Multiplying by multiples of 10
Multiplying by Multiples of 10 in Grade 4 Saxon Math Intermediate 4 gives students a two-step strategy for problems like 34 x 20. Because 20 = 2 x 10, students break the multiple of 10 into its single-digit factor and 10, compute 34 x 2 = 68, then multiply by 10 to get 680. This factoring approach simplifies mental calculation and connects to place value: multiplying by 10 shifts every digit one place to the left. For example, 25 x 30 becomes 25 x 3 x 10 = 75 x 10 = 750. The chapter also teaches the hang-out-the-zero column method for written work.
Key Concepts
To multiply a number by a multiple of 10, like 20, you can first break the multiple into its factors. For example, since 20 is equal to $2 \times 10$, you can solve $34 \times 20$ by calculating $34 \times 2 \times 10$. This turns one big multiplication problem into two smaller, more manageable steps.
Example 1: Solve $25 \times 30$ by factoring. First, rewrite 30 as $3 \times 10$. The problem becomes $25 \times 3 \times 10$. Then, calculate $25 \times 3 = 75$. Finally, multiply by 10 to get $75 \times 10 = 750$. Example 2: To solve $12 \times 30$, we can express it as $12 \times 3 \times 10$. First, $12 \times 3 = 36$. Then, $36 \times 10 = 360$.
Think of this as a strategic detour! Instead of tackling a big number like 40 all at once, you can multiply by 4 first, which is much easier, and then multiply that result by 10. It’s like breaking a long journey into two short, easy trips, ensuring you arrive at the correct answer without getting lost in large numbers.
Common Questions
How do you multiply a number by a multiple of 10 like 30?
Factor the multiple of 10: 30 = 3 x 10. Multiply by 3 first (e.g., 25 x 3 = 75), then multiply by 10 by appending a zero: 750.
What is the hang-out-the-zero method?
When setting up a column multiplication with a number ending in zero, bring the zero straight down to the answer row first, then multiply the remaining digits normally.
Why does multiplying by 10 add a zero to a number?
Multiplying by 10 promotes every digit one place value to the left. The zero is a placeholder to fill the now-empty ones place.
What is 125 x 40?
Factor 40 = 4 x 10. Multiply 125 x 4 = 500. Then multiply by 10: 500 x 10 = 5,000.
What is the most common mistake when multiplying by multiples of 10?
Forgetting the final step of multiplying by 10. Students sometimes just multiply by the single-digit factor and omit the zero, getting an answer 10 times too small.