6th Grade - Ratios and Proportions


  • A comparison of two numbers by division is called a Ratio.
  • A ratio can be expressed in three different ways: ab, a:b, or a to b.
  • A ratio ab is read as "a ratio of a to b".
  • A ratio is a fraction that can be simplified.
  • Two ratios are called equal ratios or equivalent ratios if are equal.
    • 25 and 410are equal ratios as 410=25×22 (numerator and denominator are multiplied by the same number).
  • A table of equivalent ratios is called a ratio table.
    • 2 4 6 8 10
      5 10 15 20 25
    • All ratios in the ratio table are equivalent.


  • Two ratios are said to be in proportion if their cross-product are equal.
  •  ab and cd are in proportion if a × d = b × c.

Solved Examples

1. Find the ratio of 7 to 10.

The ratio of 7 to 10 is 710

2. Find the ratio of 16 oranges to 21 apples.

The ratio of 16 to 21 is 1621

3. Complete the following ratio table:

Number of Lemons 5 10 ?
Glasses of Lemonade 10 ? 30

To keep the ratio table equal, the top and the bottom numbers should be multiplied by the same number.

Number of Lemons 5 10 (5×2) 15 (5×3)
Glasses of Lemonade 10 20 (10×2) 30 (10×3)

4. Do the following ratios form a proportion: 25 and 715?

The cross-product should be the same for the ratios to form a proportion. Since 2×15 7×5, the ratios are not in proportion.

5. 6 pastries cost $5. What should 18 pastries cost?

Put the provided information as a proportion: 65=18?.

Since 6 is multiplied by 3 to get 18, 5 must be multiplied by 3.

The answer is $15.


Cheat Sheet

  • The quantity that comes first in the ratio statement becomes the numerator in the ratio fraction.
  • A proportion consists of 4 terms. It is a comparison of two ratios.
  • If the numerator and denominator of a ratio are multiplied by the same number, the resulting ratio is equivalent to the first one.
  • ab = 3a3b = 5a5b
  • Their cross-product should be the same for the ratios to be in proportion.

Blunder Area

  • In the case of word problems, pay attention to which value goes as a numerator and which one goes as a denominator.
  • Not all ratios are in proportion.