Grade 6 Mathematics
A RATIO compares two quantities. It tells us "how many of one thing for every how many of another thing."
Example: If there are 3 cats for every 5 dogs, the ratio of cats to dogs is 3 to 5.
ORDER MATTERS! Cats to dogs (3:5) is DIFFERENT from dogs to cats (5:3).
All three mean "3 for every 5" - they are ALL correct ways to write a ratio!
Look at these shapes:
3 red circles and 5 blue circles
Part-to-Part Ratio: Red to Blue = 3:5 (or 3 to 5, or 3/5)
Part-to-Part Ratio: Blue to Red = 5:3 (notice the ORDER changed!)
Part-to-Whole Ratio: Red to Total = 3:8 (because 3+5=8 total)
Equivalent ratios show the same relationship. Multiply or divide BOTH parts by the same number!
Starting ratio: 2:3
2:3 → 4:6 (multiply both by 2)
2:3 → 6:9 (multiply both by 3)
2:3 → 8:12 (multiply both by 4)
All of these are equivalent ratios!
Simplifying: Start with 12:8
12:8 → 6:4 (divide both by 2)
6:4 → 3:2 (divide both by 2)
Simplest form: 3:2
WRONG: "The ratio of cats to dogs" is the same as "the ratio of dogs to cats"
RIGHT: If there are 4 cats and 7 dogs: Cats to dogs = 4:7, but Dogs to cats = 7:4. They are DIFFERENT ratios! Always put quantities in the order the question asks.
1. Look at these shapes:
a) Ratio of green to red:
b) Ratio of red to green:
c) Ratio of green to total:
2. A class has 14 boys and 16 girls.
a) Ratio of boys to girls:
b) Ratio of girls to boys:
c) Ratio of boys to total students:
3. Write three equivalent ratios for 4:5:
: : :
4. Simplify these ratios to lowest terms:
a) 10:15 =
b) 24:18 =
c) 20:35 =