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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.

Example:

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

Example:

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.

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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
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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!

slide10

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.
slide12
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.