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How to Subtract integers from fractions

February 17, 2024 by admin Category: How To

You are viewing the article How to Subtract integers from fractions  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 was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

This article has been viewed 55,025 times.

The calculation of whole numbers minus fractions is not as difficult as you think. There are two main methods of doing this: either you convert the integer to a fraction, or subtract the integer by 1 and convert the 1 to a fraction with the same denominator as the fraction you are subtracting. After you have two fractions with the same denominator, you can start subtracting. Both ways will help you to subtract integers from fractions faster and easier.

Table of Contents

  • Steps
    • Subtract an integer from a fraction
    • Other methods
  • Things you need

Steps

Subtract an integer from a fraction

Image titled Subtract Fractions from Whpe Numbers Step 1

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Image titled Subtract Fractions from Whpe Numbers Step 1

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/4/48/Subtract-Fractions-from-Whpe-Numbers-Step-1-Version-3.jpg/v4-728px-Subtract- Fractions-from-Whpe-Numbers-Step-1-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/4/48/Subtract-Fractions-from-Whpe- Numbers-Step-1-Version-3.jpg/v4-728px-Subtract-Fractions-from-Whpe-Numbers-Step-1-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Convert integers to fractions. Add 1 as the denominator of the integer.

  • For example: 8−45{displaystyle 8-{frac {4}{5}}}8-{frac {4}{5}}
  • =8first−45{displaystyle ={frac {8}{1}}-{frac {4}{5}}}={frac {8}{1}}-{frac {4}{5}}
Image titled Subtract Fractions from Whpe Numbers Step 2

Image titled Subtract Fractions from Whpe Numbers Step 2

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/6/6a/Subtract-Fractions-from-Whpe-Numbers-Step-2-Version-3.jpg/v4-728px-Subtract- Fractions-from-Whpe-Numbers-Step-2-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/6/6a/Subtract-Fractions-from-Whpe- Numbers-Step-2-Version-3.jpg/v4-728px-Subtract-Fractions-from-Whpe-Numbers-Step-2-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Set the denominator. The denominator of the original fraction is also the greatest common denominator of the two fractions. Multiply the numerator and denominator of the “fractional integer” by this number to reduce the two fractions’ denominator.

  • 8first−45{displaystyle {frac {8}{1}}-{frac {4}{5}}}{frac {8}{1}}-{frac {4}{5}}
  • =8∗5first∗5−45{displaystyle ={frac {8*5}{1*5}}-{frac {4}{5}}}={frac {8*5}{1*5}}-{frac {4}{5}}
  • =405−45{displaystyle ={frac {40}{5}}-{frac {4}{5}}}={frac {40}{5}}-{frac {4}{5}}
Image titled Subtract Fractions from Whpe Numbers Step 3

Image titled Subtract Fractions from Whpe Numbers Step 3

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/1/18/Subtract-Fractions-from-Whpe-Numbers-Step-3-Version-3.jpg/v4-728px-Subtract- Fractions-from-Whpe-Numbers-Step-3-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/1/18/Subtract-Fractions-from-Whpe- Numbers-Step-3-Version-3.jpg/v4-728px-Subtract-Fractions-from-Whpe-Numbers-Step-3-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Subtract the numerator from each other. Now that the two fractions have the same denominator, you can do the same as normal subtraction:

  • 405−45{displaystyle {frac {40}{5}}-{frac {4}{5}}}{frac {40}{5}}-{frac {4}{5}}
  • =40−45{displaystyle ={frac {40-4}{5}}}={frac {40-4}{5}}
  • =365{displaystyle {frac {36}{5}}}{frac {36}{5}}
Image titled Subtract Fractions from Whpe Numbers Step 4

Image titled Subtract Fractions from Whpe Numbers Step 4

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/7/78/Subtract-Fractions-from-Whpe-Numbers-Step-4-Version-3.jpg/v4-728px-Subtract- Fractions-from-Whpe-Numbers-Step-4-Version-3.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/7/78/Subtract-Fractions-from-Whpe- Numbers-Step-4-Version-3.jpg/v4-728px-Subtract-Fractions-from-Whpe-Numbers-Step-4-Version-3.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Convert the result to a mixed number (optional). If the answer is a real fraction, you can rewrite it as a mixed number:

  • Example: Write365{displaystyle {frac {36}{5}}}{frac {36}{5}} into a mixed number.
  • How many times 5 is close to 36? 5 x 7 = 35, so the integer part will be 7 .
  • What about the rest? The integer part is equivalent to355{displaystyle {frac {35}{5}}}{frac {35}{5}} , So365{displaystyle {frac {36}{5}}}{frac {36}{5}} –355{displaystyle {frac {35}{5}}}{frac {35}{5}} = first5{displaystyle {frac {1}{5}}}{frac {1}{5}}
  • Combining integers and fractions, we get:365{displaystyle {frac {36}{5}}}{frac {36}{5}} =7first5{displaystyle 7{frac {1}{5}}}7{frac {1}{5}}

Other methods

Image titled Subtract Fractions from Whpe Numbers Step 5

Image titled Subtract Fractions from Whpe Numbers Step 5

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Apply this to large integers. As you can see, in the above method, we convert the integer to a fraction, then convert the answer back to a mixed number at the end of the lesson. This method will omit some steps so that the fraction includes only small numbers.
Image titled Subtract Fractions from Whpe Numbers Step 6

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Image titled Subtract Fractions from Whpe Numbers Step 6

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/4/4d/Subtract-Fractions-from-Whpe-Numbers-Step-6-Version-2.jpg/v4-728px-Subtract- Fractions-from-Whpe-Numbers-Step-6-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/4/4d/Subtract-Fractions-from-Whpe- Numbers-Step-6-Version-2.jpg/v4-728px-Subtract-Fractions-from-Whpe-Numbers-Step-6-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Convert non-true fractions to mixed numbers. Skip this step if your fraction is a real fraction. (The fraction doesn’t actually have a larger numerator than the denominator.)

  • For example: 11−43{displaystyle 11-{frac {4}{3}}}11-{frac {4}{3}}
  • =11−firstfirst3{displaystyle =11-1{frac {1}{3}}}=11-1{frac {1}{3}}
  • =ten−first3{displaystyle =10-{frac {1}{3}}}=10-{frac {1}{3}}
Image titled Subtract Fractions from Whpe Numbers Step 7

Image titled Subtract Fractions from Whpe Numbers Step 7

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/2/28/Subtract-Fractions-from-Whpe-Numbers-Step-7-Version-2.jpg/v4-728px-Subtract- Fractions-from-Whpe-Numbers-Step-7-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/2/28/Subtract-Fractions-from-Whpe- Numbers-Step-7-Version-2.jpg/v4-728px-Subtract-Fractions-from-Whpe-Numbers-Step-7-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Split integer into 1 and another integer. For example, rewrite 5 as 4 + 1, or 22 as 21 + 1.

  • ten−first3{displaystyle 10-{frac {1}{3}}}10-{frac {1}{3}}
  • =9+first−first3{displaystyle =9+1-{frac {1}{3}}}=9+1-{frac {1}{3}}
Image titled Subtract Fractions from Whpe Numbers Step 8

Image titled Subtract Fractions from Whpe Numbers Step 8

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/d/d3/Subtract-Fractions-from-Whpe-Numbers-Step-8-Version-2.jpg/v4-728px-Subtract- Fractions-from-Whpe-Numbers-Step-8-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/d/d3/Subtract-Fractions-from-Whpe- Numbers-Step-8-Version-2.jpg/v4-728px-Subtract-Fractions-from-Whpe-Numbers-Step-8-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Convert 1 to a fraction. In this step, we use the above method to solve the rest of the problem in the “1 – (fraction)” direction. Other integers will be kept until the end of the post.

  • =9+first−first3{displaystyle =9+1-{frac {1}{3}}}=9+1-{frac {1}{3}}
  • =9+firstfirst−first3{displaystyle =9+{frac {1}{1}}-{frac {1}{3}}}=9+{frac {1}{1}}-{frac {1}{3}}
Image titled Subtract Fractions from Whpe Numbers Step 9

Image titled Subtract Fractions from Whpe Numbers Step 9

{“smallUrl”:”https://www.wikihow.com/images_en/thumb/f/f4/Subtract-Fractions-from-Whpe-Numbers-Step-9-Version-2.jpg/v4-728px-Subtract- Fractions-from-Whpe-Numbers-Step-9-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/f/f4/Subtract-Fractions-from-Whpe- Numbers-Step-9-Version-2.jpg/v4-728px-Subtract-Fractions-from-Whpe-Numbers-Step-9-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
Perform multiplication to reduce the denominator. As mentioned, we multiply the numerator and denominator of the new fraction by the denominator of the original fraction to reduce the denominator.

  • =9+first∗3first∗3−first3{displaystyle =9+{frac {1*3}{1*3}}-{frac {1}{3}}}=9+{frac {1*3}{1*3}}-{frac {1}{3}}
  • =9+33−first3{displaystyle =9+{frac {3}{3}}-{frac {1}{3}}}=9+{frac {3}{3}}-{frac {1}{3}}
  • Image titled Subtract Fractions from Whpe Numbers Step 10

    Image titled Subtract Fractions from Whpe Numbers Step 10

    {“smallUrl”:”https://www.wikihow.com/images_en/thumb/b/bb/Subtract-Fractions-from-Whpe-Numbers-Step-10-Version-2.jpg/v4-728px-Subtract- Fractions-from-Whpe-Numbers-Step-10-Version-2.jpg”,”bigUrl”:”https://www.wikihow.com/images/thumb/b/bb/Subtract-Fractions-from-Whpe- Numbers-Step-10-Version-2.jpg/v4-728px-Subtract-Fractions-from-Whpe-Numbers-Step-10-Version-2.jpg”,”smallWidth”:460,”smallHeight”:345,” bigWidth”:728,”bigHeight”:546,”licensing”:”<div class=”mw-parser-output”></div>”}
    Add two fractions. Perform the subtraction at the numerator of the fractional part of the expression.

    • =9+3−first3{displaystyle =9+{frac {3-1}{3}}}=9+{frac {3-1}{3}}
    • =9+23{displaystyle =9+{frac {2}{3}}}=9+{frac {2}{3}}
    • =923{displaystyle =9{frac {2}{3}}}=9{frac {2}{3}}
  • Things you need

    • Pencil
    • Paper
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    This article was co-written by David Jia. David Jia is a tutoring teacher and founder of LA Math Tutoring, a private tutoring facility based in Los Angeles, California. With over 10 years of teaching experience, David teaches a wide variety of subjects to students of all ages and grades, as well as college admissions counseling and prep for SAT, ACT, ISEE, etc. scoring 800 in math and 690 in English on the SAT, David was awarded a Dickinson Scholarship to the University of Miami, where he graduated with a bachelor’s degree in business administration. Additionally, David has worked as an instructor in online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math.

    READ More:   How to Get in a Good Mood

    This article has been viewed 55,025 times.

    The calculation of whole numbers minus fractions is not as difficult as you think. There are two main methods of doing this: either you convert the integer to a fraction, or subtract the integer by 1 and convert the 1 to a fraction with the same denominator as the fraction you are subtracting. After you have two fractions with the same denominator, you can start subtracting. Both ways will help you to subtract integers from fractions faster and easier.

    Thank you for reading this post How to Subtract integers from fractions at Tnhelearning.edu.vn You can comment, see more related articles below and hope to help you with interesting information.

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