Unit 8

Fractions and Ratios

Key Unit GoalsOrder and compare fractions.Find a percent of a number.Convert among fractions, decimals, and percents.Find common denominators.Convert between fractions and mixed or whole numbers.Use an algorithm to add and subtract mixed numbers.Use an algorithm to multiply fractions and mixed numbers.

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• A fraction is a part of a whole. The denominator indicates the size of the part, the numerator tells how many of those size pieces you have.

• The smaller the denominator, the larger the part because the denominator tells how many pieces the whole is divided into.

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Order and Compare Fractions

• One strategy for comparing fractions is to think about their relationship to one and zero. For example, 5/6 is almost all of the pieces, so it would be close to 1; 1/6 is close to none of the pieces, so it would be closer to zero.

• Another strategy is to convert the fractions to a decimal and then compare the decimals. (numerator divided by denominator = decimal)

• A third strategy is to find a common denominator among your fractions and compare the numerators.

It helps to simplify the fractions!

If you need a set of fraction bars, click here

Strategies for comparing and ordering fractions…

Try It Out….

3/5 _____ 4/5

< =>

You Rock!3/5 < 4/5

3/5 is < 4/5

In these two fractions, the denominators are the same.Therefore, the pieces are the same size.Three of these pieces are less than four.

Try It Out….

7/8 _____ 6/7

< =>

BEAUTIFUL!7/8 > 6/7

7/8 is > 6/7

In each of these two fractions, there is all but one piece. However, because 8ths are smaller than 7ths, the remaining 1/8 is smaller than the remaining 1/7.

Try It Out….

3/5 _____ 10/15

< =>

Looking Good!3/5 < 10/15

3/5 is < 10/15

If you change 3/5 into an equivalent fraction, it would be equal to 9/15. 9 out of 15 is less than 10 out of 15.

Find a percent of a number

• Percent means “per one hundred”. If you are trying to find a certain percent of a number, you need to find the numerator of a fraction equivalent to that percent.

•When you come across the word “of”, remember that you will need to multiply the percent by the number you are trying to find the percentage of.

Find an equivalent fraction:

For example, 30% = 30/100. If I wanted to know what 30% of 150 was, I would need to find the numerator of an equivalent fraction of 30/100 that has a denominator of 150.

30/100 = n/150 To get from 100 to 150, I need to multiply by 1.5. To be fair, 30 x 1.5 gives me a numerator of 45.

So, 30% of 150 is 45.

Strategies for finding a percent of a number….

More strategies for finding a percent of a number…

Change the percent into a decimal by dividing it by 100 and multiply that decimal by the number you are trying to find a percentage of.

For example, 30% of 150 would be found by multiplying .3 x 150= 45

Another way to find a percent of a number is to multiply the equivalent fraction of the percent by the number you are trying to find the percentage of.

For example, 30% of 150 = 30/100 x 150/14500/100 = 45

Try It Out….

75% of 120

30 9040 100

You Rock!90 is 75% of 120

90 is 75% of 120

75 is ¾ of 100120 / 4 = 303 x 30 = 90

30 30 30 30

Try It Out….

30% of 200

30 9060 120

Far Out!60 is 30% of 200

60 is 30% of 200

10% of 200 is 20.10% + 10% + 10% = 30%

3 x 20 = 60

20 20 20 20 2020 202020 20

Try It Out….

75% of 600

75 400150 450

Looking Good!75% of 600 = 450

75% of 600 = 450

50% (half) of 600 = 300Half of 300 (25%) = 150

75% of 600 would then = 450

300 150 150

Convert among fractions, decimals, and percents

•Fractions, decimals, and percents are all ways of representing a part out of a whole.

•An equivalent decimal for a fraction can be found by dividing the numerator by the denominator, or by finding an equivalent fraction out of 10, 100, etc.

•An equivalent percent for a decimal or a fraction can be found by multiplying the decimal form by 100 or by finding an equivalent fraction out of 100 since “percent” means “per 100”. In this case, the numerator would be the percent.

•A fraction or decimal can be formed from a percent by creating a fraction where the numerator is the percentage and the denominator is 100, or by dividing the percent by 100.

Examples…

3/20 = 15/100 = .15, or 3 divided by 20 = .15

35% = 35/100 = .35

.65 = 65/100 = 65%

1.25 = 125/100 = 125%

A number that is greater than 1 will have a percentage greater

than 100%

Try an online quiz

Try It Out….

5/25 =

20% .2.25 .5

5/25 = 20%

5/25 x 4/4 = 20/10020/100 = 20%

OR 5/25 = .2; .2 x 100 = 20%5, 20%

20, 80%

Way to Groove!5/25 = 20%

Try It Out….

135% =

1.3513513.5100

13.5

Far Out!135% = 1.35

135% = 1.35

135 / 100 = 1 35/100OR 1.35

Remember that decimal hundredths and fraction hundredths refer to the same amounts.

5/100 is 5 hundredths.05 is 5 hundredths

Try It Out….

.02 =

1/5020/10020% 2/10

Awesome!

.02 = 1/50

.02 = 1/50

.02 = 2/1002/100 divided by 2/2 = 1/50

Remember that decimal hundredths and fraction hundredths refer to the same amounts.

2/100 is 2 hundredths.02 is 2 hundredths

Convert between fractions, mixed, or whole numbers

•A fraction represents a part out of a whole.

•An improper, or top-heavy, fraction is one that has more parts than the whole. The numerator is larger than the denominator.

•A mixed number contains a fraction and a whole number.

•A whole number is an entire amount, these are numbers you typically count with.

•Click here for a demonstration

To convert between improper fractions and mixed numbers, think about it like filling in pieces.

1 3/5 = 5/5 (1 whole) + 3/5 = 8/5

The denominator represents the total number of pieces in one whole. The numerator tells how

many pieces you have.

Try It Out…

Click on the links below for more practice:

Take a quizPlay a game

See it and try itInteractive demonstration(click skip intro, lesson 2)

Find common denominators

* A “common denominator” is a denominator that two or more fractions have in common (or are the same).

Try It Out…

Click on the links below for more practice:

Find the least common denominator(the smallest denominator fractions have in common)

Read more about itSee it and try it

Use an algorithm for adding and subtracting mixed numbers.

•“Algorithm” is a fancy word for “way to solve”

• As it is with fractions, the fractions in your mixed numbers must have common denominators.

• When you add or subtract mixed numbers, start with the fractions

-Make sure that the denominators are the same- If you need to regroup, it may be easier to change both numbers into improper fractions- Remember that the job of the denominator is to tell you how many pieces are in one whole. The numerator tells you how many of those pieces you have.

Step by step

Try this site for a demonstration and

opportunities to practice!

Try It Out…

Use an algorithm to multiply fractions and mixed numbers.

Multiplying fractions is easy! You don’t even have to have a common denominator.Just multiply the numerator by the numerator and the denominator by the denominator.

Multiplying mixed numbers is a little trickier. When you multiply those, you need to convert any mixed numbers into improper fractions.

Click here to see a demonstration and try it out!