# 3 ways to divide a whole number by a fraction

When you divide a whole number by a fraction, you need to find how many groups of the fraction fit into the whole number. The regular method of finding the answer is to multiply the whole number by the reciprocal of the fraction. You can also use a diagram to help you visualize the process.

## Steps

### Method 1 of 3: Multiply by the reciprocal

#### Step 1. Convert the whole number to a fraction

To do this, you will have to convert the whole number into the numerator of a fraction. The denominator will be 1.

• For example, if you have to calculate 7 ÷ 34 { displaystyle 7 \ div { frac {3} {4}}}

, primero tendrás que convertir 7{displaystyle 7}

en 71{displaystyle {frac {7}{1}}}

#### Step 2. Find the reciprocal of the divisor

The reciprocal of a number is its inverted version. To find the reciprocal of a fraction, simply swap the places of the numerator and denominator.

• For example, the inverted version of 34 { displaystyle { frac {3} {4}}}

es 43{displaystyle {frac {4}{3}}}

#### Step 3. Multiply the two fractions

To do this, you must first multiply both numerators. Next, you must multiply the denominators. The product of both fractions is the quotient of the original division that you must solve.

• For example, 71 × 43 = 283 { displaystyle { frac {7} {1}} times { frac {4} {3}} = { frac {28} {3}}}

#### Step 4. Simplify the answer if necessary

If the result is an improper fraction (a fraction whose numerator is greater than the denominator), the teacher will ask you to convert it to a mixed fraction. Typically, teachers ask you to simplify proper fractions until you find the smallest equivalent.

• For example, 283 { displaystyle { frac {28} {3}}}

### Método 2 de 3: Dibujar un diagrama

#### Step 1. Draw shapes to represent the whole number

The idea is that the figure can be divided into equal parts, like a square or a circle. It should also be large enough to be divided into small parts.

• For example, if you are calculating 5 ÷ 34 { displaystyle 5 \ div { frac {3} {4}}}

, tendrás que dibujar 5 círculos para empezar.

#### Step 2. Divide each whole figure by the denominator of the fraction

The denominator of a fraction indicates how many parts a whole must have. Divide each figure into the necessary parts.

• For example, if you are dividing a whole number by 34 { displaystyle { frac {3} {4}}}

, el 4 es el denominador e indica que debes dividir cada figura en 4 partes.

#### Step 3. Shade in the parts that represent the fraction

Since you are dividing a whole number by the fraction, the idea is to see how many groups of the fraction fit into the whole number. Therefore, you will first have to create the groups. It's a good idea to use different colors to represent each group, as some of these will be scattered across two different whole shapes. Leave the remaining parts unshaded.

• For example, if you are dividing 5 by 34 { displaystyle { frac {3} {4}}}

, podrías colorear 3 cuartos de un color diferente para cada grupo. Ten en cuenta que algunos grupos tendrán 2 cuartos en una figura entera y 1 cuarto en otra.

#### Step 4. Count the number of complete groups

This way, you will find the whole number of the answer.

• For example, for the 5 whole circles you will have 6 complete groups of 34 { displaystyle { frac {3} {4}}}

#### Step 5. Interpret the remaining parts

Compare the number of parts remaining with a whole group. The fraction of the remaining group is the fraction of the answer. Make sure you don't compare the number of parts to the whole figure, as the answer will be wrong.

• For example, after dividing the 5 shapes into groups of 34 { displaystyle { frac {3} {4}}}

, te quedarán 2 cuartos, o 24{displaystyle {frac {2}{4}}}

. Dado que un grupo completo consiste en 3 partes y te quedan 2, la fracción será 23{displaystyle {frac {2}{3}}}

#### Step 6. Write down the answer

Combine the number of complete groups with the fraction of the remaining group to find the quotient of the original division.

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

### Método 3 de 3: Resolver problemas

#### Step 1. Solve the following problem:

How many 12 { displaystyle { frac {1} {2}}}

caben en 8{displaystyle 8}

?

• Dado que el problema requiere hallar cuántos grupos de 12{displaystyle {frac {1}{2}}}
• entran en 8, el problema se representa con una división.

• Convierte 8 en una fracción. Para ello, tendrás que añadir 1 como denominador: 8=81{displaystyle 8={frac {8}{1}}}
• Halla el recíproco de la fracción. Para ello, tendrás que invertir los lugares del numerador y el denominador: 12{displaystyle {frac {1}{2}}}
• se convierte en 21{displaystyle {frac {2}{1}}}

• Multiplica las fracciones: 81×21=161{displaystyle {frac {8}{1}}\times {frac {2}{1}}={frac {16}{1}}}
• Simplifica el resultado si fuera necesario: 161=16{displaystyle {frac {16}{1}}=16}

#### Step 2. Solve the following problem:

16 ÷ 58 { displaystyle 16 \ div { frac {5} {8}}}

• Convierte 16 en una fracción. Para ello, tendrás que añadir 1 como denominador: 16=161{displaystyle 16={frac {16}{1}}}
• Usa el recíproco de la fracción, que da como resultado al intercambiar los lugares del numerador y el denominador: 58{displaystyle {frac {5}{8}}}
• se convierte en 85{displaystyle {frac {8}{5}}}

• Multiplica las dos fracciones: 161×85=1285{displaystyle {frac {16}{1}}\times {frac {8}{5}}={frac {128}{5}}}
• Simplifica la respuesta si fuera necesario: 1285=2535{displaystyle {frac {128}{5}}=25{frac {3}{5}}}

#### Step 3. Solve the following problem using a diagram

Rufus has 9 cans of food. If 23 { displaystyle { frac {2} {3}}} is eaten

de una lata cada día, ¿cuántos días le durará la comida?

• utiliza 9 círculos para representar las 9 latas.
• dado que se come 23{displaystyle {frac {2}{3}}}
• cada día, tendrás que dividir los círculos en tres partes (tercios).

• sombrea los grupos de 23{displaystyle {frac {2}{3}}}
• cuenta los grupos completos. el resultado será 13.
• interpreta las partes restantes. hay 1 parte restante, que equivale a 13{displaystyle {frac {1}{3}}}
• . dado que un grupo entero es 23{displaystyle {frac {2}{3}}}

, quiere decir que te queda la mitad de un grupo. por lo tanto, la fracción resultante es 12{displaystyle {frac {1}{2}}}

• combina el número de grupos completos y la fracción de grupos restantes para hallar la respuesta final: 9÷23=1312{displaystyle 9\div {frac {2}{3}}=13{frac {1}{2}}}