Step by step
The question
Question: share $90 between Sam and Kim in the ratio 7 to 2.
Share $90 between Sam and Kim in the ratio 7 : 2
The ratio says how many equal parts each one gets: 7 for Sam and 2 for Kim.
Sam: 7 parts, Kim: 2 parts
Careful!
7 to 2 does not mean dividing $90 by 7 and by 2.
It counts parts of the same size.
Careful: not $90 ÷ 7, $90 ÷ 2 ✗
1 Count the parts
All together there are 7 plus 2: 9 equal parts.
= 7 + 2 = 9 parts
2 Draw the bar
3 Find one part
9 parts make $90.
So one part is 90 divided by 9: $10.
= 1 part = 90 ÷ 9 = $10
Every part is $10.
4 Find each share
Sam has 7 parts: 7 times 10 is $70.
= Sam: 7 × 10 = $70
Kim has 2 parts: 2 times 10 is $20.
= Kim: 2 × 10 = $20
So the shares are Sam $70 and Kim $20.
= Sam: $70, Kim: $20
5 Check
Let's check.
The shares add up: 70 plus 20 is $90.
70 + 20 = 90
And divided by 10, they give 7 to 2 again.
So the answer is right!
70 : 20 → ÷ 10 → 7 : 2
Let's look back.
First: count the parts.
Then: draw the bar.
Then: find one part.
Then: find each share.
Last: check.
Answer
= Sam: $70, Kim: $20