Adding with Doubles Up to 1000

A doubles fact is an addition problem where both numbers being added are the same, such as \( 3 + 3 = 6 \) or \( 7 + 7 = 14 \). These facts are some of the easiest addition facts to memorize because each one only has one number to remember instead of two. Once you know your doubles facts from \( 1 + 1 \) up to \( 9 + 9 \), you can use them to add much bigger numbers, all the way up to 1000, without doing long addition on paper.

Every number up to 1000 is built from hundreds, tens, and ones. Because addition respects place value, doubling a number made of neat hundreds or tens is really just doubling a small number and then attaching zeros back on. For example, since \( 4 + 4 = 8 \), it follows that:

\( 40 + 40 = 80 \)

\( 400 + 400 = 800 \)

Each time, the digit pattern from the doubles fact stays the same, only the place value changes. This connects directly to skills used when working with addition with tens and ones, where numbers are also handled by their place value parts.

Doubles Facts to Know First

Notice \( 500 + 500 \) lands exactly on 1000, which is the largest doubles sum this strategy reaches while staying within a three-digit result.

Most numbers up to 1000 are not neat multiples of 10 or 100. For a number like 350, split it into its place value parts first, double each part, then add the results back together. This is the same splitting idea used in simplifying addition by separating, applied specifically to doubling.

Worked Example 1: \( 350 + 350 \)

Step 1: Split 350 into 300 and 50.

Step 2: Double each part separately. \( 300 + 300 = 600 \) and \( 50 + 50 = 100 \).

Step 3: Add the two doubled parts together. \( 600 + 100 = 700 \).

So \( 350 + 350 = 700 \).

Worked Example 2: \( 480 + 480 \)

Step 1: Split 480 into 400 and 80.

Step 2: Double each part. \( 400 + 400 = 800 \) and \( 80 + 80 = 160 \).

Step 3: Add the parts. \( 800 + 160 = 960 \).

So \( 480 + 480 = 960 \).

Worked Example 3: \( 273 + 273 \)

Step 1: Split 273 into 200, 70, and 3.

Step 2: Double each part. \( 200 + 200 = 400 \), \( 70 + 70 = 140 \), and \( 3 + 3 = 6 \).

Step 3: Add all three doubled parts together. \( 400 + 140 = 540 \), then \( 540 + 6 = 546 \).

So \( 273 + 273 = 546 \).

Because doubling a number is the same as multiplying it by two, you can check a doubles sum by asking whether the answer is exactly twice the original number. For \( 480 + 480 = 960 \), notice that \( 960 \div 2 = 480 \), which matches. This quick check works well alongside addition using mental strategies, since doubling is one of the fastest mental strategies for addition once the basic facts are memorized.

• Memorize the doubles facts from \( 1 + 1 \) to \( 9 + 9 \) first, since every larger doubles problem is built from these.
• Always split a number by place value before doubling if it is not a round number of hundreds or tens.
• Add the doubled parts back together carefully, watching for sums that carry over into the next place value, such as \( 70 + 70 = 140 \).
• Practice with a mix of round numbers (like 600) and mixed numbers (like 340) so both cases feel familiar.

Related lessons

• Math 3