Step by step
The question
Question: share 45 in the ratio 4 to 5.
Share 45 in the ratio 4 : 5
The ratio says how many equal parts each one gets: 4 for the first and 5 for the second.
1st: 4 parts, 2nd: 5 parts
Careful!
4 to 5 does not mean dividing 45 by 4 and by 5.
It counts parts of the same size.
Careful: not 45 ÷ 4, 45 ÷ 5 ✗
1 Count the parts
All together there are 4 plus 5: 9 equal parts.
= 4 + 5 = 9 parts
2 Draw the bar
3 Find one part
9 parts make 45.
So one part is 45 divided by 9: 5.
= 1 part = 45 ÷ 9 = 5
Every part is 5.
4 Find each share
The first share has 4 parts: 4 times 5 is 20.
= 1st: 4 × 5 = 20
The second share has 5 parts: 5 times 5 is 25.
= 2nd: 5 × 5 = 25
So the shares are 20 and 25.
= 20 and 25
5 Check
Let's check.
The shares add up: 20 plus 25 is 45.
20 + 25 = 45
And divided by 5, they give 4 to 5 again.
So the answer is right!
20 : 25 → ÷ 5 → 4 : 5
Let's look back.
First: count the parts.
Then: draw the bar.
Then: find one part.
Then: find each share.
Last: check.
Answer
= 20 and 25