Hanging out the zero
When multiplying by a multiple of 10 vertically, the 'hanging out the zero' method makes calculation fast: write the zero of the multiple of 10 hanging out to the right, drop it straight down into the answer, then multiply the remaining digits normally. For example, to calculate 34 × 20: drop the 0, multiply 34 × 2 = 68, then place 68 before the 0 to get 680. This shortcut is taught in Saxon Math Intermediate 4 and is a key 4th grade multiplication strategy that speeds up multi-digit multiplication significantly.
Key Concepts
When multiplying by a multiple of 10 vertically, you can write the problem so the zero 'hangs out' to the right. First, bring the hanging zero straight down into the answer. Then, simply multiply the remaining numbers as you normally would. This is a quick and organized shortcut for these types of problems.
Example 1: To calculate $34 \times 20$, write the 20 below the 34 with the 0 hanging out. Drop the 0 into the answer. Then, multiply $34 \times 2 = 68$. The final answer is $680$. Example 2: For $45 \times 50$, let the 0 hang out and drop it down. Then, calculate $45 \times 5 = 225$. Your result is $2250$. Example 3: Solving $409 \times 70$, you drop the 0 and then multiply $409 \times 7 = 2863$. The final answer is $28630$.
Give that zero a break and let it hang out! This cool trick cleans up your workspace by letting you drop the zero straight down into the answer line. After that, you can forget about it and focus on the simpler multiplication problem that’s left over. It’s a fantastic way to keep your calculations neat and avoid simple mistakes.
Common Questions
What is the 'hanging out the zero' trick for multiplication?
When multiplying by a multiple of 10 like 20, 30, or 50, drop the zero from the multiplier straight into the ones place of your answer. Then multiply the top number by the remaining digit. For 34 × 20: drop the 0, compute 34 × 2 = 68, answer is 680.
How do you multiply a number by 20, 30, or any multiple of 10?
Write a zero in the ones place of your answer, then multiply the other number by the non-zero digit. For 45 × 30: write 0, then 45 × 3 = 135, giving 1350.
Why does multiplying by a multiple of 10 always end in zero?
Multiplying by 10 shifts every digit one place to the left, which places a 0 in the ones column. Any multiple of 10 (20, 30, 50, etc.) includes this shift, so the product always ends in at least one zero.
When do students learn to multiply by multiples of 10?
Multiplying by multiples of 10 is a 4th grade skill. Saxon Math Intermediate 4 introduces the 'hanging out the zero' technique as a fast, reliable method for these calculations.
How does this method connect to place value?
Dropping the zero represents the ones place being empty when you multiply by a ten. The remaining multiplication fills the tens, hundreds, and higher places. It is place value in action.
What are common mistakes when multiplying by multiples of 10?
Forgetting to drop the zero is the most common error, producing an answer 10 times too small. Also, students sometimes add zeros for each zero in both numbers when multiplying something like 20 × 30, which correctly gives 600 (one zero from each number).