Master the art of multiplying two-digit numbers without regrouping! Learn powerful strategies that make large number multiplication easy and fun.
School Uniform Ordering Challenge! The school needs to order new sports uniforms for the students. Each uniform costs $23, and there are 32 students who need uniforms. How much money will the school need to spend? Let's help them calculate this using the powerful decomposition method!
The decomposition method breaks down a multiplication problem into smaller, easier parts. Instead of multiplying 23 × 32 all at once, we break it into simpler multiplications and then add the results together.
Think of it like this: It's like breaking a big job into smaller tasks that are easier to handle, then combining all the results at the end!
Break down the second number
Split 32 into 30 + 2 (tens and ones)
Multiply by each part separately
23 × 30 = 690 and 23 × 2 = 46
Add the results together
690 + 46 = 736
When we write the multiplication vertically, we need to be careful about place value alignment. The second line (when multiplying by the tens digit) should be shifted one place to the left.
When we multiply by the tens digit (3 in 32), we're actually multiplying by 30, not 3. That's why we shift the result one place to the left - it represents the tens place value.
23 × 2 = 46 (ones place)
23 × 30 = 690 (tens place - shifted left)
Total: 46 + 690 = 736
Answer: 14 × 21 = 294
Answer: 12 × 33 = 396
Solve these problems using the decomposition method:
A bookstore has 18 shelves, and each shelf holds 25 books. How many books are there in total?
When multiplying by the tens digit, remember to shift the result one place to the left.
Make sure you're multiplying each part, not adding the digits together.
Always verify your answer by using estimation or the decomposition method.
A school is ordering 16 boxes of pencils. Each box contains 24 pencils. How many pencils will they receive in total?
Use the vertical algorithm to solve: 22 × 13