SME
Grade 6 Math · Problem type
Solve ratio problems with tape diagrams
Use this for “Red to blue beads is 4 to 3, with 84 beads in all. How many red? How many more red than blue?”
Diagram
4 : 3 makes 7 equal parts, each worth 12.
Total: 84.
This is an example. Type your own values to start a new problem.
a
:
b
=
x
:
y
x
+
y
=
t
Parts in all
worked out (not typed)
One part is worth
worked out (not typed)
How many more in the bigger
calculated
Formulas
4 + 3 = 7
First part + second part = parts in all
84 ÷ 7 = 12
Total ÷ parts in all = one part is worth
4 × 12 = 48
First part × one part is worth = first amount
3 × 12 = 36
Second part × one part is worth = second amount
4 and 3 boxes differ by some; that many × 12 = 12
(Bigger part − smaller part) × one part is worth = how many more
Assumptions
•
Every box in the tape is worth the same amount.
•
“How many more” is the bigger amount minus the smaller: the extra boxes times what one is worth.
•
Parts of the ratio are whole numbers to 20.
Step-by-step
WE KNOW
First part of the ratio: 4
Second part of the ratio: 3
Total: 84
FIND
parts in all, one part is worth, first amount, second amount, how many more in the bigger
Step 1 · Find parts in all
4 + 3 = ?
First part + second part = parts in all
Count the boxes in both tapes.
Parts in all = 7
Step 2 · Find one part is worth
84 ÷ 7 = ?
Total ÷ parts in all = one part is worth
Share the total equally among all the boxes.
1
2
7
)
8
4
−
7
1
4
−
1
4
0
One part is worth = 12
Step 3 · Find first amount
4 × 12 = ?
First part × one part is worth = first amount
The first tape has that many boxes, each worth the same.
First amount = 48
Step 4 · Find second amount
3 × 12 = ?
Second part × one part is worth = second amount
The second tape has that many boxes, each worth the same.
Second amount = 36
Step 5 · Find how many more in the bigger
(4 − 3) × 12 = ?
(Bigger part − smaller part) × one part is worth = how many more
One tape has more boxes. Multiply the extra boxes by what one is worth.
How many more in the bigger = 12
Check
Put the numbers back in. Both sides should match.
4 + 3 = 7 ✓
12 × 7 = 84 ✓
4 × 12 = 48 ✓
3 × 12 = 36 ✓
(4 − 3) × 12 = 12 ✓
Topic check
See what you know: 5 questions on this topic
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