How to Simplify an Improper Fraction: 12 Steps

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How to Simplify an Improper Fraction: 12 Steps
How to Simplify an Improper Fraction: 12 Steps
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Fractions are numbers that represent parts of integer values. If a fraction has a numerator greater than its denominator, it is called an "improper fraction" and can be simplified into mixed number form (combination of an integer and a fraction). There's nothing wrong with an improper fraction, and in many cases math works more easily with them than with mixed numbers. However, it is more common to use mixed numbers than improper fractions, and it is important to understand how to create them.

Steps

Method 1 of 2: Using a Template

Simplify an Improper Fraction Step 1

Step 1. Determine if the fraction is improper

An improper fraction is one that has a numerator greater than the denominator.

  • For example, 104{displaystyle {frac {10}{4}}}

    é uma fração imprópria, uma vez que 10{displaystyle 10}

    é maior do que 4{displaystyle 4}

Simplify an Improper Fraction Step 2

Step 2. Interpret the denominator

This is the value below the horizontal bar, indicating how many equal pieces the whole is being divided into.

  • In fraction 104{displaystyle {frac {10}{4}}}

    , por exemplo, 4{displaystyle 4}

    é o denominador, indicando que o inteiro está dividido em quatro partes iguais, ou quartos.

Simplify an Improper Fraction Step 3

Step 3. Interpret the numerator

This is the value above the horizontal bar, indicating how many pieces you have.

  • In fraction 104{displaystyle {frac {10}{4}}}

    , por exemplo, 10{displaystyle 10}

    é o numerador, indicando que você possui dez partes iguais, ou dez quartos.

Simplify an Improper Fraction Step 4

Step 4. Draw circles to represent the whole

Divide each of them according to the denominator of the fraction.

  • For example, if the denominator is 4{displaystyle 4}

    , divida cada círculo desenhado em quatro partes iguais, ou quartos.

Simplify an Improper Fraction Step 5

Step 5. Detach the pieces according to the numerator

The numerator value indicates how many pieces should be highlighted.

  • If the fraction is 104{displaystyle {frac {10}{4}}}

    , por exemplo, você deve destacar dez quartos.

Simplify an Improper Fraction Step 6

Step 6. Count how many whole circles were highlighted

To simplify an improper fraction, you must transform it into a mixed number, which includes an integer and fraction combined. The number of highlighted whole circles represents the whole number of the mixed fraction. Write it down.

  • In fraction 104{displaystyle {frac {10}{4}}}

    , por exemplo, você deve ter destacado dois círculos inteiros, de modo que o valor inteiro do número misto será 2{displaystyle 2}

Simplify an Improper Fraction Step 7

Step 7. Count how many parts of an integer you highlighted

The remaining highlighted portion represents the fraction in its mixed number. Write it in front of the integer value and eventually you will have the desired result.

  • In fraction 104{displaystyle {frac {10}{4}}}

    , você deve ter destacado 24{displaystyle {frac {2}{4}}}

    de um círculo, sendo que a fração de seu número misto equivalerá a 24{displaystyle {frac {2}{4}}}

    . Desse modo, pode-se dizer que 104{displaystyle {frac {10}{4}}}

    equivale a 224{displaystyle 2{frac {2}{4}}}

Simplify an Improper Fraction Step 8

Step 8. If necessary, simplify the result

Sometimes the mixed number fraction will have to be reduced before reaching the final and simplified answer.

  • If the mixed number is 224{displaystyle 2{frac {2}{4}}}

    , por exemplo, você pode simplificá-lo para 212{displaystyle 2{frac {1}{2}}}

Método 2 de 2: Fazendo uso da divisão

Simplify an Improper Fraction Step 9

Step 1. Determine if the fraction is improper

The improper fraction is one that has a numerator greater than the denominator.

  • For example, 104{displaystyle {frac {10}{4}}}

    1 />
<p>4
Simplify an Improper Fraction Step 10

Step 2. Divide the numerator by the denominator

Keep in mind that the horizontal bar can be interpreted as a division symbol. To simplify an improper fraction, you must transform it into a mixed number, which combines an integer value and a fraction. The number of times you can divide the numerator equally by the denominator will represent the integer value of your mixed number. Write it down and keep the remainder.

  • The denominator does not fit into the numerator equally. What is left will be interpreted as the fraction part of your mixed number.
  • In fraction 104{displaystyle {frac {10}{4}}}

    , por exemplo, complete o cálculo 10÷4=2 R 2{displaystyle 10\div 4=2 {text{R}}\ 2}

    . Desse modo, o número inteiro da fração será 2{displaystyle 2}

Simplify an Improper Fraction Step 11

Step 3. Transform the remainder to a fraction

To do this, take it and place it over the denominator of the original improper fraction. Combine that new fraction with the whole number and you have your mixed number.

  • For example, 10÷4=2 R 2{displaystyle 10\div 4=2 {text{R}}\ 2}

    , de modo que a fração remanescente será 24{displaystyle {frac {2}{4}}}

    . Assim sendo, 104{displaystyle {frac {10}{4}}}

    equivale a 224{displaystyle 2{frac {2}{4}}}

Simplify an Improper Fraction Step 12

Step 4. If necessary, simplify the answer

Sometimes the fraction of their mixed number will have to be reduced before reaching the final and simplified answer.

  • If your mixed number is 224{displaystyle 2{frac {2}{4}}}

    , por exemplo, você pode simplificá-lo para 212{displaystyle 2{frac {1}{2}}}

dicas

  • para converter um número misto de volta à forma de fração imprópria, multiplique o valor inteiro pelo denominador e some o produto ao numerador.
  • mantenha o denominador. por exemplo, 212{displaystyle 2{frac {1}{2}}}
  • pode ser reescrito como 52{displaystyle {frac {5}{2}}}

    , uma vez que 2×2+1=5{displaystyle 2\times 2+1=5}

  • algumas frações impróprias também podem representar números inteiros, como 243{displaystyle {frac {24}{3}}}

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