Two kids packing colorful art supplies into boxes at school

Multiply Multi-Digit Numbers

Maya's class is packing marker boxes for the art fair. Each box holds 24 markers, and there are 3 boxes. How many markers in all? Let's find out!

4th Grade Math

Step 1: Break Apart the Factor

Each factor is a number we multiply. The blue grid shows the tens in 24. The green group shows the ones. How do we break 24 apart by place value?

24 = 20 + 4. The digit 2 stands for 2 tens, which is 20. Breaking a factor apart makes multiplying easier!

Step 2: Multiply the Tens

3 × 20 = ?

First we multiply 3 by the tens part of 24. Think: 3 × 2 tens = 6 tens. What is 3 × 20?

3 × 20 = 60. Since 3 × 2 = 6, then 3 × 2 tens = 6 tens. That is 60, not 6!

Step 3: Multiply the Ones, Then Add

3 × 4 = 12 60 + 12 = ?

Now multiply the ones: 3 × 4 = 12. Add both parts to find the product. How many markers does Maya's class have in all?

60 + 12 = 72, so 24 × 3 = 72 markers. Tens part plus ones part gives the whole product!

See It: The Area Model

3

20 3 × 20 = 60

4 3 × 4 = 12

An area model is a rectangle split by place value. Each part holds one small product. Add the parts: 60 + 12 = 72.

The Break-Apart Strategy

          Step 1: Break the big factor apart by place value.

          Step 2: Multiply each part.

          Step 3: Add the partial products.

Watch Out!

A Common Mistake

          Some kids write 30 × 4 = 12. That is wrong!

          30 means 3 tens, so 30 × 4 = 12 tens = 120.

          Never drop the zero!

Maya says: I always analyze my answer to check the size. If 30 × 4 gave only 12, that would be smaller than 30. A product of tens should be much bigger!

Solve It!

36 × 4 = ?

Break 36 into 30 + 6. Then multiply each part by 4.

36 × 4 = 144. Tens: 30 × 4 = 120. Ones: 6 × 4 = 24. Add: 120 + 24 = 144.

Word Problem

A theater has 6 rows of seats. Each row holds 58 people. How many people can the theater hold?

58 × 6 = 348. Tens: 50 × 6 = 300. Ones: 8 × 6 = 48. Add: 300 + 48 = 348.

What Goes in the Blank?

7 × ? = 210

Determine the missing factor. Hint: 7 × 3 = 21, so think in tens!

7 × 30 = 210. Since 7 × 3 = 21, then 7 × 3 tens = 21 tens = 210.

Two Digits × Two Digits

23 × 14 = ?

Break 14 into 10 + 4. Multiply 23 by each part, then add both partial products.

23 × 14 = 322. First: 23 × 10 = 230. Then: 23 × 4 = 92. Add: 230 + 92 = 322.

Go Big: Four Digits!

2,134 × 3 = ?

Break 2,134 into 2,000 + 100 + 30 + 4. Multiply every part by 3, then add.

2,134 × 3 = 6,402. Parts: 2,000 × 3 = 6,000. 100 × 3 = 300. 30 × 3 = 90. 4 × 3 = 12. Sum: 6,402.

Challenge!

A stadium has 46 rows. Each row has 25 seats. Every seat is sold for the big game. How many tickets were sold?

46 × 25 = 1,150 tickets. First: 46 × 20 = 920. Then: 46 × 5 = 230. Add: 920 + 230 = 1,150.

Think About It

Compare the area model and the break-apart strategy. How are they alike? When might you multiply big numbers in real life?

Great Work!

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factor product area determine analyze