How to Subtract Mixed Numbers? (+FREE Worksheet!)

In this article, you will learn how to Subtract Mixed Numbers with similar (like) or Unlike Denominators in a few easy and simple steps.

How to Subtract Mixed Numbers? (+FREE Worksheet!)

Fractions greater than \(1\) are usually represented as mixed numbers. In this case, the mixed number consists of an integer part and a standard fraction less than \(1\). The integer part is the same as the quotient part and the numerator of the fraction is the remainder of the division and the denominator of the fraction will also be the divisor.

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Step by step guide for Subtracting Mixed Numbers

The main method of subtracting mixed numbers is close to the way you add them. However, along the way, you may encounter mazes. We will keep you on this path so that at the end of this section you can solve the subtraction problems for any kind of mixed number. The subtraction of mixed numbers has two forms:

1- Subtraction of mixed numbers when their denominators are the same:

Similar to the adding of mixed numbers, in subtracting mixed numbers, if the denominators are the same, the operation becomes much simpler.

  • Step 1: First, subtract the integers part: Subtract the whole number of the second mixed number from the whole number of the first mixed number.
  • Step 2: In the next step, subtract the fraction part: Subtract the second fraction from the first one.
  • Step 3: Write your answer in the lowest terms.

2- Subtraction of mixed numbers when their denominators are different:

Subtracting mixed numbers with different denominators is probably the hardest thing you can do in pre-algebra. However, fortunately, if you have learned this chapter well, you have all the skills needed to do so.

  • Step 1: First, subtract the integers part: Subtract the whole number of the second mixed number from the whole number of the first mixed number.
  • Step 2: In the next step, subtract the fraction part: Subtract the second fraction from the first one. Because the denominators are different, subtracting fractions becomes more difficult. you must first find the Least Common Denominator (LCD), then you can then subtract the second fraction from the first fraction.
  • Step 3: Write your answer in the lowest terms.

A complication occurs when the second fraction is bigger than the first fraction. You do not want to encounter a negative number in your final answer. You can manage this problem by borrowing from the first mixed number. This idea is very similar to borrowing in the ordinary subtraction of integers, but there is a key difference.

When borrowing in subtraction of mixed numbers:

  • Step 1: Borrow \(1\) unit from the first integers part and add it to the fraction part, this will turn your fraction into a mixed number.
  • Step 2: Convert this new mixture number to a fraction.
  • Step 3: Use this result in your subtraction
  • Step 4: Write your answer in the lowest terms.

Subtract Mixed Numbers – Example 1:

Subtract . \( 2 \ \frac{3}{5} \ – \ 1 \ \frac{1}{3} = \)

Solution:

Rewriting our equation with parts separated, \(2 \ + \ \frac{3}{5} \ – \ 1 \ – \ \frac{1}{3}\)
Solving the whole number parts \(2 \ – \ 1=1\) , Solving the fraction parts, \(\frac{3}{5} \ – \ \frac{1}{3}=\frac{(3×3) \ – \ (1×5)}{5×3}=\frac {9-5}{15} =\frac{4}{15}\)
Combining the whole and fraction parts, \(1 \ + \ \frac{4}{15}=1 \ \frac{4}{15}\)

Subtract Mixed Numbers – Example 2:

Subtract . \( 5 \ \frac{5}{8} \ – \ 2 \ \frac{1}{4} = \)

Solution:

Rewriting our equation with parts separated, \(5 \ +\ \frac{5}{8} \ – \ 2 \ – \ \frac{1}{4}\)
Solving the whole number parts \(5 \ – \ 2=3\) , Solving the fraction parts, \(\frac{5}{8} \ – \ \frac{1}{4}=\frac{5 \ – \ (1 × 2)}{8}=\frac {5-2} {8} =\frac{3}{8}\)
Combining the whole and fraction parts, \(3 \ + \ \frac{3}{8}=3 \ \frac{3}{8}\)

Subtract Mixed Numbers – Example 3:

Subtract . \( 5 \ \frac{2}{3} \ – \ 2 \ \frac{1}{4} = \)

Solution:

Rewriting our equation with parts separated, \(5+\frac{2}{3}–2-\frac{1}{4}\)
Solving the whole number parts \(5-2=3\), Solving the fraction parts,

\(\frac{2}{3}-\frac{1}{4}=\frac{(2 × 4)-(1 × 3)}{3 × 4}= \frac{8-3}{12}\) \(=\)\(\frac{5}{12}\)
Combining the whole and fraction parts, \(3+\frac{5}{12}=3 \ \frac{5}{12}\)

Subtract Mixed Numbers – Example 4:

Subtract . \( 3 \ \frac{4}{5} \ – \ 1 \ \frac{1}{2} = \)

Solution:

Rewriting our equation with parts separated, \(3+\frac{4}{5}-1-\frac{1}{2}\)
Solving the whole number parts \(3-1=2\), Solving the fraction parts, \(\frac{4}{5}-\frac{1}{2}=\frac{(4 × 2)-(1 × 5)}{5× 2}=\frac {8-5} {10}= \frac{3}{10}\)
Combining the whole and fraction parts, \(2+\frac{3}{10}=2 \ \frac{3}{10}\)

Subtract Mixed Numbers – Exercises

Subtract.

  1. \(\color{blue}{4\frac{1}{2}-3\frac{1}{2}}\)
  2. \(\color{blue}{3\frac{3}{8}-3\frac{1}{8}}\)
  3. \(\color{blue}{6\frac{3}{5}-5\frac{1}{5}}\)
  4. \(\color{blue}{2\frac{1}{3}-1\frac{2}{3}}\)
  5. \(\color{blue}{6\frac{1}{6}-5\frac{1}{2}}\)
  6. \(\color{blue}{3\frac{1}{3}-1\frac{1}{3}}\)

Download Adding and Subtracting Mixed Numbers Worksheet

  1. \(\color{blue}{1}\)
  2. \(\color{blue}{\frac{1}{4}}\)
  3. \(\color{blue}{1\frac{2}{5}}\)
  4. \(\color{blue}{\frac{2}{3}}\)
  5. \(\color{blue}{\frac{2}{3}}\)
  6. \(\color{blue}{2}\)

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