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How to Divide an Integer by Fraction

February 16, 2024 by admin Category: How To

You are viewing the article How to Divide an Integer by Fraction  at Tnhelearning.edu.vn you can quickly access the necessary information in the table of contents of the article below.

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This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.

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This article has been viewed 43,920 times.

When you divide an integer by a fraction, you will find how many groups of fractions match that integer. The standard way to divide an integer by a fraction is to multiply the integer by the reciprocal of the given fraction. You can also draw diagrams to help you visualize the process.

Table of Contents

  • Steps
    • Multiply by the inverse
    • Draw map
    • Sample problem solving

Steps

Multiply by the inverse

Image titled Divide a Whipe Number With a Fraction Step 1

Image titled Divide a Whipe Number With a Fraction Step 1

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Convert integers to fractions. To do this, put the integer in the numerator position of the fraction. The denominator will be 1. [1] X Research Source

  • For example, if you calculate 7÷34{displaystyle 7div {frac {3}{4}}}{displaystyle 7div {frac {3}{4}}} , first you need to change 7{displaystyle 7}7 wall 7first{displaystyle {frac {7}{1}}}{displaystyle {frac {7}{1}}} .
Image titled Divide a Whipe Number With a Fraction Step 2

Image titled Divide a Whipe Number With a Fraction Step 2

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Find the reciprocal of the divisor. The reciprocal of a number is the number that is reversed. To find the reciprocal of a fraction, invert the numerator and denominator. [2] X Research Source

  • For example, the reciprocal of the fraction 34{displaystyle {frac {3}{4}}}{frac {3}{4}} To be 43{displaystyle {frac {4}{3}}}{displaystyle {frac {4}{3}}} .
Image titled Divide a Whipe Number With a Fraction Step 3

Image titled Divide a Whipe Number With a Fraction Step 3

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Multiply two fractions. To multiply fractions, first multiply the numerators together. Then multiply the denominators together. The product of two fractions is equal to the quotient of the original division. [3] X Research Sources

  • For example, 7first×43=283{displaystyle {frac {7}{1}}times {frac {4}{3}}={frac {28}{3}}}{displaystyle {frac {7}{1}}times {frac {4}{3}}={frac {28}{3}}}
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Image titled Divide a Whpe Number by a Fraction Step 4

Image titled Divide a Whpe Number by a Fraction Step 4

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Shorten if necessary. If you have a fraction greater than 1 (a fraction with a larger numerator than the denominator), your teacher may ask you to change it to a mixed number. Often your teacher will ask you to reduce fractions to a minimum.

  • For example,283{displaystyle {frac {28}{3}}}{displaystyle {frac {28}{3}}} shorten to mixed numbers9first3{displaystyle 9{frac {1}{3}}}{displaystyle 9{frac {1}{3}}} .

Draw map

Image titled Divide a Whipe Number With a Fraction Step 5

Image titled Divide a Whipe Number With a Fraction Step 5

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Draw an integer representation. The drawing must be a shape that can be divided into equal groups, such as a square or a circle. Draw the shapes large enough that you can divide them into smaller parts.

  • For example, if you have the calculation 5÷34{displaystyle 5div {frac {3}{4}}}{displaystyle 5div {frac {3}{4}}} , you need to draw 5 circles.
Image titled Divide a Whipe Number With a Fraction Step 6

Image titled Divide a Whipe Number With a Fraction Step 6

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Divide each figure by the denominator of the fraction. The denominator of a fraction tells you how many parts an integer is divided into. Divide the form into equal proportions. [4] X Research Sources

  • For example, if you do the math 34{displaystyle {frac {3}{4}}}{displaystyle {frac {3}{4}}} , the number 4 in the denominator indicates that the figure is divided into four parts.
Image titled Divide a Whipe Number With a Fraction Step 7

Image titled Divide a Whipe Number With a Fraction Step 7

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Color the group representing the sections. Since you’re converting integers to fractions, you want to know how many groups of fractions are in the integer. [5] X Research Resources So first you need to create groups. Coloring each group a different color will help, as some groups will have parts at two different integers. Do not color the rest.

  • For example, if you divide 5 by 34{displaystyle {frac {3}{4}}}{frac {3}{4}} , you will color 3/4 of each group a different color. Note that many groups can contain 2 quarters of one integer and 1 quarter of another.
Image titled Divide a Whipe Number With a Fraction Step 8

Image titled Divide a Whipe Number With a Fraction Step 8

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/6/6d/Divide-a-Whpe-Number-With-a-Fraction-Step-8.jpg/v4-728px-Divide- a-Whpe-Number-With-a-Fraction-Step-8.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/6/6d/Divide-a-Whpe-Number- With-a-Fraction-Step-8.jpg/v4-728px-Divide-a-Whpe-Number-With-a-Fraction-Step-8.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Count the number of groups of integers. This will help you know the integer part of the answer.

  • For example, you should create 6 groups 34{displaystyle {frac {3}{4}}}{displaystyle {frac {3}{4}}} out of 5 circles.
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Image titled Divide a Whpe Number With a Fraction Step 9

Image titled Divide a Whpe Number With a Fraction Step 9

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Explain the rest. Compare the number of remains with a complete group. The fraction of the group of remaining parts will indicate the fractional part of the answer. Make sure you don’t compare the number of parts with the whole figure as doing so will give incorrect fractions.

  • For example, after dividing 5 form groups 34{displaystyle {frac {3}{4}}}{displaystyle {frac {3}{4}}} , you have 2 quarters or 24{displaystyle {frac {2}{4}}}{displaystyle {frac {2}{4}}} remaining. Since the group has a total of 3 parts and you have 2 parts, your fraction is 23{displaystyle {frac {2}{3}}}{displaystyle {frac {2}{3}}} .
Image titled Divide a Whipe Number With a Fraction Step 10

Image titled Divide a Whipe Number With a Fraction Step 10

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/2/2e/Divide-a-Whpe-Number-With-a-Fraction-Step-10.jpg/v4-728px-Divide- a-Whpe-Number-With-a-Fraction-Step-10.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/2/2e/Divide-a-Whpe-Number- With-a-Fraction-Step-10.jpg/v4-728px-Divide-a-Whpe-Number-With-a-Fraction-Step-10.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Write the answer. Combine groups of integers with groups of fractions to find the quotient of the original division.

  • For example, 5÷34=623{displaystyle 5div {frac {3}{4}}=6{frac {2}{3}}}{displaystyle 5div {frac {3}{4}}=6{frac {2}{3}}} .

Sample problem solving

Image titled Divide a Whipe Number With a Fraction Step 11

Image titled Divide a Whipe Number With a Fraction Step 11

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/f/f2/Divide-a-Whpe-Number-With-a-Fraction-Step-11.jpg/v4-728px-Divide- a-Whpe-Number-With-a-Fraction-Step-11.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/f/f2/Divide-a-Whpe-Number- With-a-Fraction-Step-11.jpg/v4-728px-Divide-a-Whpe-Number-With-a-Fraction-Step-11.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Solve the following problem: Multiply first2{displaystyle {frac {1}{2}}}{frac {1}{2}} with how much to get 8{displaystyle 8}{displaystyle 8} ?

  • Because the problem asks how many groups first2{displaystyle {frac {1}{2}}}{frac {1}{2}} in 8, the problem is division.
  • Convert 8 to a fraction with a denominator of 1: 8=8first{displaystyle 8={frac {8}{1}}}{displaystyle 8={frac {8}{1}}} .
  • Find the reciprocal of a fraction by reversing the numerator and denominator: first2{displaystyle {frac {1}{2}}}{frac {1}{2}} wall 2first{displaystyle {frac {2}{1}}}{displaystyle {frac {2}{1}}} .
  • Multiply two fractions together: 8first×2first=16first{displaystyle {frac {8}{1}}times {frac {2}{1}}={frac {16}{1}}}{displaystyle {frac {8}{1}}times {frac {2}{1}}={frac {16}{1}}} .
  • Shorten if needed: 16first=16{displaystyle {frac {16}{1}}=16}{displaystyle {frac {16}{1}}=16} .
Image titled Divide a Whipe Number With a Fraction Step 12

Image titled Divide a Whipe Number With a Fraction Step 12

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/0/08/Divide-a-Whpe-Number-With-a-Fraction-Step-12.jpg/v4-728px-Divide- a-Whpe-Number-With-a-Fraction-Step-12.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/0/08/Divide-a-Whpe-Number- With-a-Fraction-Step-12.jpg/v4-728px-Divide-a-Whpe-Number-With-a-Fraction-Step-12.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Solve the following problem: 16÷58{displaystyle 16div {frac {5}{8}}}{displaystyle 16div {frac {5}{8}}} .

  • Convert 16 to a fraction with a denominator of 1: 16=16first{displaystyle 16={frac {16}{1}}}{displaystyle 16={frac {16}{1}}} .
  • Find the reciprocal of a fraction by reversing the numerator and denominator: 58{displaystyle {frac {5}{8}}}{displaystyle {frac {5}{8}}} wall 85{displaystyle {frac {8}{5}}}{displaystyle {frac {8}{5}}} .
  • Multiply two fractions together: 16first×85=1285{displaystyle {frac {16}{1}}times {frac {8}{5}}={frac {128}{5}}}{displaystyle {frac {16}{1}}times {frac {8}{5}}={frac {128}{5}}} .
  • Shorten if needed: 1285=2535{displaystyle {frac {128}{5}}=25{frac {3}{5}}}{displaystyle {frac {128}{5}}=25{frac {3}{5}}} .
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  • Image titled Divide a Whipe Number With a Fraction Step 13

    Image titled Divide a Whipe Number With a Fraction Step 13

    {“smallUrl”:”https://www.wikihow.com/images_en/thumb/6/6f/Divide-a-Whpe-Number-With-a-Fraction-Step-13.jpg/v4-728px-Divide- a-Whpe-Number-With-a-Fraction-Step-13.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/6/6f/Divide-a-Whpe-Number- With-a-Fraction-Step-13.jpg/v4-728px-Divide-a-Whpe-Number-With-a-Fraction-Step-13.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
    Solve the following problem by drawing a diagram. Rufus has 9 boxes of food. Every day, she eats it all 23{displaystyle {frac {2}{3}}}{displaystyle {frac {2}{3}}} box. How many days can the food last?

    • Draw 9 circles representing 9 food boxes.
    • Because every time she eats it all 23{displaystyle {frac {2}{3}}}{displaystyle {frac {2}{3}}} box, divide the circle into three parts.
    • Color the group of fractions 23{displaystyle {frac {2}{3}}}{displaystyle {frac {2}{3}}} .
    • Counting the number of groups that have been shaded, we get 13.
    • Explain the rest. There is 1 remaining part, which is first3{displaystyle {frac {1}{3}}}{frac {1}{3}} . Because the group is 23{displaystyle {frac {2}{3}}}{displaystyle {frac {2}{3}}} , you have half of the group left. So the fraction will be first2{displaystyle {frac {1}{2}}}{frac {1}{2}} .
    • Calculating the sum of groups of integers and groups of fractions, we have the answer: 9÷23=13first2{displaystyle 9div {frac {2}{3}}=13{frac {1}{2}}}{displaystyle 9div {frac {2}{3}}=13{frac {1}{2}}} .
  • X

    This article is co-authored by a team of editors and trained researchers who confirm the accuracy and completeness of the article.

    The wikiHow Content Management team carefully monitors the work of editors to ensure that every article is up to a high standard of quality.

    This article has been viewed 43,920 times.

    When you divide an integer by a fraction, you will find how many groups of fractions match that integer. The standard way to divide an integer by a fraction is to multiply the integer by the reciprocal of the given fraction. You can also draw diagrams to help you visualize the process.

    Thank you for reading this post How to Divide an Integer by Fraction at Tnhelearning.edu.vn You can comment, see more related articles below and hope to help you with interesting information.

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