that $$11(8−3) is rewritten as the difference of two integers.
$$11(8−3)=88−
Hermione and Yuri both earn $$$11 per hour in their casual job. In a day where one works for $$7 hours and the other works for $$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 = $$(−)