# 10 14 11 Lesson 3 5 Equivalent Fractions and Decimals Class 5B Notes

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```					 3-5 Equivalent Fractions and Decimals

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Warm Up
California Standards
Lesson Presentation

Holt CA Course 1
3-5 Equivalent Fractions and Decimals

Warm Up
Write each fraction in the simplest form.

1.    4        1        2. 18     9
12       3           46    23

3.     21      1        4. 100    25 or 1 7
63      3           72     18      18

Holt CA Course 1
3-5 Equivalent Fractions and Decimals

California
Standards
Preparation for Number Sense (NS1.1) -
Compare and order positive and negative
fractions, decimals, and mixed numbers
and place them on a number line.
Also covered: Number Sense (NS2.4)

Holt CA Course 1
3-5 Equivalent Fractions and Decimals

Vocabulary
terminating decimal
repeating decimal

Holt CA Course 1
3-5 Equivalent Fractions and Decimals
In baseball, a player’s batting average compares the number of
hits with the number of times the player has been at bat.
At     Hits       Batting Average
Player               Hits
Bats   At Bats      (thousandths)
172
Lance Berkman        172    544              172 ÷ 544 ≈ 0.316
544
172
Alex Rodriguez       172    601
601   172 ÷ 601 ≈ 0.286

To convert a fraction to a
decimal, divide the numerator
by the denominator.

Holt CA Course 1
3-5 Equivalent Fractions and Decimals

The decimals 0.75 and 1.2 are terminating decimals
because the decimals comes to an end. The decimal
0.333… is a repeating decimal because it includes a
group of one or more digits (where all digits are not
zero) that repeats forever. You can also write a
repeating decimal with a bar over the repeating
part.

0.333… = 0.3
0.8333… = 0.83
0.727272… = 0.72

Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Example 1: Writing Fractions as Decimals
Write each fraction as a decimal. Round
to the nearest hundredth, if necessary.
1               9              5
(A) 4             (B) 5         (C) 3
1 .8             1.666     5 ≈ 1.67
0.2 5                                        3
4 1               5 9            3 5
– 8              – 5            – 3
20               4 0             2 0
– 20             – 4 0           – 1 8
0                0                2 0
– 1 8      SMART Resp
1 = 0.25        9 = 1.8
5                       2 0 To set the properties right click and
4                                     – 1 8 SMART Response Question Object
2

Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Check It Out! Example 2
Write each fraction as a decimal. Round
to the nearest hundredth, if necessary.
3                6               7
(A) 4              (B) 5          (C) 3
1.2             2.333         7 ≈ 2.33
0.75                                           3
5 6            3 7
4 3
– 2 8                            – 6
– 5
20              10             10
– 20            – 10             – 9
0              0               10
– 9
6 = 1.2                    SMART Resp
3 = 0.75                              10
4                5                    – 9   To set the properties right click a
SMART Response Question Ob
1

Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Example 3: Using Mental Math
to Write Fractions as Decimals
Write each fraction as a decimal.

(A) 4
5
4 × 2 = 8 = 0.8       Multiply to get a
power of ten in the
5 2     10            denominator.

(B) 37
50
37 × 2 = 74                   Multiply to get a
= 0.74           power of ten in
50 2     100                  the denominator.

Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Check It Out! Example 4
Write each fraction as a decimal.

(A) 3
5
3 × 2 = 6 = 0.6      Multiply to get a
power of ten in the
5 2     10           denominator.

(B) 18
25
Multiply to get a
SMART Respons
18 × 4 = 72 = 0.72         power of ten in the   To set the properties right click and selec

25 4     100
SMART Response Question Object->Pro
denominator.

Holt CA Course 1
3-5 Equivalent Fractions and Decimals

You can also use place value to write a
terminating decimal as a fraction. Use the place
value of the last digit to the right of the decimal
point as the denominator of the fraction.

Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Example 5: Writing Decimals
as Fractions
Write each decimal as a fraction in simplest form.

(A) 0.018                            (B) 1.55
18                                155
0.018 =                                 1.55 = 100
1,000
18 ÷ 2
=
1,000 ÷ 2                          = 155 ÷ 5
100 ÷ 5
9
= 500                                  31 or 1 11
=
20      20
You read the decimal 0.018 as “eighteen thousandths.”

Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Check It Out! Example 6

Write each decimal as a fraction in simplest form.

(A) 0.015                  (B) 1.30

0.015 =        15                    130
1.30 =
1,000                   100

= 15 ÷ 5                = 130 ÷ 10
1,000 ÷ 5                100 ÷ 10
SMART Respon
= 3                 = 13 or 1 3    To set the properties right click and sele

200                         10
SMART Response Question Object->Pr
10

Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Example 7: Sports Application

A football player completed 1,546 of the 3,875
passes he attempted. Find his completion rate. Write
thousandth.
0.3989…   Divide the numerator
by the denominator.

His completion rate is 0.399.

Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Check It Out! Example 8
Johnny Unitas, a former professional quarterback,
completed 2,830 of the 5,186 passes he attempted.
decimal rounded to the nearest thousandth.
0.5456…   Divide the numerator
by the denominator.

His completion
rate is 0.546.
SMART Respons
To set the properties right click and selec
SMART Response Question Object->Pro

Holt CA Course 1
3-5 Equivalent Fractions and Decimals

On-Line
Tutoring

Equivalent
Line ‘Em Up!
Pairs

Holt CA Course 1
3-5 Equivalent Fractions and Decimals
Lesson Quiz

Write each fraction as a decimal.
2. 21    2.625
1. 16 3.2                   8
5
7                         11
3. 10  0.7                4. 20 0.55
Write each decimal as a fraction in simplest form.
5. 0.42 21                6. 8.625 69 or 8
5
50                                 8
8
7. If your soccer team wins 21 out of 30 games,
what is your team’s winning rate? 0.70

Holt CA Course 1

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