# Repeated Addition - Multiplication

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## Repeated Addition – Definition

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 = 12 is the repeated addition equation of two added to itself six times. We can recognise multiplication as a shorter way to write repeated addition. This is how repeated addition is like multiplication. Therefore, multiplication can always be written as repeated addition.

## Multiplication by Repeated Addition

In multiplication, we start with two numbers. The first number tells us how many times we should add the second number together to find the answer, or product. Repeated addition is actually the operation of multiplication expressed as addition. So, we can use repeated addition for multiplication problems. Repeated addition and multiplication sentences can be used to help find products.

## Repeated Addition – 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 number. This number tells us how many spaces to make.

Next, look at the second number. This tells us what number to write in each of the spaces.

Then, write addition signs between each number.

Finally, calculate the sum to determine the product of the original equation.

## Repeated Addition Sentences

A repeated addition sentence is the expression of a number added to itself multiple times. So, how does repeated addition work? For example, 5 x 3 could be written as 5 + 5 + 5 = 15. This 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 examples showing repeated addition problems in order to help understanding multiplication using repeated addition.

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 number to determine
how many spaces to make.
2 Look at the second number 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 find repeated addition KS1 resources. Try these repeated addition word problems and repeated addition activities now. You can also find a repeated addition worksheet too!

## Frequently Asked Questions concerning Repeated Addition

What does repeated addition look like?
What is a repeated addition sentence?

### TranscriptRepeated Addition - Multiplication

"Welcome back to 'Stuff Your Cheeks with Mr. Squeaks!' "During the break, I finished spreading the sauce on 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." Uh-oh, 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 are finding out how many lots of something we need. The FIRST number tells us how many times we should add the SECOND number 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 number THREE, tells us to make three spaces. Then, the second number, NINE, tells us how many belong 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 twenty-seven. The product of three times nine is twenty-seven. Chef Squeaks will need twenty-seven slices of pepperoni for this recipe, nine pieces for each of the three pizzas! His second recipe card says mozzeralla 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!

## Repeated Addition - Multiplication exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Repeated Addition - Multiplication.
• ### Using repeated addition and multiplication.

Hints

There 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.

Solution

There are 5 pizzas in total.

There are 4 slices of pepperoni on each.

This can be seen as 5 lots of 4 pepperoni slices or 5 x 4.

It can also be solved by adding the pepperoni slices from each of the 5 pizzas together, 4 + 4 + 4 + 4 + 4.

• ### Use repeated addition and multiplication.

Hints

How many groups are there? This is your first factor.

How many are in each group? This is your second factor.

Solution

There 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.

Hints

One 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?

Look at this image of the pizzas to help you find the repeated addition.

Solution

3 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 in finding the total number of toppings.

Hints

Remember that the first factor in a multiplication is how many groups there are. The second factor is how many within 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.

Solution

To 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 lots 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 lots of 4, so 4 + 4 + 4.
• ### Find how many pepperonis are on the pizzas.

Hints

Start by checking how many pizzas there are altogether. Then look at how many pepperoni slices are on each pizza.

There are 3 pizzas, each with 5 slices of pepperoni.

Solution

There are 3 pizzas each with 5 pepperoni slices.

3 x 5 = 15

5 + 5 + 5 = 15

• ### Match the number sentences to the correct image.

Hints

How many groups (pizzas) are there? If there are 6 groups (6 pizzas) then you need to have 6 addends. _+_+_+_+_+_

'Lots of' means times/multiply. So 5 lots 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

Solution

The first image is of 5 pizzas each with 7 toppings

5 x 7

5 lots of 7

7 + 7 + 7 + 7 + 7

The second image is of 6 pizzas each with 5 toppings

6 x 5

6 lots of 5

5 + 5 + 5 + 5 + 5 + 5