Step by step
The question
Question: share 120 in the ratio 7 to 5.
Share 120 in the ratio 7 : 5
The ratio says how many equal parts each one gets: 7 for the first and 5 for the second.
1st: 7 parts, 2nd: 5 parts
Careful!
7 to 5 does not mean dividing 120 by 7 and by 5.
It counts parts of the same size.
Careful: not 120 ÷ 7, 120 ÷ 5 ✗
1 Count the parts
All together there are 7 plus 5: 12 equal parts.
= 7 + 5 = 12 parts
2 Draw the bar
3 Find one part
12 parts make 120.
So one part is 120 divided by 12: 10.
= 1 part = 120 ÷ 12 = 10
Every part is 10.
4 Find each share
The first share has 7 parts: 7 times 10 is 70.
= 1st: 7 × 10 = 70
The second share has 5 parts: 5 times 10 is 50.
= 2nd: 5 × 10 = 50
So the shares are 70 and 50.
= 70 and 50
5 Check
Let's check.
The shares add up: 70 plus 50 is 120.
70 + 50 = 120
And divided by 10, they give 7 to 5 again.
So the answer is right!
70 : 50 → ÷ 10 → 7 : 5
Let's look back.
First: count the parts.
Then: draw the bar.
Then: find one part.
Then: find each share.
Last: check.
Answer
= 70 and 50