Class Notes: Converting Improper Fractions to Decimals Using Long Division

Objective

Learn how to convert an improper fraction into a decimal using long division.

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Key Concepts

• Improper Fraction: A fraction where the numerator is greater than or equal to the denominator.
• Long Division: The process used to divide the numerator by the denominator to convert the fraction to a decimal.

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Steps to Convert an Improper Fraction to a Decimal

1. Set Up Long Division

   • The denominator (bottom number) is the divisor (goes outside).
   • The numerator (top number) is the dividend (goes inside).

2. Divide as Usual

   • Divide the numerator by the denominator.
   • If the numerator is not divisible, bring down zeros and add a decimal point.

3. Continue Division

   • Keep dividing and bringing down zeros until the remainder is zero or you reach the desired decimal places.

4. Result

   • The final quotient is the decimal equivalent of the improper fraction.

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Example 1: ( \frac{6}{5} )

1. Set up: 5 (divisor), 6 (dividend).
2. 5 goes into 6 once (1). ( 5 \times 1 = 5 ), remainder ( 6 - 5 = 1 ).
3. Add decimal and zero: 5 into 10 is 2 (( 5 \times 2 = 10 )), remainder ( 10 - 10 = 0 ).
4. Quotient/Decimal: 1.2

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Example 2: ( \frac{7}{4} )

1. Set up: 4 (divisor), 7 (dividend).
2. 4 goes into 7 once (1). ( 4 \times 1 = 4 ), remainder ( 7 - 4 = 3 ).
3. Add decimal and zero: 4 into 30 is 7 (( 4 \times 7 = 28 )), remainder ( 30 - 28 = 2 ).
4. Bring down another zero: 4 into 20 is 5 (( 4 \times 5 = 20 )), remainder ( 20 - 20 = 0 ).
5. Quotient/Decimal: 1.75

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Example 3: ( \frac{21}{8} )

1. Set up: 8 (divisor), 21 (dividend).
2. 8 goes into 21 twice (2). ( 8 \times 2 = 16 ), remainder ( 21 - 16 = 5 ).
3. Add decimal and zero: 8 into 50 is 6 (( 8 \times 6 = 48 )), remainder ( 50 - 48 = 2 ).
4. Bring down another zero: 8 into 20 is 2 (( 8 \times 2 = 16 )), remainder ( 20 - 16 = 4 ).
5. Bring down another zero: 8 into 40 is 5 (( 8 \times 5 = 40 )), remainder ( 40 - 40 = 0 ).
6. Quotient/Decimal: 2.625

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Summary

• Converting improper fractions to decimals involves dividing the numerator by the denominator using long division.
• Add decimal points and zeros as needed to continue the process until the division ends with a remainder of zero (or desired decimal places).
• The quotient you find is the decimal form of the improper fraction.

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Practice

Try converting the following improper fractions to decimals using long division:

• ( \frac{11}{3} )
• ( \frac{17}{6} )
• ( \frac{45}{7} )