Math Tutor Explains: What is 172/165 as a mixed number?

A math tutor would guide you through mixed numbers by explaining that they’re just another way to represent an improper fraction—made up of a whole number and a proper fraction. To convert an improper fraction into a mixed number, a math tutor would show you how to divide the numerator by the denominator. The quotient becomes the whole number, while the remainder forms the new numerator, keeping the denominator the same. With the right approach, this process becomes simple and intuitive. Read more below for a detailed step-by-step walkthrough shared by a Thinkster math tutor.

Math Tutor's Solution: 172/165 as a mixed number is 1 7/165

Methods

Step-by-step solution from a math tutor for converting 172/165 as a mixed number

A math tutor would guide you through converting an improper fraction to a mixed number with these three simple steps:

Divide the numerator by the denominator (you can use long division if you want to!) to find out what the quotient and the remainder are. If the fraction is made up of whole numbers, you will always get an integer quotient and an integer remainder.
Note down what your quotient, remainder, and original denominator is.
Now rewrite these three numbers in Step 2 in a mixed number format where:
1. the quotient is the whole number next to the proper fraction
2. the remainder is the numerator of the proper fraction
3. the original denominator is the new denominator of the proper fraction

Now, let’s apply these steps to our problem. A math tutor would ask: What is 172 divided by 165? If you do some thinking or long division, you should get:

172 ÷ 165 → Quotient of 1 and a remainder of 7.

Now that we have all the numbers we need, let’s piece together our answer:

172 ÷ 165 = 1 7/165

Math Tutor Suggests: Practice solving other mixed number problems

Our math tutors share that the best way to become a pro at converting improper fractions to mixed numbers is by practicing. Take a look at some more problems below so that you can solve it without hesitation!

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