Multiplying a fraction by a mixed or whole number is very simple. Start by transforming the mixed or whole number into an improper fraction, then multiply the numerators of the improper fractions together and then perform the same operation with the denominators. As a last step, simplify the result you have obtained.
Steps
Method 1 of 2: Multiply a Fraction by a Mixed Number
Step 1. Convert mixed fractions (or mixed numbers) to improper fractions
To do this, multiply the integer part of the mixed number by the denominator of the fractional part and add the result to the numerator. At this point, he places the result obtained in the numerator of a fraction, returning the original value of the fractional part to the denominator. Repeat this step for all mixed numbers you need to turn into improper fractions.
For example if you need to do the following multiplication 1 1/2 x 4 4/7 start by transforming mixed fractions into improper fractions. The mixed fraction 1 1/2 will become 3/2, while the 4 4/7 fraction will become 32/7. At the end of this phase the initial problem will have assumed the following form 3/2 x 32/7
Step 2. Multiply the numerators of the improper fractions together
Now that you have to perform the product of two improper fractions, without an integer part, you can simply multiply their respective numerators together. Return the result of the product to the numerator of the final fraction.
- The numerator of a fraction is the value shown at the top of the fraction itself.
- Continuing with the previous example, 3/2 x 32/7, you will have to multiply 3 by 32 to get 96 as a result.
Step 3. Multiply the denominators of the improper fractions together
Run the product by multiplying the numbers shown at the bottom of the fraction line and report the result under the numerator of the final fraction.
Continuing with the previous example, 3/2 x 32/7, you will have to multiply 2 by 7 to get the result 14
Step 4. Transform the final result into a mixed fraction if possible
If the numerator of the final fraction is greater than the denominator, you can turn it into a mixed fraction by extrapolating the integer part. Divide the numerator by the denominator to get the whole part, then report the remainder of the division as a fraction. This way you will have obtained a mixed fraction.
- For example, to transform the improper fraction 96/14, resulting from the example problem, into a mixed fraction, divide the numerator by the denominator. The result will be 6 with the remainder of 12. Return the remainder as a fraction by placing it in the numerator and returning the original denominator of the improper fraction (14) as the denominator.
- Many teachers require that the final result be reported in the same form as the initial problem, so if you started out with mixed fractions you will need to convert the final result, an improper fraction, into a mixed number.
Step 5. Simplify the final result if possible
The final result of the multiplication will most likely consist of an integer part and a fractional part. Focus on the fractional part to see if it can be simplified further. For example, if you got the mixed number 6 12/14, you can simplify the fraction 12/14 by dividing the numerator and denominator by 2 to get 6/7.
The final result of the example problem will then be 6 6/7
Method 2 of 2: Multiply a Fraction by an Integer
Step 1. Convert integers as a fraction
To do this, simply return the whole number as the numerator of a fraction whose denominator is equal to 1. This will result in an improper fraction.
For example, if you need to solve the following problem 5 x 8/10, turn the integer 5 into an improper fraction by adding the denominator 1. This way the initial problem will become 5/1 x 8/10
Step 2. Multiply the numerators of the two fractions
Remember that the numerators are the values shown at the top of the fraction line. Report the result of the product as the numerator of the final fraction.
Continuing with the previous example, 5/1 x 8/10, multiply 5 by 8 to get 40
Step 3. Multiply the denominators of the two fractions
Calculate the product of the numbers shown at the bottom of the fractions in question. By now you should have gotten the final fraction of your problem.
Continuing with the previous example, 5/1 x 8/10, multiply 1 by 10 to get 10. Return the value obtained as the denominator of the final fraction to get 40/10
Step 4. Simplify the final result as much as possible
Since the end result will most likely be an improper fraction, you will need to simplify it to a minimum. Divide the numerator by the denominator.
- To simplify the fraction 40/10, divide 40 by 10 to get the final result 4.
- In many cases you will end up with a mixed number made up of the integer part of the improper fraction and the rest of the division.
