Step by step
The question
Question: share 40 in the ratio 3 to 1.
Share 40 in the ratio 3 : 1
The ratio says how many equal parts each one gets: 3 for the first and 1 for the second.
1st: 3 parts, 2nd: 1 part
Careful!
3 to 1 does not mean dividing 40 by 3 and by 1.
It counts parts of the same size.
Careful: not 40 ÷ 3, 40 ÷ 1 ✗
1 Count the parts
All together there are 3 plus 1: 4 equal parts.
= 3 + 1 = 4 parts
2 Draw the bar
3 Find one part
4 parts make 40.
So one part is 40 divided by 4: 10.
= 1 part = 40 ÷ 4 = 10
Every part is 10.
4 Find each share
The first share has 3 parts: 3 times 10 is 30.
= 1st: 3 × 10 = 30
The second share has 1 part: 1 times 10 is 10.
= 2nd: 1 × 10 = 10
So the shares are 30 and 10.
= 30 and 10
5 Check
Let's check.
The shares add up: 30 plus 10 is 40.
30 + 10 = 40
And divided by 10, they give 3 to 1 again.
So the answer is right!
30 : 10 → ÷ 10 → 3 : 1
Let's look back.
First: count the parts.
Then: draw the bar.
Then: find one part.
Then: find each share.
Last: check.
Answer
= 30 and 10