Multiply 2-Digit by 2-Digit

Grade 4 · mathematics · 89 practice problems · read aloud

🔊 Listen to this explanation

Multiplying 2-Digit by 2-Digit Numbers

🧠 What is it and Why is it Useful?

This is when you multiply a number with two digits (like 34) by another two-digit number (like 25). It's a super useful skill for real life! You use it to find the total number of items in several boxes, calculate the area of a space, or figure out how many days are in multiple months.

📝 Step-by-Step Guide

We use a method called partial products or the standard algorithm. Let's break it down:

  1. Step 1: Write the numbers vertically, lining up the ones and tens places.
  2. Step 2: Multiply the ones digit of the bottom number by the entire top number. Write this partial product below the line.
  3. Step 3: Multiply the tens digit of the bottom number by the entire top number. Remember to write a zero (0) in the ones place first, because you're really multiplying by tens!
  4. Step 4: Add the two partial products together to get your final answer.

🔍 Visual Examples

Example 1: 34 x 25


    34

  x 25

  ————

   170   ← (4 x 5 = 20, write 0, carry 2; 3 x 5 = 15, +2 = 17)

  +680   ← (4 x 2 = 8, but it's really 20, so write 80; 3 x 2 = 6, so 600. Don't forget the zero!)

  ————

   850

Example 2: 47 x 16


    47

  x 16

  ————

   282   ← (47 x 6)

  +470   ← (47 x 10, remember the zero!)

  ————

   752

⚠️ Common Mistakes to Avoid

  • Forgetting the placeholder zero: This is the #1 mistake! When you move to multiply by the tens digit, you MUST write a zero in the ones column first.
  • Messy handwriting: If your numbers aren't lined up neatly in the correct place value columns, you'll add incorrectly.
  • Skipping the addition step: Remember, you have to add the two partial products together at the end.

💡 Tips & Tricks

  • Zero is your hero! Chant this: "When you multiply by the tens place, put a zero in the ones space!"
  • Estimate first: Round the numbers. For 34 x 25, think "30 x 30 = 900." If your answer is close, it's probably right!
  • Check your work: Multiply in the opposite order (e.g., 25 x 34 instead of 34 x 25). You should get the same answer!

🎯 How to Practice

The best way to get better is to practice a little bit every day.

  • Solve 2-3 problems each night.
  • Create your own problems about things you like (e.g., "If I have 15 packs of stickers with 12 stickers each, how many do I have total?").
  • Use online math games or flashcards to make it fun!

Practice problems

6 of the 89, worked through step by step — try them before opening the answer.

1 24 × 36 = ?

Hint: Break the problem into smaller parts by multiplying each digit separately, then combine the results.

Show the answer

Answer: 864

  1. Break 36 into tens and units. 36 = 30 + 6
  2. Multiply 24 by each part separately. First, 24 × 30: 24 × 3 = 72 Then 72 × 10 = 720 So, 24 × 30 = 720.
  3. Multiply 24 × 6: 24 × 6 = 144
  4. Add the two results together: 720 + 144 = 864.
  5. Check quickly: 24 × 36 = (20 × 36) + (4 × 36) 20 × 36 = 720 4 × 36 = 144 720 + 144 = 864. Therefore, the final answer is 864.

Let's multiply 24 × 36 step by step.

2 42 × 36 = ?

Hint: Break the problem into smaller parts by multiplying each digit separately and then combine the results.

Show the answer

Answer: 1512

  1. Multiply 42 by 6 (the ones digit of 36). 42 × 6 = 252.
  2. Multiply 42 by 30 (the tens digit of 36). 42 × 30 = 1260.
  3. Add the two partial products together. 252 + 1260 = 1512.

The answer is 1512.

3 23 × 47 = ?

Hint: Break the multiplication into smaller parts by multiplying each digit separately and then adding the results together.

Show the answer

Answer: 1081

  1. Multiply 23 by 7 (the ones digit of 47): 23 × 7 = 161
  2. Multiply 23 by 40 (the tens digit of 47): 23 × 40 = 920
  3. Add the two partial products: 161 + 920 = 1081

The answer is 1081.

4 34 × 27 = ?

Hint: Break the problem into smaller multiplication steps using place value

Show the answer

Answer: 918

  1. Multiply 34 by 7 (the ones digit of 27) 34 × 7 = 238
  2. Multiply 34 by 20 (the tens digit of 27) 34 × 20 = 680
  3. Add the two partial products together 238 + 680 = 918

The answer is 918.

5 34 × 26 = ?

Hint: Break the problem into smaller multiplication steps using place value

Show the answer

Answer: 884

  1. Multiply 34 by 20: 34 × 20 = 680
  2. Multiply 34 by 6: 34 × 6 = 204
  3. Add the partial products: 680 + 204 = 884

The answer is 884.

6 34 × 56 = ?

Hint: Break the problem into smaller multiplication steps using place value

Show the answer

Answer: 1904

  1. Multiply 34 by 6 (the ones digit of 56) 34 × 6 = 204
  2. Multiply 34 by 50 (the tens digit of 56) 34 × 50 = 1700
  3. Add the two partial products 204 + 1700 = 1904

The answer is 1904.

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