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Unit 8

- Fractions and Ratios

Key Unit Goals

- Order 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.

Click me for help!

Click the space ship to return to the goals page.

Order and Compare Fractions

- 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. - Play a game

Strategies for comparing and ordering 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

Try It Out.

3/5 _____ 4/5

lt

gt

You Rock!

3/5 lt 4/5

3/5 is lt 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

lt

gt

BEAUTIFUL! 7/8 gt 6/7

7/8 is gt 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

lt

gt

Looking Good! 3/5 lt 10/15

3/5 is lt 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.

Strategies for finding a percent of a number.

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.

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 150/1 4500/100 45

Try It Out.

75 of 120

30

90

40

100

You Rock!

90 is 75 of 120

90 is 75 of 120 75 is ¾ of 100 120 / 4 30 3 x

30 90

30

30

30

30

Try It Out.

30 of 200

30

90

60

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

20

20

20

20

20

20

Try It Out.

75 of 600

75

400

150

450

Looking Good! 75 of 600 450

75 of 600 450 50 (half) of 600 300 Half 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

35 35/100 .35

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

.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 20/100 20/100 20 OR

5/25 .2 .2 x 100 20

Way to Groove!

5/25 20

Try It Out.

135

1.35

135

13.5 100

13.5

Far Out!

135 1.35

135 1.35 135 / 100 1 35/100 OR

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

1/50

20/100

20

2/10

Awesome!

.02 1/50

.02 1/50 .02 2/100 2/100 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 quiz Play a game See it and try it Interactive

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 it See 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.

Try It Out

Step by step Try this site for a demonstration

and opportunities to practice!

Use an algorithm to multiply fractions and mixed

numbers.

Multiplying fractions is easy! You dont 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!