Share 30 sweets between two children in the ratio 2 : 3.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Try it first
Maya and Dev share stickers. For every 1 sticker Maya gets, Dev gets 2. Maya gets 7 stickers. How many stickers does Dev get?
stickers
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Count the parts
The bar has 2 parts for one child and 3 for the other, so 5 parts in all.
Find one part
5 parts make 30, so one part is 30 ÷ 5 = 6.
Then build each share
One child gets 2 parts, so 12. The other gets 3 parts, so 18. Together that is 30.
Step 2: Try It Yourself
Tap and try it out.
First share
12
6
Second share
18
18 is 6 more than 12.
Step 3: In Real Life
Splitting a prize
Two friends split 90 dollars in the ratio 2 to 1. Draw 3 equal bars. Each bar is 30. 60 and 30. The picture does the dividing.
Step 4: Watch an Example
One step at a time.
Watch Ana Share $56
Ana shares $56 between two clubs in the ratio 3 : 4.
- Step 1
Ana draws the bar first. The first club takes 3 boxes and the second takes 4, and every box is the same size.
Watch Leo Share $63
Leo shares $63 between two teams in the ratio 5 : 4. He starts it, and you finish it.
- Step 1
Leo reads the ratio. One team takes 5 boxes of the bar and the other takes 4.
Watch Priya Work Backwards
Priya and Noor share the cost of a tent in the ratio 3 : 5. Noor pays $45. The total is what nobody has yet.
- Step 1
The bar is drawn the same way as before. Priya holds 3 boxes and Noor holds 5, but this time the number given sits on one share instead of under the whole bar.
Step 5: Your Turn
Practice makes it stick.
The Car Wash
Problem 1 of 17
Maya and Dev wash cars and make $84. They share it in the ratio 3 : 4. How many dollars does Maya get?
dollars
The Gift
Problem 2 of 17
Ravi and Ana buy a gift together and split the cost in the ratio 2 : 5. Ana pays $35. How many dollars does the gift cost in all?
dollars
Count the Parts
Join the two ratio numbers to count the parts. Divide the total by that. Then build the share you were asked for.
Problem 3 of 17
Share 20 marbles in the ratio 1 : 4. What is the smaller share?
marbles
Problem 4 of 17
Share 35 stickers in the ratio 2 : 5. What is the larger share?
stickers
Problem 5 of 17
Share 50 beads in the ratio 3 : 7. What is one part worth?
beads
Problem 6 of 17
Share 27 cards in the ratio 2 : 7. What is the smaller share?
cards
Problem 7 of 17
Share 55 shells in the ratio 5 : 6. What is the larger share?
shells
Whose Step?
One line in each page is a slip. Find it, then fix it.
Problem 8 of 17
Dev was asked to share $40 in the ratio 3 : 5 and give the larger share. One line is a slip. Which?
Dev's answer for: share $40 in the ratio 3 : 5, larger share
- 13 + 5 = 8 parts
- 2$40 ÷ 8 = $5 in one part
- Answerlarger share = 3 × $5 = $15
Problem 9 of 17
What should the larger share be, in dollars?
dollars
Problem 10 of 17
Noor was asked to share 45 counters in the ratio 4 : 5 and give the smaller share. One line is a slip. Which?
Noor's answer for: share 45 counters in the ratio 4 : 5, smaller share
- 14 + 5 = 9 parts
- 245 ÷ 2 = 22.5 in one part
- Answersmaller share = 4 × 22.5 = 90
Problem 11 of 17
What should the smaller share be?
counters
Problem 12 of 17
Ana and Sam split money in the ratio 2 : 3. Sam's share is $18, and Sam was asked for the total. One line is a slip. Which?
Sam's answer for: Ana : Sam = 2 : 3, Sam's share is $18, find the total
- 12 + 3 = 5 parts
- 2$18 ÷ 3 = $6 in one part
- Answertotal = 3 × $6 = $18
Problem 13 of 17
What should the total be, in dollars?
dollars
Pick the Move
Decide the first move before you make it. What you were given decides it.
Problem 14 of 17
A prize of $60 is shared in the ratio 1 : 5. What is the first move?
Problem 15 of 17
Two shares are in the ratio 3 : 7. The smaller share is $21, and the total is wanted. What is the first move?
Same Share?
Decide what is true of the bar. Some of these you can settle without finishing the arithmetic.
Problem 16 of 17
24 is shared in the ratio 1 : 2. Select every statement that is true.
Problem 17 of 17
Leo shares $30 in the ratio 1 : 2. Maya shares $30 in the ratio 2 : 4. Select every statement that is true.
Step 6: Quick Check
Show what you know.
Question 1 of 2
Share 48 in the ratio 1 : 3. What is the larger share?
Question 2 of 2
To share a total in a ratio, what do you find first?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
Two friends share $60. The first gets twice as much as the second. How many dollars does the first get?
dollars
Stretch 2 of 2
A prize of $48 is shared between three friends in the ratio 1 : 2 : 3. How many dollars does the friend with the largest share get?
dollars
What You Learned
- Draw the ratio as parts of a bar.
- Divide the total by the number of parts to find one part.
- Then build each share from the parts it has.
For the grown-up
The misconception this lesson targets is that the two ratio numbers are the shares. Asked to share 30 in the ratio 2 : 3, a child holding it answers "2 and 3", and nothing about the wording corrects them. The tape diagram is the cure, because it makes the numbers count boxes rather than candy.
The first slip is dividing by 2, the number of people, instead of by the number of parts. It is the most common wrong first line on this page, and it always produces a share bigger than the total.
The second slip appears when a share is given instead of the total, and the child divides by the whole bar rather than by the boxes that share covers. Asking "how many boxes does that number cover?" out loud catches both.
What a tape diagram shows — Draw one box for each part of the ratio: 3 boxes for red and 2 for blue. Every box is the same size, whatever that size turns out to be. The picture holds the relationship steady while you work out what one box is worth.
Find the value of one box — If a 3 : 2 mix makes 40 liters altogether, there are 5 boxes and 40 ÷ 5 = 8 liters per box. So red is 3 × 8 = 24 and blue is 2 × 8 = 16. Almost every ratio problem reduces to finding what one box is worth.
When the difference is given — If there are 12 more red than blue in a 3 : 2 mix, the difference is 1 box, so a box is 12. Red is 36 and blue is 24. The diagram tells you which quantity corresponds to the number you were given, which is what makes these problems tractable.
Check against the original ratio — Once you have both amounts, reduce them: 36 : 24 reduces to 3 : 2. If it does not match the ratio you were given, something went wrong. This check is quick and it verifies the answer rather than the arithmetic.
Draw the parts as boxes — Red to blue is 3 : 2, and there are 30 counters. Draw 3 boxes for red, 2 for blue. Five boxes in all. 30 ÷ 5 = 6 in each box. Red: 3 × 6 = 18. Blue: 2 × 6 = 12. Check: 18 + 12 = 30.