Transcript Fractions and Decimals - Gateway School District

COURSE 3 LESSON 4-2
Equivalent Forms of Rational Numbers
Write a fraction in lowest terms, with a single digit numerator, that is about
the same as each decimal: 0.52, 0.13, 0.74, 0.88.
1 1 3 7
2 , 8 , 4, 8
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COURSE 2 LESSON 3-9
Fractions and Decimals
The total amount of rainfall yesterday was reported as 1 in.
4
Express the amount of rainfall as a decimal.
Method 2 Calculator
Method 1 Paper and Pencil
0.25
1
or 1 ÷ 4 = 4 1.00
4
–8
20
–20
0
quotient
1
The remainder
is 0.
1
So, 4 = 0.25. The total amount of rainfall was 0.25 in.
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4
0.25
COURSE 2 LESSON 3-9
Fractions and Decimals
Write
7
as a decimal.
15
Method 1 Paper and Pencil
0.4666
7
or 7 ÷ 15 = 15 7.0000
15
–60
100
–90
100
–90
10
Method 2 Calculator
The digit “6”
repeats.
There will always
be a remainder.
7
So, 15 = 0.46.
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7
15
0.46666667
COURSE 3 LESSON 4-2
Equivalent Forms of Rational Numbers
Write 3.225 as a mixed number.
3.225 =
3.225
1
Write as a fraction with the denominator 1.
Since there are 3 digits to the right of the
decimal, multiply the numerator and
denominator by 103 or 1,000.
3,225
= 1,000
3,225 ÷ 25
129
= 1,000 ÷ 25 = 40
9
= 3 40
Simplify using the GCF, 25.
Write as a mixed number.
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COURSE 2 LESSON 3-9
Fractions and Decimals
Write 4.105 as a fraction in simplest form.
105
105
Since 0.105 = 1,000 , 4.105 = 4 1,000 .
105
105 ÷ 5
4 1,000 = 4 1,000 ÷ 5
Use the GCF to write the
fraction in simplest form.
21
= 4 200
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COURSE 2 LESSON 3-9
Fractions and Decimals
In a survey of next year’s seventh-grade students, 0.25 said
they will come to school by bus, 5 said they will walk, 0.375 said
24
1
they will come in a car, and
said they will ride their bicycles. Order
16
the means of transportation from most used to least used.
walk
5
24
= 0.2083
bicycles
1
16
= 0.0625
Use a calculator to change the
fractions to decimals.
Since 0.375 > 0.25 > 0.2083 > 0.0625, the means of transportation are
car, bus, walking, and bicycle.
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COURSE 3 LESSON 4-2
Equivalent Forms of Rational Numbers
Write the repeating decimal 0.23 as a fraction in
simplest form.
Step 1 Let the variable n represent the given decimal.
n = 0.23
Step 2 Since 2 digits repeat, multiply each side by 102, or 100.
100n = 23.23
Step 3 Subtract to eliminate the repeating part, 0.23.
100n = 23.232323 . . .
– n = – 0.232323 . . .
Use the Subtraction Property of Equality.
99n = 23.000000
Simplify.
99n = 23
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COURSE 3 LESSON 4-2
Equivalent Forms of Rational Numbers
(continued)
Step 4 Solve the new equation.
99n
23
=
99
99
23
n = 99
Divide each side by 99.
Simplify.
The repeating decimal 0.23 equals
23
.
99
Check Use a calculator to divide 23 by 99.
23
99
0.23232323
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COURSE 2 LESSON 3-9
Fractions and Decimals
Write each fraction as a decimal.
1. 7
0.875
2. 4
3. 3
0.6
4.
8
5
9
5
16
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0.4
0.3125
COURSE 3 LESSON 4-2
Equivalent Forms of Rational Numbers
Write each as a fraction in simplest form.
1. 30
42
5
7
2. – 12
18
3. 2.75
–2
23
3
4. 0.2
5. 0.4
2
9
2
5
4
6. 7.25
7 25
99
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