Step by step
The question
Question: share $84 between Tom and Ella in the ratio 4 to 3.
Share $84 between Tom and Ella in the ratio 4 : 3
The ratio says how many equal parts each one gets: 4 for Tom and 3 for Ella.
Tom: 4 parts, Ella: 3 parts
Careful!
4 to 3 does not mean dividing $84 by 4 and by 3.
It counts parts of the same size.
Careful: not $84 ÷ 4, $84 ÷ 3 ✗
1 Count the parts
All together there are 4 plus 3: 7 equal parts.
= 4 + 3 = 7 parts
2 Draw the bar
3 Find one part
7 parts make $84.
So one part is 84 divided by 7: $12.
= 1 part = 84 ÷ 7 = $12
Every part is $12.
4 Find each share
Tom has 4 parts: 4 times 12 is $48.
= Tom: 4 × 12 = $48
Ella has 3 parts: 3 times 12 is $36.
= Ella: 3 × 12 = $36
So the shares are Tom $48 and Ella $36.
= Tom: $48, Ella: $36
5 Check
Let's check.
The shares add up: 48 plus 36 is $84.
48 + 36 = 84
And divided by 12, they give 4 to 3 again.
So the answer is right!
48 : 36 → ÷ 12 → 4 : 3
Let's look back.
First: count the parts.
Then: draw the bar.
Then: find one part.
Then: find each share.
Last: check.
Answer
= Tom: $48, Ella: $36