Content

• Steps

When dividing an integer by a fraction, you will find out how many groups of fractions fit that whole number. The standard way to divide an integer by a fraction is to multiply the whole number by the inverse of the given fraction. You can also draw a diagram to help you visualize the process.

Steps

Method 1 of 3: Multiply by the inverse number

1. 

   Convert the whole number to a fraction. To do this, place the whole number in the numerator position of the fraction. The denominator will be 1.
   • For example, if you are calculating, you need to first change to.

2. 

   
   
   Find the inverse of the divisor. The inverse of a number is the number that is reversed. To find the inverse of a fraction, invert the numerator and denominator positions.
   • For example, the inverse of the fraction is.

3. 

   
   
   Multiply two fractions. To multiply fractions, first multiply the numerators together. Then, multiply the denominators together. Product of two fractions is equal to the quotient of the original division.
   • For example,

4. 

   
   
   Shorten if needed. If you have a fraction greater than 1 (the fraction has the numerator greater than the denominator), your teacher may ask you to convert it to a mixed number. Usually, your teacher will ask you to reduce the fraction to a minimum.
   • For example, reduce to mixed numbers.
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Method 2 of 3: Draw diagrams

1. 

   Draw an image to represent an integer. The figure should be a shape that can be divided into equal groups, such as a square or circle. Draw shapes large enough that you can divide them into smaller sections.
   • For example, if you have a calculation, you need to draw 5 circles.

2. 

   Divide each figure by the denominator of the fraction. The denominator of a fraction tells you how many parts an integer is divided into. Divide the formation into equal proportions.
   • For example, if you do the math, the number 4 in the denominator indicates the figure is divided into four parts.

3. 

   The group color represents the sections. Because you convert an integer to a fraction, you want to know how many groups of fractions there are in that whole number. So first you need to create groups. Coloring each group a different color helps, as some groups will have sections on two different integers. Do not color the rest.
   • For example, if you divide 5 by, you would fill 3/4 of each group with a different color.Note that multiple groups can contain 2 quarters of one integer and 1 quarter of another integer.

4. 

   Count the number of groups of integers. This will help you get the integer part of your answer.
   • For example you should create 6 groups out of 5 circles.

5. 

   Interpret the rest. Compare the number of servings to a complete group. The fraction of the remaining group of sections will indicate the fractional part of the answer. Make sure that you do not compare the number of parts with the whole figure because doing so will result in inaccurate fractions.
   • For example, after dividing 5 into groups, you have 2 quarters or the remainder. Since the group has a total of 3 parts and you have 2 parts, your fraction is.

6. 

   Write your answer. Combine groups of integers with groups of fractions to find the quotient of the initial division calculation.
   • For example, .
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Method 3 of 3: Solve sample problem

1. 

   Solve the following problem: Multiply by how many to get?
   • Because the problem asks how many groups in 8, the problem is division.
   • Convert 8 to a fraction with the denominator of 1:.
   • Find the inverse of the fraction by reversing the positions of the numerator and denominator: to.
   • Multiply two fractions together:.
   • Simplify if needed:.

2. 

   Solve the following problem: .
   • Convert 16 to a fraction with denominator 1:.
   • Find the inverse of the fraction by reversing the positions of the numerator and denominator: to.
   • Multiply two fractions together:.
   • Simplify if needed:.

3. 

   Solve the following problem by drawing a diagram. Rufus has 9 food boxes. Every day, she finishes the box. How many days to eat food?
   • Draw 9 circles to represent 9 food boxes.
   • Since each time she finishes the can, divide the circle into three servings.
   • Color the fraction group.
   • Counting the number of filled groups, we get 13.
   • Interpret the rest. There is 1 rest, that is. Since the whole group is, you have the other half. So the fraction would be.
   • Sum the groups of integers and fraction groups, we have the answer:.
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