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Rates, Ratios and Proportions. a:b = c:d. What is a ratio?. A ratio is a comparison of two quantities that can be written as a to b, a : b , or . The quantities in the ratio are called terms. The first term in the ratio above is a , and the second term is b.

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what is a ratio
What is a ratio?

A ratio is a comparison of two quantities that can be written as

a to b, a:b, or .

The quantities in the ratio are called

terms. The first term in the ratio above is a, and the second term is b.

rates and ratios
Rates and Ratios
  • A part-to-part ratio compares a part of the whole to another part of the whole.


There are 8 boys to every 12 girls or 8:12 (8 to 12 ratio). This can also be written as the fraction 8/12.

8/12 is reduced to its simplest form of 2/3 and we can say that we have a 2:3, or 2 to 3, ratio of boys to girls.

a part to whole ratio compares a part of the whole to the whole
A part-to-whole ratio compares a part of the whole to the whole.

Rates and Ratios


8 out of 20 students are boys

  • 8 to 20; 8:20 or 8/20
  • We can write this in simplest form as a 2:5 ratio of boys to the total

12 out of 20 students are girls

  • 12/20 or 6/10 or 3/5.
  • We can write this as a 3:5 ratio of girls to the total.
how can you find equal ratios
How can you find equal ratios?
  • Sometimes you need to find ratios that are equal to a known ratio. You can create equal ratios by multiplying and dividing both terms of the ratio by the same nonzero amount.

Just like when you find equivalent fractions!

rates a special kind of ratio

RatesA special kind of ratio

Some Common Rates

• 22 miles per gallon

• 3 cups of water to 1 can of lemonade mix

• $1.50 per pound

• 72 heartbeats per minute

A rate is a special kind of ratio that compares two quantities with different units of measure. A common rate you already know is miles per hour. Some other examples of rates are shown below.

Rates often contain the word per, meaning for each or for every.


Unit rateAnother special kind of ratio!

If the comparison is to 1 unit, the rate is called a unit rate .

  • Examples of unit rates:
  • Miles per gallon
  • Cost per unit
  • Dollars per hour, mile, pound, ounce

When you compare unit rates, you can really see what is the faster rate or better buy because you are comparing one unit to one unit!


What is a proportion?

  • A proportion states that two ratios are equal.
  • In a proportion, the units must be the same across the top and bottom, or down the left and right sides.
  • When ratios are equal, we say that the quantities vary proportionally.
Do You Have a True Proportion?

True Proportion Checklist

Same labels - across the top and bottom OR on the left and right side?

Equal Ratios? - You can use multiplication or division to create equal ratios or you may need to simplify one ratio and then compare to the other ratio to see!

Cross products equal?

what is a formula
What is a formula?

A formula is a rule that uses symbols to relate two or more quantities.