Estimating Sums and Differences

Sometimes in math, you don't need the exact answer—you just need to know about how much something is. This is called estimating. Estimating is a fast and easy way to find a number that is close to the exact answer.

To estimate sums (addition) and differences (subtraction), we use rounding.

How to Estimate by Rounding

When estimating sums and differences, the easiest method is to round each number to the nearest ten before you add or subtract.

Remember the rounding rule:

• Look at the digit in the ones place.
• If it is $0, 1, 2, 3,$ or $4$, round down (keep the tens digit the same and change the ones to zero).
• If it is $5, 6, 7, 8,$ or $9$, round up (add one to the tens digit and change the ones to zero).

Example 1: Estimating a Sum

Let's estimate: $47 + 32 \approx ?$

(Note: The squiggly equals sign $\approx$ means "is approximately equal to".)

1. Round the first number: $47$ has a $7$ in the ones place, so it rounds up to $50$.
2. Round the second number: $32$ has a $2$ in the ones place, so it rounds down to $30$.
3. Add the rounded numbers: $50 + 30 = 80$

So, $47 + 32 \approx 80$.

Example 2: Estimating a Difference

Let's estimate: $83 - 29 \approx ?$

1. Round the first number: $83$ has a $3$ in the ones place, so it rounds down to $80$.
2. Round the second number: $29$ has a $9$ in the ones place, so it rounds up to $30$.
3. Subtract the rounded numbers: $80 - 30 = 50$

So, $83 - 29 \approx 50$.

Why Do We Estimate?

Estimating is a great tool for mental math! If you are buying a toy for $56$ cents and a piece of candy for $38$ cents, you can quickly think "$60 + 40 = 100$ cents" to make sure you have enough money. It also helps you check your exact addition and subtraction to see if your final answer makes sense.