SME
Grade 6 Math · Ratios & Proportions
Understand and use ratios
Use this for “A recipe uses 3 cups of flour for every 2 cups of milk. How much milk goes with 12 cups of flour?”
Diagram
3 : 2 is the same ratio as 12 : 8.
Both parts were multiplied by 4.
This is an example. Type your own values to start a new problem.
a
:
b
=
x
:
y
Multiplier
calculated
Formulas
3 × 4 = 12
First part × multiplier = first amount
2 × 4 = 8
Second part × multiplier = second amount
Assumptions
•
Equivalent ratios multiply both parts by the same number.
•
Adding the same number to both parts does not keep the ratio.
•
The order matters: 3:2 is flour to milk, not milk to flour.
•
Parts of the ratio are whole numbers to 50.
Step-by-step
WE KNOW
First part of the ratio: 3
Second part of the ratio: 2
First amount: 12
FIND
multiplier, second amount
Step 1 · Find multiplier
3 × ? = 12
First part × multiplier = first amount
How many times bigger is the first amount than its part? Divide to find out.
Multiplier = 12 ÷ 3
Multiplier = 4
Step 2 · Find second amount
2 × 4 = ?
Second part × multiplier = second amount
Multiply the second part by the same number, so the ratio stays the same.
Second amount = 8
Check
Put the numbers back in. Both sides should match.
3 × 4 = 12 ✓
2 × 4 = 8 ✓
Topic check
See what you know: 5 questions on this topic
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More problem types
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?”
Ratios with three parts
Use this for “A ratio of 3:4:5 with 96 people in all. How many in each part?”
Ratio language
Use this for “For every 2 cats there are 3 dogs”: the ratio of cats to dogs.
Equivalent ratios
Use this for “Is 4:6 equivalent to 2:3?”