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## Fractions and Ratios

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### For example, 5/6 is almost all of the pieces, so it would be close to 1; 1/6 is ... Make sure that the denominators are the same ... – PowerPoint PPT presentation

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Title: Fractions and Ratios

1
Unit 8
• Fractions and Ratios

2
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!
3
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

4
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
5
Try It Out.
3/5 _____ 4/5
lt

gt
6
You Rock!
3/5 lt 4/5
7
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.
8
Try It Out.
7/8 _____ 6/7
lt

gt
9
BEAUTIFUL! 7/8 gt 6/7
10
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.
11
Try It Out.
3/5 _____ 10/15
lt

gt
12
Looking Good! 3/5 lt 10/15
13
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.
14
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.

15
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.
16
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
17
Try It Out.
75 of 120
30
90
40
100
18
You Rock!
90 is 75 of 120
19
90 is 75 of 120 75 is ¾ of 100 120 / 4 30 3 x
30 90
30
30
30
30
20
Try It Out.
30 of 200
30
90
60
120
21
Far Out!
60 is 30 of 200
22
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
23
Try It Out.
75 of 600
75
400
150
450
24
Looking Good! 75 of 600 450
25
75 of 600 450 50 (half) of 600 300 Half of
300 (25) 150 75 of 600 would then 450
300
150
150
26
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.

27
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
28
Try It Out.
5/25
20
.2
.25
.5
29
5/25 20 5/25 x 4/4 20/100 20/100 20 OR
5/25 .2 .2 x 100 20
30
Way to Groove!
5/25 20
31
Try It Out.
135
1.35
135
13.5 100
13.5
32
Far Out!
135 1.35
33
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
34
Try It Out.
.02
1/50
20/100
20
2/10
35
Awesome!
.02 1/50
36
.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
37
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.

38
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.
39
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)
40
Find common denominators
A common denominator is a denominator that
two or more fractions have in common (or are the
same).
41
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
42
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.

43
Try It Out
Step by step Try this site for a demonstration
and opportunities to practice!
44
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