repeated addition — Definition, Formula & Examples
Repeated addition is adding the same number a certain number of times. For example, 3 + 3 + 3 + 3 is the same as 4 × 3 because you are adding 3 four times.
Repeated addition is the process of summing a fixed addend a specified number of times, producing a result equivalent to the product of that addend and the number of times it appears. If the addend is added times, the sum equals .
Key Formula
Where:
- = The number being added each time (the addend)
- = How many times the addend is added
How It Works
Pick the number you want to add (the addend) and decide how many times to add it (the count). Write out the addend that many times with plus signs between them, then find the total. Once you see the pattern, you can replace the long addition with a multiplication fact: count × addend. This is exactly why multiplication is often called a shortcut for repeated addition.
Worked Example
Problem: There are 5 bags with 4 apples in each bag. Use repeated addition to find the total number of apples.
Write the addition: Add 4 five times, once for each bag.
Add step by step: 4 + 4 = 8, then 8 + 4 = 12, then 12 + 4 = 16, then 16 + 4 = 20.
Write as multiplication: Because you added 4 a total of 5 times, the multiplication fact is:
Answer: There are 20 apples in all.
Why It Matters
Repeated addition is the bridge between addition and multiplication. Understanding it helps students make sense of times tables instead of just memorizing them, and it lays the groundwork for concepts like area and arrays in later grades.
Common Mistakes
Mistake: Confusing which number to repeat and how many times. For 5 × 4, students sometimes add 5 four times instead of 4 five times (or vice versa).
Correction: Both 5 + 5 + 5 + 5 and 4 + 4 + 4 + 4 + 4 give 20, so the product is the same. However, read the problem context carefully: "5 groups of 4" means add 4 five times.