1. Equivalent Forms of Rational Numbers
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 2
, , , 8 3 4 7
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2. Equivalent Forms of Rational Numbers
COURSE 3 LESSON 4-2
Equivalent Forms of Rational Numbers
Write as a mixed number.
3.225 =
Write as a fraction with the denominator 1.
3.225 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
Simplify using the GCF, 25. =
3,225 ÷ 25
1,000 ÷ 25
129 40
Write as a mixed number.
= 3 9 40
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3. Equivalent Forms of Rational Numbers
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
100n =
– n = –
99n =
99n = 23
Use the Subtraction Property of Equality.
Simplify.
Step 3 Subtract to eliminate the repeating part, 0.23.
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4. Equivalent Forms of Rational Numbers
COURSE 3 LESSON 4-2
Equivalent Forms of Rational Numbers
(continued)
Step 4 Solve the new equation.
Divide each side by 99.
99n 99 23 =
Simplify.
n = 23 99
The repeating decimal 0.23 equals 23 99
Check Use a calculator to divide 23 by 99.
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5. Equivalent Forms of Rational Numbers
COURSE 3 LESSON 4-2
Equivalent Forms of Rational Numbers
Write each as a fraction in simplest form.
1. 2. – 30 42 12 18 5 7 2 3 – 3 4 2 2 9 2 5 25 99 7
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