Repeated Addition as Multiplication Up to 99

Repeated addition happens whenever you add the same number to itself over and over. For example, \( 7 + 7 + 7 \) is repeated addition because the number 7 appears three times. Instead of adding one number at a time, it helps to notice a pattern: the same amount is being repeated a certain number of times.

This pattern is exactly what multiplication describes. Multiplication is a shortcut for repeated addition, so once you can see the repeating group, you can turn the whole addition sentence into a much shorter multiplication statement.

Every repeated addition sentence has two important pieces of information: how many groups there are, and how many are in each group. If a number repeats \(n\) times, and that number is \(g\), then:

\( g + g + g + \dots + g = n \times g \)

For example, \( 6 + 6 + 6 + 6 = 4 \times 6 = 24 \). Here \(g = 6\) is the size of each group, and \(n = 4\) is the number of groups (or the number of times 6 is added). Learning to read a multiplication statement this way makes it much faster to work with larger totals up to 99.

Picture four equal groups of 5 dots each. Adding them one group at a time gives \( 5 + 5 + 5 + 5 = 20 \). Counting the groups instead gives \( 4 \times 5 = 20 \), the same total written a shorter way.

This is the same idea used when counting groups and arrays, where objects are arranged in neat rows and columns so the total is easy to check both ways.

Example 1: Write \( 9 + 9 + 9 \) as a multiplication statement.

The number 9 repeats 3 times, so \( 9 + 9 + 9 = 3 \times 9 = 27 \).

Example 2: A classroom has 8 tables with 6 chairs at each table. Write the total as repeated addition and as multiplication.

Repeated addition: \( 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 \) (6 added 8 times). Multiplication: \( 8 \times 6 = 48 \) chairs in total.

Example 3: Ribbons are cut in pieces of 11 centimetres. If there are 9 pieces, how long is the ribbon altogether?

Adding 11 nine times gives \( 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 + 11 = 99 \), which matches \( 9 \times 11 = 99 \). Since 99 is the largest total in this range, it is a useful check that the repeated addition and the multiplication agree.

Adding the same number many times can get slow once the numbers grow. Instead of writing out every addend, you can jump straight to the total by skip counting, landing on each multiple of the group size until you reach the right number of groups. This is a faster path to the same multiplication answer.

Seeing multiplication as repeated addition builds the foundation for every multiplication fact learned later. Once a student can turn \( g + g + \dots + g \) into \( n \times g \) confidently, multiplying larger numbers, working with arrays, and solving word problems all become much more manageable, even as totals grow closer to 99 and beyond.

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• Math 2