Transcript 2-10

2-10 Equivalent Fractions and Decimals
Warm Up
Write each fraction in the simplest form.
1.
4
8
1
2
2. 6
9
3.
12
48
1
4
4.
5
25
2
3
1
5
2-10 Equivalent Fractions and Decimals
Simplest Form (Fractions)
• A fraction is in simplest form when the top and
bottom cannot be any smaller (while still being
whole numbers).
Example: 2/4 can be simplified to 1/2
To simplify a fraction, divide the top and bottom
by the highest number that can divide into both
numbers exactly.
2-10 Equivalent Fractions and Decimals
Rational Number
• A rational number is a number that can
be written as a fraction with integers as
the numerator and denominator.
• This includes fractions, regular
counting numbers, negative
numbers, terminating
decimals and repeating decimals.
2-10 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.
2-10 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.
2-10 Equivalent Fractions and Decimals
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 .6 6 6
3 5.000
–3
20
– 18
20
– 18
5
20 3 ≈ 1.67
– 18
2
2-10 Equivalent Fractions and Decimals
Check It Out: Example 1
Write each fraction as a decimal. Round to the
nearest hundredth, if necessary.
3
A. 4
0.7 5
4 3.00
–28
20
– 20
0
3 = 0.75
4
6
B. 5
1.2
5 6.0
–5
10
– 10
0
6 = 1.2
5
7
C. 3
2 .3 3 3
3 7.000
–6
10
–9
10
–9
7
10 3 ≈ 2.33
–9
1
2-10 Equivalent Fractions and Decimals
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.
2-10 Equivalent Fractions and Decimals
Check It Out: Example 2
Write each fraction as a decimal.
3
A. 5
3x2 = 6
5 2
10
18
B. 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.
2-10 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
2-10 Equivalent Fractions and Decimals
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.”
2-10 Equivalent Fractions and Decimals
Check It Out: Example 3
Write each decimal as a fraction in simplest
form.
A. 0.015
0.015 = 15
1,000
B. 1.30
130
1.30 =
100
= 15 ÷ 5
1,000 ÷ 5
= 130 ÷ 10
100 ÷ 10
= 3
200
3
13
or
1
=
10
10
2-10 Equivalent Fractions and Decimals
Lesson Quiz
Write each fraction as a decimal.
1.
3.
16
5
7
10
3.2
0.7
21
2. 8
11
4. 20
2.625
0.55
Write each decimal as a fraction in simplest
form.
5. 0.42 21
6. 8.625 69 or 8 5
8
50
8
7. If your soccer team wins 21 out of 30 games,
what is your team’s winning rate? 0.70
2-10 Equivalent Fractions and Decimals
Lesson Quiz for Student Response Systems
1. Which of the following represents the
fraction 18 as a decimal?
5
A. 3.4
B. 3.5
C. 3.6
D. 3.7
2-10 Equivalent Fractions and Decimals
Lesson Quiz for Student Response Systems
2. Which of the following represents the
fraction 13 as a decimal?
20
A. 0.65
B. 0.75
C. 0.85
D. 0.95
2-10 Equivalent Fractions and Decimals
Lesson Quiz for Student Response Systems
3. Which of the following represents the
decimal 0.32 as a fraction in simplest
form?
A. 8
C. 6
25
25
B. 7
25
D. 1
5
2-10 Equivalent Fractions and Decimals
Lesson Quiz for Student Response Systems
4. Which of the following represents the
decimal 6.125 as a fraction in simplest
form?
A. 49 or 8 1
C. 37 or 6 1
6
6
6
6
B. 49 or 61
8
8
D. 31 or 6 1
5
5
2-10 Equivalent Fractions and Decimals
Lesson Quiz for Student Response Systems
5. If Rita scores 34 out of 50 in a class test,
what is Rita’s scoring rate?
A. 0.65
B. 0.66
C. 0.67
D. 0.68