Worked examples
The question
Question: share 35 in the ratio 2 to 3.
Share 35 in the ratio 2 : 3
The ratio says how many equal parts each one gets: 2 for the first and 3 for the second.
1st: 2 parts, 2nd: 3 parts
Careful!
2 to 3 does not mean dividing 35 by 2 and by 3.
It counts parts of the same size.
Careful: not 35 ÷ 2, 35 ÷ 3 ✗
1 Count the parts
All together there are 2 plus 3: 5 equal parts.
= 2 + 3 = 5 parts
2 Draw the bar
3 Find one part
5 parts make 35.
So one part is 35 divided by 5: 7.
= 1 part = 35 ÷ 5 = 7
Every part is 7.
4 Find each share
The first share has 2 parts: 2 times 7 is 14.
= 1st: 2 × 7 = 14
The second share has 3 parts: 3 times 7 is 21.
= 2nd: 3 × 7 = 21
So the shares are 14 and 21.
= 14 and 21
5 Check
Let's check.
The shares add up: 14 plus 21 is 35.
14 + 21 = 35
And divided by 7, they give 2 to 3 again.
So the answer is right!
14 : 21 → ÷ 7 → 2 : 3
Let's look back.
First: count the parts.
Then: draw the bar.
Then: find one part.
Then: find each share.
Last: check.
▶ Watch it solved
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
▶ Watch it solved
The question
Question: share 90 in the ratio 1 to 2 to 3.
Share 90 in the ratio 1 : 2 : 3
The ratio says how many equal parts each one gets: 1 for the first, 2 for the second and 3 for the third.
1st: 1 part, 2nd: 2 parts, 3rd: 3 parts
Careful!
1 to 2 to 3 does not mean dividing 90 by 1 and by 2 and by 3.
It counts parts of the same size.
Careful: not 90 ÷ 1, 90 ÷ 2, 90 ÷ 3 ✗
1 Count the parts
All together there are 1 plus 2 plus 3: 6 equal parts.
= 1 + 2 + 3 = 6 parts
2 Draw the bar
3 Find one part
6 parts make 90.
So one part is 90 divided by 6: 15.
= 1 part = 90 ÷ 6 = 15
Every part is 15.
4 Find each share
The first share has 1 part: 1 times 15 is 15.
= 1st: 1 × 15 = 15
The second share has 2 parts: 2 times 15 is 30.
= 2nd: 2 × 15 = 30
The third share has 3 parts: 3 times 15 is 45.
= 3rd: 3 × 15 = 45
So the shares are 15, 30 and 45.
= 15, 30 and 45
5 Check
Let's check.
The shares add up: 15 plus 30 plus 45 is 90.
15 + 30 + 45 = 90
And divided by 15, they give 1 to 2 to 3 again.
So the answer is right!
15 : 30 : 45 → ÷ 15 → 1 : 2 : 3
Let's look back.
First: count the parts.
Then: draw the bar.
Then: find one part.
Then: find each share.
Last: check.
▶ Watch it solved
