Step by step
The question
Question: share 72 in the ratio 5 to 3.
Share 72 in the ratio 5 : 3
The ratio says how many equal parts each one gets: 5 for the first and 3 for the second.
1st: 5 parts, 2nd: 3 parts
Careful!
5 to 3 does not mean dividing 72 by 5 and by 3.
It counts parts of the same size.
Careful: not 72 ÷ 5, 72 ÷ 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 72.
So one part is 72 divided by 8: 9.
= 1 part = 72 ÷ 8 = 9
Every part is 9.
4 Find each share
The first share has 5 parts: 5 times 9 is 45.
= 1st: 5 × 9 = 45
The second share has 3 parts: 3 times 9 is 27.
= 2nd: 3 × 9 = 27
So the shares are 45 and 27.
= 45 and 27
5 Check
Let's check.
The shares add up: 45 plus 27 is 72.
45 + 27 = 72
And divided by 9, they give 5 to 3 again.
So the answer is right!
45 : 27 → ÷ 9 → 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
= 45 and 27