Download Unit 3: Ratios and Proportional Relationships

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Fractional Unit Rates
Many real world questions do not use whole numbers. Fractions and decimals can
be used in a ratio. This is known as a complex fraction where either the numerator,
denominator, or both are fractions. The process to find the unit rate is still the same,
divide the ratio to get a denominator of one. Dividing fractions in a ratio is the same as
dividing fractions.
1.) Make sure they are either a fraction or an improper fraction not a mixed number.
2.) Keep the first number the same.
3.) Change division to multiplication.
4.) Take the reciprocal (flip) the second number.
5.) Also known as “invert and multiply” “keep, change, flip”
Example: You can read 3½ pages in 10 minutes. How many pages can you read in an
hour.
*Note there are many ways to answer this!
Method 1:
Two things to remember:
1
3
2
1
6
10
1.) 10 minutes is 60 , 𝑜𝑟
hour.
1
2.) 3 2 =
7
1
÷
2
6
7
×
2
6
1
=
42
2
1
6
of an
7
2
or 21 pages per hour
Method 2: (this only works on certain denominators)
There are 6 (10 minutes) in an hour.
1
32
1
6
×
6
6
=
21
1
or 21 pages per hour
*With Method 2, there are only certain times this will work. It is easier and quicker if you
can recognize a number you can multiply to get the denominator to 1.
There are 4 (15 minutes, ¼ of an hour) in 1 hour. So, multiply by four.
There are 2 (6 inches, ½ of a foot) in 1 foot. So, multiply by two.
There are 10 (10¢ (dime), 1⁄10 of a dollar) in 1 dollar. So, multiply by ten.
If you see this relationship, you can multiply instead of dividing.
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