Ratios & Proportions
Grades 6–8 Ratios Fractions
A ratio compares two quantities: "3 cats per 2 dogs" is 3:2 — or 3/2, a fraction wearing a different hat. A proportion says two ratios are equal.
Equivalent ratios scale together
3 : 2 = 6 : 4 = 9 : 6 = 30 : 20
← multiply both sides by the same number — same comparison
Solving proportions
Cross-multiply: if a/b = c/d then a·d = b·c.
x 3
-- = --
14 7
7x = 3 × 14 = 42
x = 6 Check: 6/14 = 3/7 ✓
Where it hides
- Recipes: double 3 eggs : 2 cups flour → 6 eggs : 4 cups
- Maps and scale models (see similarity)
- Mixing paint, sharing money, odds
Watch out
3:2 and 2:3 are different comparisons — order names the
relationship. "3 wins for every 2 losses" flipped is a very
different season.
Practice
x/15 = 2/3 → x = ___
4:x = 12:27 → x = ___
Which equals the ratio 5:4?
12 pencils per 3 students = ___ pencils per 2 students
Next: unit rates · Back: quadratic equations