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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.
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A mixed number is a combination of an integer and a fraction. We can divide two mixed numbers together, however, you need to convert them to non-conforming fractions first. After the mixed number is converted, you can do division as you would with fractions.
Steps
Convert mixed numbers to improper fractions
- Example: calculate 6first2÷2first4{displaystyle 6{frac {1}{2}}div 2{frac {1}{4}}} . First you need to get 6×2=twelfth{displaystyle 6times 2=12} and 2×4=8{displaystyle 2times 4=8} .
- Continuing the example, we have twelfth+first=13{displaystyle 12+1=13} and 8+first=9{displaystyle 8+1=9} .
- In the example above,6first2{displaystyle 6{frac {1}{2}}} will become132{displaystyle {frac {13}{2}}} and2first4{displaystyle 2{frac {1}{4}}} converted to 94{displaystyle {frac {9}{4}}} .
- For example: 3=3first{displaystyle 3={frac {3}{1}}} .
Divide fractions that don’t fit
- The problem will become: 132÷94{displaystyle {frac {13}{2}}div {frac {9}{4}}} .
- In the above example, the inverse of 94{displaystyle {frac {9}{4}}} To be 49{displaystyle {frac {4}{9}}} . So, 132÷94{displaystyle {frac {13}{2}}div {frac {9}{4}}} will become 132×49{displaystyle {frac {13}{2}}times {frac {4}{9}}}
- Continuing the example, to calculate 132×49{displaystyle {frac {13}{2}}times {frac {4}{9}}} , you need to multiply the numerators: 13×4=52{displaystyle 13times 4=52} .
- In the above example, to calculate 132×49{displaystyle {frac {13}{2}}times {frac {4}{9}}} Then you need to multiply the two denominators: 2×9=18{displaystyle 2times 9=18} . Then combine the numerator and denominator to get the result: 5218{displaystyle {frac {52}{18}}} .
- In the example, we see 52{displaystyle 52} and 18{displaystyle 18} are divisible by 2{displaystyle 2} .
52÷2=26{displaystyle 52div 2=26}
18÷2=9{displaystyle 18div 2=9}
So, 5218=269{displaystyle {frac {52}{18}}={frac {26}{9}}}
Convert the wrong fraction to a mixed number
- Continuing the example in the previous section: we have 26÷9=2{displaystyle 26div 9=2} residual 8{displaystyle 8} . Therefore, the integer of this mixed number will be 2.
- For example, if the denominator of the original fraction is 9{displaystyle 9} and the balance is 8{displaystyle 8} , the fraction in the mixed number will be 89{displaystyle {frac {8}{9}}} .
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.
There are 8 references cited in this article that you can see at the bottom of the page.
This article has been viewed 3,418 times.
A mixed number is a combination of an integer and a fraction. We can divide two mixed numbers together, however, you need to convert them to non-conforming fractions first. After the mixed number is converted, you can do division as you would with fractions.
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