2-6 Equivalent Fractions and Decimals
Warm Up
Problem of the Day
Lesson Presentation
Lesson Quizzes
2-6 Equivalent Fractions and Decimals
Warm Up
Write each fraction in the simplest form.
1.
3.
4
12
21
63
1
3
2. 18
46
1
3
4. 100
72
9
23
25 or 1 7
18
18
2-6 Equivalent Fractions and Decimals
I will…
Learn to write fractions as decimals, and
vice versa, and to determine whether a
decimal is terminating or repeating.
2-6 Equivalent Fractions and Decimals
Vocabulary
terminating decimal
repeating decimal
2-6 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. The statistics on the next slide are
for the 2006 Major League Baseball season.
2-6 Equivalent Fractions and Decimals
Player
Hits
At
Hits
Bats at Bats
Miguel Cabrera
195
576
195
576
195 ÷ 576 ≈ 0.339
Ichiro Suzuki
224
695
224
695
224 ÷ 695 ≈ 0.322
Batting Average
(thousandths)
To convert a fraction to a decimal, divide the
numerator by the denominator.
2-6 Equivalent Fractions and Decimals
Example 1: Writing Fractions as Decimals
Write each fraction as a decimal. Round to the
nearest hundredth, if necessary.
1
A. 4
0.2 5
4 1.00
–8
20
– 20
0
1 = 0.25
4
9
B. 5
1.8
5 9.0
–5
40
– 40
0
9 = 1.8
5
5
C. 3
1.666
3 5.000
–3
20
– 18
20
– 18
5
20 3 ≈ 1.67
– 18
2
2-6 Equivalent Fractions and Decimals
Helpful Hint
You can use a calculator to check your division:
1 ÷
4
9 ÷
5 =
1.8
5 ÷
3 =
1.66…
33
=
0.25
2-6 Equivalent Fractions and Decimals
Practice 1
Write each fraction as a decimal. Round to the
nearest hundredth, if necessary.
3
D. 4
0.7 5
4 3.00
–28
20
– 20
0
3 = 0.75
4
6
E. 5
1.2
5 6.0
–5
10
– 10
0
6 = 1.2
5
7
F. 3
2.333
3 7.000
–6
10
–9
10
–9
7
10 3 ≈ 2.33
–9
1
2-6 Equivalent Fractions and Decimals
The decimals 0.75 and 1.2 in Example 1 are
terminating decimals because the decimals
comes to an end. The decimal 0.333…is a
repeating decimal because the decimal
repeats a pattern 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
2-6 Equivalent Fractions and Decimals
Example 2:
Using Mental Math to Write Fractions as Decimals
Write each fraction as a decimal.
4
A. 5
4x2 = 8
5 2
10
37
B. 50
Multiply to get a power of
ten in the denominator.
= 0.8
37 x 2 = 74
50 2
100
= 0.74
Multiply to get a power of
ten in the denominator.
2-6 Equivalent Fractions and Decimals
Practice 2
Write each fraction as a decimal.
3
C. 5
3x2 = 6
5 2
10
18
D. 25
Multiply to get a power of
ten in the denominator.
= 0.6
18 x 4 = 72
25 4
100
= 0.72
Multiply to get a power of
ten in the denominator.
2-6 Equivalent Fractions and Decimals
End Day #1
2-6 Equivalent Fractions and Decimals
Day #2
2-6 Equivalent Fractions and Decimals
Problem of the Day
Martin recorded how much a bean plant
grew each week. The first week the plant
grew 47 of an inch, 78 of an inch the second
week, and 79 of an inch the third week.
During which week did the plant grow the
least?
week 1
2-6 Equivalent Fractions and Decimals
Example 3: Writing Decimals as Fractions
Write each decimal as a fraction in simplest
form.
A. 0.018
18
1,000
18 ÷ 2
=
1,000 ÷ 2
9
=
500
0.018 =
B. 1.55
155
1.55 = 100
= 155 ÷ 5
100 ÷ 5
31 or 1 11
=
20
20
Reading Math
You read the decimal 0.018 as “eighteen thousandths.”
2-6 Equivalent Fractions and Decimals
Practice 3
Write each decimal as a fraction in simplest
form.
C. 0.015
0.015 = 15
1,000
D. 1.30
130
1.30 =
100
= 15 ÷ 5
1,000 ÷ 5
= 130 ÷ 10
100 ÷ 10
= 3
200
3
13
or
1
=
10
10
2-6 Equivalent Fractions and Decimals
Example 4: Sports Application
A football player completed 1,546 of the 3,875
passes he attempted. Find his completion rate.
Write your answer as a decimal rounded to
the nearest thousandth.
Fraction
1,546
3,875
What the Calculator Shows
1546 ÷ 3875 ENTER 0.398967742
His completion rate is 0.399.
Completion Rate
0.399
2-6 Equivalent Fractions and Decimals
Practice 4
Johnny Unitas, a former professional
quarterback, completed 2,830 of the 5,186
passes he attempted. Find his completion rate.
Write your answer as a decimal rounded to the
nearest thousandth.
Fraction
2,830
5,186
What the Calculator Shows
2830 ÷ 5186 ENTER 0.54569996
His completion rate is 0.546.
Completion Rate
0.546
2-6 Equivalent Fractions and Decimals
Lesson
Quiz
2-6 Equivalent Fractions and Decimals
Write each fraction as a decimal.
1.
3.
16
5
7
10
21
2. 8
11
4. 20
Write each decimal as a fraction in simplest
form.
5. 0.42
6. 8.625
7. If your soccer team wins 21 out of 30 games,
what is your team’s winning rate?
2-6 Equivalent Fractions and Decimals
Lesson Quiz
ANSWERS
Write each fraction as a decimal.
1.
3.
16 3.2
5
7
10 0.7
21
2. 8 2.625
11
4. 20 0.55
Write each decimal as a fraction in simplest
form.
21
69 or 8 5
5. 0.42
6. 8.625
8
50
8
7. If your soccer team wins 21 out of 30 games,
what is your team’s winning rate? 0.70