How to Multiply Fractions by Integers: 9 Steps

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How to Multiply Fractions by Integers: 9 Steps
How to Multiply Fractions by Integers: 9 Steps
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Multiplying fractions by mixed fractions or whole numbers is pretty easy. To start with, turn mixed fractions or whole numbers into improper fractions and multiply the numerators of both. Finally, multiply the denominators and simplify the result.

Steps

Method 1 of 2: Multiplying mixed fractions by mixed fractions

Multiply Fractions With Whole Numbers Step 1

Step 1. Convert fractions to inappropriate fractions

To transform one of the mixed fractions, multiply the denominator by the integer. Then add the numerator, place the result on the line and leave the denominator as it is. Repeat this procedure with the other mixed fraction.

  • For example, if you start with 112×447{displaystyle 1{frac {1}{2}}\times 4{frac {4}{7}}}

    , transforme-as em frações impróprias. 112{displaystyle 1{frac {1}{2}}}

    se transformará em 32{displaystyle {frac {3}{2}}}

    e 447{displaystyle 4{frac {4}{7}}}

    se transformará em 327{displaystyle {frac {32}{7}}}

    . A equação, nesse ponto, será 32×327{displaystyle {frac {3}{2}}\times {frac {32}{7}}}

Multiply Fractions With Whole Numbers Step 2

Step 2. Multiply the numerators of improper fractions

Now that you have two improper fractions and no whole numbers in the equation, multiply the numerators together, write the result, and place a line below it.

  • The numerator is always the top value in a fraction.
  • In 32×327{displaystyle {frac {3}{2}}\times {frac {32}{7}}}

    , por exemplo, multiplique 3{displaystyle 3}

    por 32{displaystyle 32}

    para obter 96{displaystyle 96}

Multiply Fractions With Whole Numbers Step 3

Step 3. Multiply the denominators of the improper fractions

Multiply the numbers below the line and write the result under the numerator.

  • In 32×327{displaystyle {frac {3}{2}}\times {frac {32}{7}}}

    , por exemplo, multiplique 2{displaystyle 2}

    por 7{displaystyle 7}

    para obter 14{displaystyle 14}

Multiply Fractions With Whole Numbers Step 4

Step 4. If possible, turn the answer into a mixed fraction

If the numerator of the result is greater than the denominator, see how many times the denominator fits into the numerator. Then place the rest over the denominator to get a mixed fraction.

  • If you are working with 9614{displaystyle {frac {96}{14}}}

    , por exemplo, analise quantas vezes 14{displaystyle 14}

    pode estar contido em 96{displaystyle 96}

    . Nesse caso, o resultado será 6{displaystyle 6}

    com um resto igual a 12{displaystyle 12}

    . Coloque 12{displaystyle 12}

    sobre o denominador (14{displaystyle 14}

    ).

  • A maioria dos professores pedirá a você que coloque a resposta no mesmo formato da questão. Se havia frações mistas no início, converta a resposta para uma fração mista.
Multiply Fractions With Whole Numbers Step 5

Step 5. If possible, simplify further

You will likely end up with an integer and a fraction. Analyze now if it is possible to simplify it. In the case of 61214{displaystyle 6{frac {12}{14}}}

, por exemplo, divida 1214{displaystyle {frac {12}{14}}}

por 2{displaystyle 2}

para chegar em 67{displaystyle {frac {6}{7}}}

  • Nesse exemplo, a resposta final será igual a 667{displaystyle 6{frac {6}{7}}}

Método 2 de 2: Multiplicando frações por números inteiros

Multiply Fractions With Whole Numbers Step 6

Step 1. Rewrite the whole number as a fraction

To rewrite it this way, just put the integer over 1{displaystyle 1}

a fim de se obter uma fração imprópria.

  • No caso de 5×810{displaystyle 5\times {frac {8}{10}}}
  • , por exemplo, coloque o 5{displaystyle 5}

    sobre 1{displaystyle 1}

    . Agora, essa operação estará escrita como 51×810{displaystyle {frac {5}{1}}\times {frac {8}{10}}}

Multiply Fractions With Whole Numbers Step 7

Step 2. Multiply the numerators of both fractions

Remember that numerators are the numbers above the lines. Write the result and place a line below it.

  • In the example, 51×810{displaystyle {frac {5}{1}}\times {frac {8}{10}}}

    , multiplique 5{displaystyle 5}

    por 8{displaystyle 8}

    a fim de obter 40{displaystyle 40}

Multiply Fractions With Whole Numbers Step 8

Step 3. Multiply the denominators of both fractions

It will now be possible to multiply the numbers below the lines to get the denominator. You will have the answer to the equation in fraction form.

  • By multiplying 51×810{displaystyle {frac {5}{1}}\times {frac {8}{10}}}

    , por exemplo, multiplique 1{displaystyle 1}

    por 10{displaystyle 10}

    a fim de obter 10{displaystyle 10}

    . Coloque esse valor abaixo da linha para chegar à resposta 4010{displaystyle {frac {40}{10}}}

Multiply Fractions With Whole Numbers Step 9

Step 4. If possible, reduce the answer

Since the answer is likely to be an improper fraction, reduce it to its minimum values. Divide the numerator by the denominator to get a simplified answer.

  • To simplify 4010{displaystyle {frac {40}{10}}}

    , divida 40{displaystyle 40}

    por 10{displaystyle 10}

    para obter 4{displaystyle 4}

    como nova resposta.

  • em muitos casos, você chegará em um número misto, uma vez que a resposta terá um remanescente.

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