Estimate products – multiply by larger numbers
Understanding Estimation
- Definition: Estimation is finding an approximate value rather than an exact number.
- Purpose: Helps in making quick calculations and understanding if an answer is reasonable.
Rounding Numbers
- Rounding: To simplify multiplication, round numbers to the nearest ten, hundred, or thousand.
- Examples:
- Round 48 to 50: For 48 × 6, estimate 50 × 6 = 300.
- Round 235 to 200: For 235 × 4, estimate 200 × 4 = 800.
Using Compatible Numbers
- Definition: Numbers that are easy to multiply mentally.
- Examples:
- Round 49 to 50 and 8 to 10: For 49 × 8, estimate 50 × 10 = 500.
Basic Multiplication Strategies
- Break Down Numbers: Use smaller, easier-to-multiply numbers.
- Example: For 27 × 8, break it into (20 × 8) + (7 × 8) = 160 + 56 = 216.
- Use Multiples of 10: If multiplying by 10, 20, etc., adjust the numbers accordingly.
- Example: For 32 × 20, estimate 30 × 20 = 600.
Estimating Products
- Check Reasonableness: After estimating, compare with the actual product to see if it makes sense.
- Examples:
- For 58 × 9: Estimate 60 × 10 = 600.
- For 134 × 5: Estimate 130 × 5 = 650.
Learn with an example
🔥 Estimate the product. Round each factor to the nearest ten, then multiply.
67 × 48
Round the first factor to the nearest ten.
67 | × | 48 | = ? |
70 | × | 48 | = ? |
Round the second factor to the nearest ten.
70 | × | 48 | = ? |
70 | × | 50 | = ? |
Now multiply:
70 × 50 = 3,500
The product is approximately 3,500.
Compare your estimate to the exact answer:
67 × 48 = 3,216
🔥 Estimate the product. Round each factor to the nearest ten, then multiply.
77 × 41
Round the first factor to the nearest ten.
77 | × | 41 | = ? |
80 | × | 41 | = ? |
Round the second factor to the nearest ten.
80 | × | 41 | = ? |
80 | × | 40 | = ? |
Now multiply:
80 × 40 = 3,200
The product is approximately 3,200.
Compare your estimate to the exact answer:
77 × 41 = 3,157
🔥 Estimate the product. Round each factor to the nearest ten, then multiply.
93 × 68
Round the first factor to the nearest ten.
93 | × | 68 | = ? |
90 | × | 68 | = ? |
Round the second factor to the nearest ten.
90 | × | 68 | = ? |
90 | × | 70 | = ? |
Now multiply:
90 × 70 = 6,300
The product is approximately 6,300.
Compare your estimate to the exact answer:
93 × 68 = 6,324
Let’s practice!🖊️