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Estimating Differences

This lesson explains how to estimate differences by rounding numbers before subtracting, so students can check subtraction answers quickly and solve problems without needing an exact result.

What Does It Mean to Estimate a Difference?

Estimating a difference means finding a number that is close to the answer of a subtraction problem, without doing the exact subtraction. Instead of subtracting the original numbers, you round each number first, and then subtract the rounded numbers. This gives you a fast, reasonable answer that shows about how big the difference should be.

When you estimate, you use the symbol \( \approx \) (which means "is approximately equal to") instead of an equals sign, because the answer is close but not exact. For example, \( 62 - 28 \approx 30 \) is an estimate, while \( 62 - 28 = 34 \) is the exact answer.

Why Estimate Instead of Subtracting Exactly?

Estimating is useful when you need a quick answer, when exact numbers are not important, or when you want to check whether an exact subtraction answer makes sense. If you subtract two numbers and get an answer that is very different from your estimate, that is a signal you may have made a mistake somewhere.

Estimating differences also builds on skills you already know, like rounding numbers to the nearest ten and using mental math to subtract up to 20. Once numbers are rounded to friendly values like 10, 20, 30, or 40, subtracting them becomes much easier to do in your head.

Steps to Estimate a Difference

Follow these steps every time you estimate a difference:

Look at each number in the subtraction problem.
Round each number to the nearest ten (or whatever place value the problem asks for).
Subtract the two rounded numbers using mental math.
Write the estimate using the \( \approx \) symbol.

Worked Example 1

Estimate the difference \( 78 - 43 \).

Round 78 to the nearest ten: 78 is closer to 80 than to 70, so it rounds to 80.
Round 43 to the nearest ten: 43 is closer to 40 than to 50, so it rounds to 40.
Subtract the rounded numbers: \( 80 - 40 = 40 \).

So \( 78 - 43 \approx 40 \). The exact answer, \( 78 - 43 = 35 \), is close to this estimate, which tells you the exact subtraction was likely done correctly.

Worked Example 2

Estimate the difference \( 91 - 26 \).

91 rounds to 90.
26 rounds to 30.
\( 90 - 30 = 60 \).

So \( 91 - 26 \approx 60 \).

Seeing the Rounding Step on a Number Line

The diagram below shows how each number in a subtraction problem gets rounded to its nearest ten before the subtraction happens.

Round each number to the nearest ten, then subtract the rounded numbers to get the estimate.

Estimating with Larger or Word Problems

Estimating differences also helps with word problems, where you may only need a rough idea of the answer rather than an exact count. If you have practiced mental math word problems, you already know how to pull the important numbers out of a story before working with them, and estimating works the same way: round first, then subtract.

Estimating differences pairs closely with estimating sums. Both skills use the same rounding step first; the only change is whether you add or subtract the rounded numbers afterward.

Common Mistakes to Avoid

Rounding after subtracting instead of before. Always round first, then subtract the rounded numbers.
Rounding both numbers to different place values. Round both numbers the same way, usually to the nearest ten.
Forgetting that an estimate is not the exact answer. Use \( \approx \), not \( = \), when writing an estimate.

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Math 1