Step by step
The question
Question: share $48 between Ann and Ben in the ratio 5 to 3.
Share $48 between Ann and Ben in the ratio 5 : 3
The ratio says how many equal parts each one gets: 5 for Ann and 3 for Ben.
Ann: 5 parts, Ben: 3 parts
Careful!
5 to 3 does not mean dividing $48 by 5 and by 3.
It counts parts of the same size.
Careful: not $48 ÷ 5, $48 ÷ 3 ✗
1 Count the parts
All together there are 5 plus 3: 8 equal parts.
= 5 + 3 = 8 parts
2 Draw the bar
3 Find one part
8 parts make $48.
So one part is 48 divided by 8: $6.
= 1 part = 48 ÷ 8 = $6
Every part is $6.
4 Find each share
Ann has 5 parts: 5 times 6 is $30.
= Ann: 5 × 6 = $30
Ben has 3 parts: 3 times 6 is $18.
= Ben: 3 × 6 = $18
So the shares are Ann $30 and Ben $18.
= Ann: $30, Ben: $18
5 Check
Let's check.
The shares add up: 30 plus 18 is $48.
30 + 18 = 48
And divided by 6, they give 5 to 3 again.
So the answer is right!
30 : 18 → ÷ 6 → 5 : 3
Let's look back.
First: count the parts.
Then: draw the bar.
Then: find one part.
Then: find each share.
Last: check.
Answer
= Ann: $30, Ben: $18