**Multiplication is a shortcut to adding.** Think of it as a way to add numbers without doing it over and over again.

You can say 2 + 2 + 2, or you can say 2 x 3 (that is, 3 sets of 2) and get the same answer: 6.

**Working with larger numbers gets more difficult.**

For example, it'll be more work to add 9 + 9 + 9 than to multiply 9 x 3!

If you **haven't memorized your multiplication tables**, then multiplying 9 x 3 may be hard for you! This is where a** multiplication chart can help**.

Multiplication charts can also help with fractions and division too!

**Which tables do you not have to learn?** Dinner tables!

## Finding Patterns

**Patterns are like the building blocks of math skills!**

They **show relationships** between things and can help you understand numbers. Our very number system is a pattern based on multiplying by 10! For example, 100 is 10 times bigger than 10.

You can find a bunch of number patterns in a multiplication chart! Patterns are **repeated lineups **of numbers.

Look at these patterns:

### Even Number Pattern

**Do you know what seems odd?** Numbers that aren’t divisible by 2!

### Odd Number Pattern

Did you notice that the odd numbers chart fills in the spaces in the even numbers chart?

### Square Number Pattern

Notice the diagonal line down the center? These are **square numbers**:

2² (or "2 squared") = 2 x 2 = 4

3² (or "3 squared") = 3 x 3 = 9, and so on

Compare the numbers on either side of the diagonal line that runs across the chart above.

Do you see the **numbers are mirrored**? The same numbers are on both sides of the diagonal!

## What other patterns can you find?

Use these ideas to get you started:

### Times Tables

Starting with 1 x 1, color in the answer (product) and all the blocks on the same row/column

Then color in the row/column answer to 2 x 2 with a different color

Then 3 x 3 and so on (see the sneak peek below)

**What pattern does this make?**

Answer: It makes "L-shapes" or an arrow, depending on how you look at it!

### Boxed Numbers

Pick a number on the chart

Color the numbers around it to form a box (see the sneak peek below)

Add and subtract the corner numbers or the numbers above/below

Multiply and divide the corner numbers or the numbers above/below

**What do you notice when you add/subtract or multiply/divide the numbers?**

Answer: Some of your answers are the numbers around the center number! Most of the numbers can be divided by 4.

**Answer #3: adding/subtracting**

Corner numbers:

16 + 4 = 20

8 + 8 = 16

16 - 4 = 12

8 - 8 = 0

Above/below numbers:

12 + 6 = 18

12 - 6 = 6

**Answer #4: multiplying/dividing**

Corner numbers:

16 x 4 = 64

8 x 8 = 64

16/4 = 4

8/8 = 1

(Above/below numbers:

12 x 6 = 72

12/6 = 6

## Mutliplying Numbers

**What tool is best suited for math?** Multi-pliers!

Multiplication charts can help you easily find the product of two numbers.

### Here's how...

Work in rows and columns. Try multiplying 6 x 7:

Find 6 in the first column

Move along the row until you come to the 7 column

The number where the 6 row and 7 column meet is the product of 6 x 7, which is 42

### Challenge

See if you get the same answer when you choose 7 from the first column then follow the row to the 6 column!

## Dividing Numbers

Multiplication charts can also help you with dividing numbers.

Start by finding the number you're dividing, then follow the row/column that made that number. For example, if you want to know what two numbers or factors multiply to get 40:

Find 40 on the chart

Move up the column and across the row to get the numbers 8 and 5 — these are the factors of 40

### Challenge:

Do you see any other blocks with 40 on the chart? What factors do you get when you move along those rows/columns?

#### Quiz

What other factors multiply to get 40? Select all that apply:

## Reducing Fractions

Need to reduce a fraction? A multiplication chart can help with that!

Fractions are just division problems in disguise. And, we learned how to divide using a mutliplication chart in the last section.

Take a look at a division symbol...now replace the dots with numbers and presto, you have a fraction!

You can find this same pattern in a multiplication chart! This means you can use a multiplication chart to **find and reduce fractions**!

### To reduce a fraction using the multiplication chart...

Find the fraction in the chart — just look down the columns

Move along the rows to the left to find the reduced fraction

In the example above, the fraction was 5/10. Moving along the rows to the left, you see that 5/10 reduces to 1/2. You know this is correct because 5 is half of 10!

### What about larger fractions?

In the example below, the fraction of 28/42 is being reduced. Notice that the numbers aren't directly under each other, but if you move along the rows to the left, you still get the reduced fraction 4/6.

Here's another example:

The fraction 20/90 gets reduced to 2/9. See how easy that is!

### Challenge

The fraction 4/6 can still be reduced. Can you figure out how by using your multiplication chart?

#### Quiz

Did you figure out what 4/6 reduces to?

## Take Action

**Why did the student do multiplication problems on the floor?** The teacher told him not to use tables.

You learned how handy a multiplication table can be! Want to learn more about the multiplication table?

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