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学習ガイド > Prealgebra

Converting Between Improper Fractions and Mixed Numbers

Learning Outcomes

  • Convert mixed numbers to improper fractions
  • Convert improper fractions to mixed numbers
In an earlier example, we converted the improper fraction 116\frac{11}{6} to the mixed number 1561\frac{5}{6} using fraction circles. We did this by grouping six sixths together to make a whole; then we looked to see how many of the 1111 pieces were left. We saw that 116\frac{11}{6} made one whole group of six sixths plus five more sixths, showing that 116=156\frac{11}{6}=1\frac{5}{6}. The division expression 116\frac{11}{6} (which can also be written as 6)11‾6\overline{)11} ) tells us to find how many groups of 66 are in 1111. To convert an improper fraction to a mixed number without fraction circles, we divide.

Example

Convert 116\frac{11}{6} to a mixed number. Solution:
116\frac{11}{6}
Divide the denominator into the numerator. Remember 116\frac{11}{6} means 11÷611\div 6 .
.
Identify the quotient, remainder and divisor.
Write the mixed number as quotientremainderdivisor\text{quotient}\frac{\text{remainder}}{\text{divisor}} . 1561\frac{5}{6}
So, 116=156\frac{11}{6}=1\frac{5}{6}
 

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  #145979 [ohm_question]145979[/ohm_question]
 

Convert an improper fraction to a mixed number.

  1. Divide the denominator into the numerator.
  2. Identify the quotient, remainder, and divisor.
  3. Write the mixed number as quotient remainderdivisor\frac{\text{remainder}}{\text{divisor}} .

Example

Convert the improper fraction 338\frac{33}{8} to a mixed number.

Answer: Solution:

338\frac{33}{8}
Divide the denominator into the numerator. Remember, 338\frac{33}{8} means 8)33‾8\overline{)33} .
Identify the quotient, remainder, and divisor. .
Write the mixed number as quotient remainderdivisor\frac{\text{remainder}}{\text{divisor}} . 4184\frac{1}{8}
So, 338=418\frac{33}{8}=4\frac{1}{8}

 

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  #145979 [ohm_question height="270"]145979[/ohm_question]
Now you can watch worked examples of how to convert an improper fraction to a mixed number in the following video. https://youtu.be/e6uoYVg5Q30 In an earlier example, we changed 1451\frac{4}{5} to an improper fraction by first seeing that the whole is a set of five fifths. So we had five fifths and four more fifths. 55+45=95\frac{5}{5}+\frac{4}{5}=\frac{9}{5} Where did the nine come from? There are nine fifths—one whole (five fifths) plus four fifths. Let us use this idea to see how to convert a mixed number to an improper fraction.

Example

Convert the mixed number 4234\frac{2}{3} to an improper fraction.

Answer: Solution:

4234\frac{2}{3}
Multiply the whole number by the denominator.
The whole number is 4 and the denominator is 3. .
Simplify. .
Add the numerator to the product.
The numerator of the mixed number is 2. .
Simplify. .
Write the final sum over the original denominator.
The denominator is 3. 143\frac{14}{3}

 

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  #145980 [ohm_question height="270"]145980[/ohm_question]
 

Convert a mixed number to an improper fraction.

  1. Multiply the whole number by the denominator.
  2. Add the numerator to the product found in Step 1.
  3. Write the final sum over the original denominator.

Example

Convert the mixed number 102710\frac{2}{7} to an improper fraction.

Answer: Solution:

102710\frac{2}{7}
Multiply the whole number by the denominator.
The whole number is 10 and the denominator is 7. .
Simplify. .
Add the numerator to the product.
The numerator of the mixed number is 2. .
Simplify. .
Write the final sum over the original denominator.
The denominator is 7. 727\frac{72}{7}

 

Try it

  #145980 [ohm_question height="270"]145980[/ohm_question]
In the following video we show more example of how to convert a mixed number to an improper fraction. https://youtu.be/p_YRBcZ4u4g

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