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Adding with 3 Numbers up to 100

This lesson explains how to add three two-digit numbers with sums up to 100. It covers grouping friendly pairs, making a ten, and column addition with regrouping, using a place-value diagram and a fully worked example so the steps are easy to follow and repeat.

What It Means to Add Three Numbers up to 100

Adding with three numbers up to 100 means combining three two-digit numbers, such as \( 24 + 35 + 18 \), where the total never goes above 100. The good news is that you already know how to add two numbers. Adding three numbers just means doing that same job twice: combine two numbers first, then add the third number to that result. Because of the associative property of addition, it never matters which two numbers you pick first, the final sum stays the same. This flexibility is what makes the strategies below so useful.

Strategy One: Find a Friendly Pair

Before adding in order, scan the three numbers for a pair that is easy to combine, especially one that makes a ten. Look at the ones digits: if two of them add up to 10, pairing those numbers first turns the problem into a much simpler one.

For example, add \( 45 + 25 + 12 \). Look at the ones digits: 5 and 5 make a ten, so pair \( 45 \) and \( 25 \) first.

\( 45 + 25 = 70 \)

Then add the remaining number.

\( 70 + 12 = 82 \)

So \( 45 + 25 + 12 = 82 \). Spotting the friendly pair turned a three-number problem into two simple steps. This is the same idea used when adding with doubles up to 100, where matching numbers make the sum quicker to find.

Strategy Two: Add in Column Form with Regrouping

When no obvious friendly pair appears, stack the numbers by place value and add straight down. Add the ones column first. If that total is 10 or more, write the ones digit and carry the extra ten into the tens column. Then add the tens column, including any number you carried.

Try \( 24 + 35 + 18 \).

Adding the ones column first (4 + 5 + 8 = 17) means writing the 7 and carrying a 1 into the tens column.

Add the ones: \( 4 + 5 + 8 = 17 \). Write 7 in the ones place and carry 1 into the tens column. Add the tens, including the carried ten: \( 2 + 3 + 1 + 1 = 7 \). Reading the columns gives a final sum of 77, so \( 24 + 35 + 18 = 77 \).

Choosing a Strategy

Both methods lead to the same answer, so the best choice depends on the numbers in front of you. If the ones digits combine easily into a ten, group that friendly pair first. If nothing stands out, line the numbers up by place value and add column by column, carrying whenever a column totals 10 or more. Comparing this problem to adding digits up to 100 with just two numbers shows that the extra step is really just repeating the same column addition one more time. If you would rather check a sum visually, using a number line to add up to 100 is another reliable way to confirm your total.

Practice Tips

Before adding, always scan all three ones digits for a pair that reaches 10. This single habit turns many hard-looking problems into a two-step calculation. When you do use column addition, write the numbers neatly under one another by place value so ones stay lined up with ones and tens with tens, since a shifted digit is the most common source of mistakes. Finally, estimate first by rounding each number to the nearest ten. If your exact answer is far from that rough estimate, recheck your work.

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