Multiplying by Multiples of 10 and 100
Multiplying by multiples of 10 and 100 in Grade 4 math uses a shortcut: multiply the non-zero leading digits, then append all the zeros from the multiple to the product. For example, 4 × 300: first 4 × 3 = 12, then add two zeros to get 1,200. Covered in Chapter 5 of Saxon Math Intermediate 4, this technique extends the single-digit times-10 rule to more complex factors and is essential for mental estimation and multi-digit multiplication.
Key Concepts
Property When multiplying by multiples of 10 and 100, we focus our attention on the first digit of the multiple. Then, we write as many zeros in the product as there are in the multiple of 10 or 100.
Examples To solve $4 \times 300$, first calculate $4 \times 3 = 12$. Then, add the two zeros from 300 to get $1200$. To solve $7 \times 50$, first calculate $7 \times 5 = 35$. Then, add the zero from 50 to get $350$. To solve $8 \times 500$, first calculate $8 \times 5 = 40$. Then, add the two zeros from 500 to get $4000$.
Explanation Become a math wizard! Multiply the front digits, then count all the zeros in the original problem and attach them to the end of your answer. It's a simple trick for solving huge problems in your head, making you look like a genius.
Common Questions
How do you multiply by a multiple of 10?
Multiply the non-zero digits first, then attach the zeros. For 7 × 50: 7 × 5 = 35, then add one zero to get 350.
How do you multiply by a multiple of 100?
Multiply the non-zero digits, then attach two zeros. For 8 × 500: 8 × 5 = 40, then add two zeros to get 4,000.
Why does this shortcut work?
Because 300 = 3 × 100, multiplying 4 × 300 is the same as 4 × 3 × 100 = 12 × 100 = 1,200. The zeros represent factors of 10 that accumulate at the end of the product.
When do Grade 4 students learn multiplying by multiples of 10 and 100?
This shortcut is covered in Chapter 5 of Saxon Math Intermediate 4, after students have mastered the basic times-10 rule.
How does this skill help with estimation?
When estimating products, you often round factors to multiples of 10 or 100 and then use this shortcut to multiply quickly in your head.
What is a common mistake when multiplying by multiples of 10?
Forgetting to count and attach all the zeros. For 6 × 400, 6 × 4 = 24, and 400 has two zeros, so the answer is 2,400—not 240.