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• To step
• Method 1 of 3: Multiply by the reverse

If you want to divide an integer by a fraction, you are actually calculating how many "groups" of the fraction go into the whole. The standard way of dividing an integer by a fraction is to multiply the whole number by the reciprocal of the fraction. You can also create a diagram to help visualize this calculation.

To step

Method 1 of 3: Multiply by the reverse

1. Convert the whole number to a fraction. You do this by making the numerator of a fraction from the whole number. Make the denominator 1.
   • For example: Calculate your ${ displaystyle 7 div { frac {3} {4}}}$Find the inverse of the fraction. The inverse of a number is equal to the inverse of that number. To find the reverse of a fraction, swap the numerator and denominator.
     • For example: the reverse (the inverse) of ${ displaystyle { frac {3} {4}}}$Multiply the two fractions. To multiply fractions, you first multiply the numerators together. Then multiply the denominators together. The product of the two fractions is equal to the quotient of your original division problem.
       • For instance: ${ displaystyle { frac {7} {1}} times { frac {4} {3}} = { frac {28} {3}}}$Simplify if necessary. If you have an improper fraction (where the numerator is greater than the denominator), the problem may ask you to change it to a mixed number. Normally, the problem will ask to simplify fractions to the lowest terms.
         • For instance: ${ displaystyle { frac {28} {3}}}$Draw shapes that represent the whole number. Your shape should be able to be divided into equal groups, such as a square or a circle. Draw the shapes so big that you can divide them into smaller pieces.
           • For example: in the calculation ${ displaystyle 5 div { frac {3} {4}}}$Divide each whole shape by the denominator of the fraction. The denominator of a fraction indicates how many pieces a whole shape is divided into. Divide each entire shape into the parts as indicated by the fraction.
             • For example, if you divide by ${ displaystyle { frac {3} {4}}}$Shade the groups that represent the fraction. Since you're dividing the whole number by the fraction, see how many groups of the fraction are in the whole number. So first you indicate the groups. It can be helpful to give each group a different color, as some groups have parts in two different integer shapes. Leave the remaining pieces blank.
               • For example: pass through part 5 ${ displaystyle { frac {3} {4}}}$Count the number of whole groups. This will give you the whole number of your answer.
                 • For example, you had six groups of ${ displaystyle { frac {3} {4}}}$Interpret the remaining pieces. Compare the number of pieces you have left with a full group. The fraction of a group you have left indicates the fraction of your answer. Make sure not to compare the number of pieces you have with the number of pieces you have with a whole shape, as this will give you the wrong fraction.
                   • For example: after dividing the five shapes into groups of ${ displaystyle { frac {3} {4}}}$Write down the answer. Combine the groups of the whole number with the groups of the fraction to find the quotient of your original division sum.
                     • For instance: ${ displaystyle 5 div { frac {3} {4}} = 6 { frac {2} {3}}}$Solve: How often goes ${ displaystyle { frac {1} {2}}}$Solve:${ displaystyle 16 div { frac {5} {8}}}$Solve the following problem by drawing a diagram. Rufus has nine cans of beans. She eats every day ${ displaystyle { frac {2} {3}}}$ a can. For how many days does she have cans?
                       • Draw nine circles to represent the nine cans.
                       • Because she ${ displaystyle { frac {2} {3}}}$ at a time, you divide each circle into thirds.
                       • Color the groups of ${ displaystyle { frac {2} {3}}}$.
                       • Count the number of complete groups. This should be 13.
                       • Interpret the remaining pieces. There's still a lot left, and that is ${ displaystyle { frac {1} {3}}}$. Because a whole group ${ displaystyle { frac {2} {3}}}$ you have half a group left. So is the fraction ${ displaystyle { frac {1} {2}}}$.
                       • Combine the number of groups of integers and fractions to find your final answer: ${ displaystyle 9 div { frac {2} {3}} = 13 { frac {1} {2}}}$.