How to Subtract Mixed Numbers When You Need to Borrow

Students usually start working with mixed-number operations around grades 4 and 5. From our experience at Mathnasium, we’ve noticed that subtracting mixed numbers can trip them up at first because borrowing works a little differently with fractions. 

Today, we’ll learn how to tell when borrowing is needed and work through mixed-number subtraction step by step.

Quick Review: How to Subtract Mixed Numbers

When we subtract mixed numbers, we subtract the whole-number parts, subtract the fractional parts, and then combine the results. 

Take 5\(\Large\frac{3}{5}\) - 2\(\Large\frac{1}{5}\):

• Step 1: We subtract the wholes, 5 − 2 = 3.

• Step 2: Next, we subtract the fractional parts: \(\Large\frac{3}{5}\) − \(\Large\frac{1}{5}\) = \(\Large\frac{2}{5}\).

• Step 3: Finally, we combine the two results. We have 3 and \(\Large\frac{2}{5}\), so our answer is 3\(\Large\frac{2}{5}\).

This works as long as the fractional part of the first mixed number is large enough to subtract the second fraction from it.

But what if the fraction on top is smaller? In that case, we need to borrow, or, in other words, regroup.

How to Know When to Borrow With Mixed Numbers

We need to borrow when the fraction we are starting with (the top or first number) is smaller than the fraction you are taking away (the bottom or second number).

The idea is similar to borrowing in whole-number subtraction:

• With whole numbers, we take 1 from the place to the left and rewrite it as 10 of the next smaller unit.

• With mixed numbers, we take 1 from the whole-number part and rewrite it as an equivalent fraction with the same denominator as the fractional part. We then combine it with the original fraction so we have enough fractional pieces to subtract. 

Let’s make this concrete. Imagine you have 2\(\Large\frac{1}{4}\) pizzas left after a party, and you want to give \(\Large\frac{3}{4}\) of it to a friend. The \(\Large\frac{1}{4}\) from 2\(\Large\frac{1}{4}\) you have as an extra piece is smaller than \(\Large\frac{3}{4}\), so you’ll need to use part of one whole pizza. Before we subtract mixed numbers, we make the same check and compare the fractional parts to see whether the fraction on top is large enough.

Let’s make this concrete with a pizza example:

Imagine you have 2\(\Large\frac{1}{4}\) pizzas left after a party and want to give \(\Large\frac{3}{4}\) of a pizza to a friend. Your single \(\Large\frac{1}{4}\) slice isn't enough, so you have to slice open one of the whole pizzas.

That extra pizza gives you 4 more slices (\(\Large\frac{4}{4}\)), bringing your total to 1\(\Large\frac{5}{4}\) pizzas. Now you have more than enough slices to give your friend \(\Large\frac{3}{4}\)!

“Borrow or Not?”

To help you quickly tell whether borrowing is needed, our tutors put together this simple decision table.

With practice, this check will become more automatic, and you’ll be able to tell whether you need to borrow without referring back to the table.

How to Borrow in Mixed-Number Subtraction

To subtract mixed numbers with borrowing, we first find a common denominator. Then we borrow 1 whole, rewrite it as a fraction with that denominator, subtract the fractional and whole-number parts, and simplify the answer if needed.

At Mathnasium, we like explaining math through examples. So, let’s walk through the steps with this subtraction: : 4\(\Large\frac{1}{3}\) − 1\(\Large\frac{5}{6}\).

Step 1: Find a common denominator

Before we can subtract the fractions, they need to be written in equal-sized parts. In our example, the fractions \(\Large\frac{1}{3}\) and \(\Large\frac{5}{6}\) have different denominators, so we first need to find a common denominator.

The smallest number both 3 and 6 divide into evenly is 6. To rewrite \(\Large\frac{1}{3}\) with a denominator of 6, we multiply both the numerator and denominator by 2: 

\(\Large\frac{1×2}{3×2}\) = \(\Large\frac{2}{6}\)

The fraction \(\Large\frac{5}{6}\) already has a denominator of 6, so it stays the same. Our problem, now, looks like this:

 4\(\Large\frac{2}{6}\) − 1\(\Large\frac{5}{6}\).

📕 You May Also Like: What Is the Least Common Denominator? A Kid-Friendly Guide

Step 2: Borrow 1 whole from the top mixed number

As we can’t subtract \(\Large\frac{5}{6}\) from \(\Large\frac{2}{6}\), we’ll need to borrow 1 whole from the starting mixed number. We’ll break that into three smaller moves. 

Because we cannot subtract \(\Large\frac{5}{6}\) from \(\Large\frac{2}{6}\), we borrow 1 whole from 4 in our starting number 4\(\Large\frac{2}{6}\): 

• Reduce the whole number: Take 1 away from 4, leaving 3.

• Convert the borrowed 1: Rewrite that 1 as \(\Large\frac{6}{6}\) to match our denominator.

• Combine with your starting fraction: Add \(\Large\frac{6}{6}\) + \(\Large\frac{2}{6}\) = \(\Large\frac{8}{6}\)

So 4\(\Large\frac{2}{6}\) can be rewritten as 3\(\Large\frac{8}{6}\). The amount is the same, but the fractional part is large enough for us to subtract \(\Large\frac{5}{6}\).

Our example is now :

3\(\Large\frac{8}{6}\) − 1\(\Large\frac{5}{6}\).

📕 You May Also Like: A Simple Guide to Mixed Numbers and Improper Fractions

Step 3: Subtract the parts

Now that our starting fraction \(\Large\frac{8}{6}\) is large enough, we can subtract the fractions and whole numbers separately.

• Subtract the fractions: \(\Large\frac{8}{6}\) − \(\Large\frac{5}{6}\) = \(\Large\frac{3}{6}\).

• Subtract the whole parts: 3 − 1 = 2.

We have 2 wholes and \(\Large\frac{3}{6}\), so we put them together and get: 2\(\Large\frac{3}{6}\).

Step 4: Simplify the answer if needed

We check whether the fraction in 2\(\Large\frac{3}{6}\) can be simplified. Because both 3 and 6 are divisible by 3, we divide the numerator and denominator by 3.

\(\Large\frac{3÷3}{6÷3}\) = \(\Large\frac{1}{2}\).

So our final answer is:

2\(\Large\frac{1}{2}\).

📕 You May Also Like: How to Subtract Fractions With Like and Unlike Denominators

Common Mistakes to Avoid When Borrowing With Mixed Numbers

In our work with students, we’ve noticed a few common mistakes that can come up when borrowing with mixed numbers. Take a look at this table to see what to watch for.

📕 You May Also Like: Common Math Misconceptions & How to Fix Them (K-8)

Try Subtracting Mixed Numbers Yourself

Ready to try it on your own? For each practice problem below, first decide whether borrowing is needed, then subtract. You can check your answers at the bottom of the page.

Problem 1

4\(\Large\frac{2}{3}\) − 2\(\Large\frac{1}{4}\).

Problem 2

6\(\Large\frac{1}{10}\) − 3\(\Large\frac{7}{10}\).

📕 You May Also Like: 5 Ways Math Practice Impacts Brain Development + Benefits

Mathnasium tutors help students build problem-solving skills and greater independence in math by guiding them through the reasoning instead of simply giving them the correct answer.

How Mathnasium Helps Students Make Sense of Mixed-Number Subtraction (and Beyond)

Mathnasium is a math-only learning center dedicated to helping K–12 students of all skill levels excel in math. 

We help students build true understanding of math concepts, including mixed-number subtraction and its connection to equivalent fractions, so they can see why the method works instead of simply memorizing procedures.

To support that understanding, we use the Mathnasium Method™, our proprietary teaching approach, to meet students where they are and guide them forward step by step. 

Each student begins with a diagnostic assessment that helps us understand their current skill level, knowledge gaps, goals, and how they think and feel about math. 

Using these insights, we create a personalized learning plan focused on the skills the student needs most, whether that means reinforcing fraction equivalence, building fluency with mixed numbers, or preparing for more advanced fraction operations.

Our specially trained tutors follow the plan closely and provide live, face-to-face instruction in a caring and fun group environment. They use mental, verbal, visual, tactile, and written techniques to help students see how whole numbers and fractions fit together and why regrouping preserves the value of a mixed number.

Students also get room to think through problems before tutors step in. Our tutors guide students through the reasoning process instead of simply giving them the correct answer. This helps students build problem-solving skills, critical thinking, and greater independence in math.

Fun is part of the approach, too. Game-based activities, rewards, and consistent encouragement help students stay engaged as they build fraction fluency and become more comfortable with mixed-number operations.

Families see the difference:

• 94% of parents report an improvement in their child's math skills and understanding

• 93% of parents report their child's improved attitude toward math after attending Mathnasium

• 90% of students saw an improvement in their school grades

With over 1,100 learning centers across North America, there is likely a Mathnasium close to you.

For families in and near Irvine, Mathnasium of University Irvine brings that same approach close to home, with specially trained tutors who help students make sense of mixed numbers, fraction operations, and the skills that build from them.

Whether your child needs to work on foundational concepts, keep up with current coursework, or get ahead, a free diagnostic assessment is a great place to start. Using what we learn, we create a personalized learning plan focused on the skills they need next.

📅 Schedule a Free Assessment at Mathnasium of University Irvine

Pssst… Check Your Answers Here

Here are the answers to the practice problems above.

Problem 1

4\(\Large\frac{2}{3}\) − 2\(\Large\frac{1}{4}\) = 2\(\Large\frac{5}{12}\):

1. Rewrite the fractions with a common denominator of 12: \(\Large\frac{2}{3}\) = \(\Large\frac{8}{12}\) and \(\Large\frac{1}{4}\) = \(\Large\frac{3}{12}\). 

2. Since \(\Large\frac{8}{12}\) is greater than \(\Large\frac{3}{12}\), we don’t need to borrow. 

3. Then, we subtract the fractions, \(\Large\frac{8}{12}\) - \(\Large\frac{3}{12}\) = \(\Large\frac{5}{12}\), and the whole numbers,  4 − 2 = 2. 

4. We put the results together and get: 2\(\Large\frac{5}{12}\).

Problem 2

6\(\Large\frac{1}{10}\) − 3\(\Large\frac{7}{10}\) = 2\(\Large\frac{2}{5}\):

1. The fractions already have a common denominator of 10. 

2. Since \(\Large\frac{1}{10}\) is less than \(\Large\frac{7}{10}\), we need to borrow. We borrow 1 whole from 6, so 6\(\Large\frac{1}{10}\) becomes 5\(\Large\frac{11}{10}\).

3. Then, we subtract the fractions, \(\Large\frac{11}{10}\) − \(\Large\frac{7}{10}\) = \(\Large\frac{4}{10}\), and the whole numbers, 5 − 3 = 2.

4. We put the results together to get 2\(\Large\frac{4}{10}\), which simplifies to 2\(\Large\frac{2}{5}\).