Repeated Addition: Multiplication
Basics on the topic Repeated Addition: Multiplication
Repeated Addition
Repeated addition is a strategy used to solve multiplication problems. Every multiplication problem can be rewritten as a repeated addition sentence. Repeated addition is what we call the addition of a number to itself many times. For example, 2 + 2 + 2 + 2 + 2 + 2 = 6x2 is the repeated addition equation of two added to itself six times. We can recognize multiplication as a shorter way to write repeated addition. This is how repeated addition is like multiplication. Thus, multiplication can always be written as repeated addition.
Repeated Addition and Multiplication
In multiplication, we call the numbers being multiplied together factors. The first factor tells us how many times we should add the second factor together to find the answer, or product. Repeated addition is actually the operation of multiplication expressed as addition. So, we can use repeated addition to solve multiplication problems. Repeated addition and multiplication sentences can be used to help find products.
Repeated Addition and Multiplication – Strategy
Multiplication is related to repeated addition so we can restate any multiplication equation as a repeated addition one:
Begin by looking at the first factor. This number tells us how many spaces to make.
Next, look at the second factor. This tells us what number to write on the spaces.
Then, write addition signs between each number.
Finally, calculate the sum to determine the product of the original equation.
Repeated Addition Sentences and Multiplication
A repeated addition sentence is the expression of a number added to itself multiple times. So, what does repeated addition mean? For example, it means 5 + 5 + 5 = 15 is the repeated addition sentence for five added to itself three times. Repeated addition could also be used as a strategy to solve 5x3.
Repeated Addition – Example
Below are repeated addition examples.
A general example of a repeated addition problem.
Multiplication with a repeated addition model.
Repeated Addition – Summary of Steps
The following steps describe how you can solve multiplication problems with repeated addition:
Step #  What to do 

1  Look at the initial factor to determine how many spaces to make. 
2  Look at the second factor to determine what number to write on the spaces. 
3  Write addition signs between each number. 
4  Calculate the sum to determine the product of the original multiplication equation. 
Have you practiced yet? On this website, you can also find 3rd grade and primary resources on repeated addition. Try these word problems and activities on multiplication with repeated addition now. There are many repeated addition worksheets with pictures as well.
Frequently Asked Questions regarding Repeated Addition
Transcript Repeated Addition: Multiplication
"Welcome to back to 'Stuff Your Cheeks with Mr. Squeaks!' "Over the commercial break, I finished saucing our pizzas." "They are now ready for all sorts of toppings." "Let's check our recipe cards to see how many toppings we'll need for each batch." Uhoh, Chef Squeaks has not learned multiplication yet! But, he will need to solve the equation to calculate how many toppings each batch will need! Let's help him solve his problems using "Multiplication: Repeated Addition". There is no reason for Chef Squeaks to worry every multiplication problem can be rewritten as a repeated addition problem. Multiplication is just a shorter way to write how many times we add a number to itself. In multiplication, we call the numbers being multiplied together factors. The first factor tells us how many times we should add the second factor together to find the answer, or product. For example, our first recipe card says pepperoni: three times nine. Using repeated addition, we can restate this as three groups of nine added together. The first factor, three, tells us to make three spaces. Then, the second factor, nine, tells us what number belongs in each space. Next, we write addition symbols in between the numbers. Then we can solve! Nine plus nine is eighteen plus nine more is twentyseven. The product of three times nine is twentyseven. Chef Squeaks will need twentyseven pepperonis for this recipe, nine pieces for each of the three pizzas! His second recipe card says mozzarella cheese: five times seven. Remember, using repeated addition, we can say this is five groups of seven added together. Let's begin by making five spaces. Then, put the number seven in each space. Now, write the addition signs in between the numbers. Our multiplication problem is now a repeated addition one! How do we solve it? We add seven together five times! Seven plus seven equals fourteen. Fourteen plus seven equals twentyone. Twentyone plus seven equals twentyeight. And, twentyeight plus seven equals thirtyfive. So, what is the product of five times seven? The product is thirty five! Chef Squeaks will need thirtyfive mozzarella cheese slices for this recipe seven slices for each of the five pizzas! The last recipe card says mushrooms: seven times five. This looks a lot like our last card, but something has changed. What is different about this problem from the previous recipe card? This problem says seven times five instead of five times seven. This time we have seven groups of five added together. If we write this problem using repeated addition, how many spaces should we make? We should make seven spaces. What number do we write in each space? We write the number five in each space and put the addition sign in between. How can we solve this repeated addition problem? Finally, we can add five together seven times! Let's go: five plus five equals ten. Ten plus five equals fifteen. Fifteen plus five equals twenty. Twenty plus five equals twentyfive. Twentyfive plus five equals thirty. And, thirty plus five equals thirtyfive. What is the product of seven times five? The product is also thirtyfive! The only difference is the way we grouped our numbers. So this time Chef Squeaks has seven pizzas with five microchips on each, wait microchips!? Before we figure out why there are microchips on our last pizzas, let's review. Remember, multiplication is just a shorter way of writing the addition of equal groups. Every multiplication problem can be rewritten as repeated addition. Begin by using the first factor to determine how many spaces to make. Next, use the second factor to write the number that belongs in each space. Then, put addition symbols in between. And finally, calculate the total by adding up all the numbers. The SUM is the product of the original multiplication problem! Now, who on earth would put microchips on a pizza?! Imani!!!!
Repeated Addition: Multiplication exercise

Using repeated addition and multiplication.
HintsThere are two ways to solve this: using repeated addition and using multiplication.
There are 5 pizzas, so the 4 pieces of pepperoni need to be added up 5 times.
SolutionThere are 5 pizzas in total.
There are 4 pieces of pepperoni on each.
This can be seen as 5 groups of 4 pepperoni pieces or 5 x 4.
It can also be solved by adding the pepperoni pieces from each of the 5 pizzas together, 4 + 4 + 4 + 4 + 4.

Use repeated addition and multiplication.
HintsHow many groups are there? This is your first factor.
How many are in each group? This is your second factor.
SolutionThere are 3 vases with 4 flowers
There are 3 groups. Each group has 4 parts.
3 x 4

There are 3 groups of 3 chicks
There are 3 groups. Each group has 3 parts.
3 x 3

There are 9 pairs of shoes
There are 9 groups. Each group has 2 parts.
9 x 2

There are 6 groups of 3 balloons
There are 6 groups. Each group has 3 parts.
6 x 3

There are 4 lots of 4 stars
There are 4 groups. Each group has 4 parts.
4 x 4

There are 2 lots of 3 mushrooms
There are 2 groups. Each group has 3 parts.
2 x 3

Matching repeated addition with multiplication.
HintsOne pizza with 9 toppings is a group of 9. If there are 3 groups of 9 think about how many spaces you would need and what would go in each space.
For 3 x 9 there would be 3 groups of what amount?
Look at this image of the pizzas to help you figure out the repeated addition expression.
Solution3 pizzas each with 8 slices can be written as: 3 x 8 OR 8 + 8 + 8.
For the other recipe cards:
3 x 9 = 9 + 9 + 9
4 x 5 = 5 + 5 + 5 + 5
4 x 6 = 6 + 6 + 6 + 6

Highlight the errors for finding the total number of toppings.
HintsRemember that the first factor in a multiplication expression is how many groups there are. The second factor is how many there are in each group.
For 3 x 4, what do we need to add three times?
Check that the mathematical operation symbol is correct, as well as the digits.
SolutionTo find the total number of toppings:
 For the first question, there are 3 pizzas with 9 toppings, this means we need to add 9 three times, so 9 + 9 + 9.
 For the second question, there are 4 pizzas with 5 toppings, this means we need to have 4 groups of 5 or 4 x 5.
 For the third question it says there are 3 pizzas each with 4 toppings, this means we need to add three groups of 4, so 4 + 4 + 4.

Find how many pepperonis are on the pizzas.
HintsStart by checking how many pizzas there are altogether. Then look at how many pieces of pepperoni are on each pizza.
There are 3 pizzas, each with 5 pieces of pepperoni.
SolutionThere are 3 pizzas each with 5 pieces of pepperoni.
3 x 5 = 15
5 + 5 + 5 = 15

Match the number sentences to the correct image.
HintsHow many groups (pizzas) are there? If there are 6 groups (6 pizzas) then you need to have 6 addends. _+_+_+_+_+_
'groups of' means times/multiply. So 5 groups of 6 means 5 x 6
How many items are on each pizza? This is your second factor. So 7 items would be _ x 7
SolutionThe first image is of 5 pizzas each with 7 toppings
5 x 7
5 groups of 7
7 + 7 + 7 + 7 + 7
The second image is of 6 pizzas each with 5 toppings
6 x 5
6 groups of 5
5 + 5 + 5 + 5 + 5 + 5