Multiplying by Multiples of 10
Grade 4 students learn to multiply by multiples of 10 in Saxon Math Intermediate 4 Chapter 7 using the hang-out-the-zero method. For 258 × 30: let the trailing zero hang out to the right side, bring it down to the answer line first, then multiply 258 × 3 = 774, and combine to get 7,740. A library receiving 30 boxes of 258 books each receives 7,740 books. The most common error is completing the multiplication and then forgetting to attach the zero that was set aside, so students must establish the habit of bringing the zero down before computing.
Key Concepts
New Concept To multiply a whole number or a decimal number by a multiple of 10, we may write the multiple of 10 so that the zero 'hangs out' to the right.
What’s next Next, you’ll apply this 'hang out' method to multiply whole numbers, decimals, and solve word problems.
Common Questions
What is the hang-out-the-zero method for multiplying by multiples of 10?
When multiplying by a multiple of 10 (like 20, 30, 400), let the trailing zero(s) hang out to the right. Bring them straight down to the answer line first. Then multiply by the non-zero part of the multiplier.
How do you calculate 258 × 30 using the hang-out-the-zero method?
Set up 258 × 30. Let the 0 hang out. Bring the 0 down into the answer. Multiply 258 × 3 = 774. Attach: answer is 7,740.
What is the mathematical reason the method works?
Multiplying by 30 is the same as multiplying by 3 × 10. You can multiply by 3 first (258 × 3 = 774) and then multiply by 10 (shift everything one place left, or append a zero): 774 × 10 = 7,740.
How do you multiply by multiples of 100 or 1000?
Apply the same method, but with two or three zeros. For 258 × 300: bring down 00 first, then compute 258 × 3 = 774, giving 77,400. Each zero in the multiplier adds one zero to the answer.
What is the most critical step to remember when using this method?
Bring the zero down to the answer line before you start the main multiplication. This builds the habit of not forgetting it after finishing the computation, which is the most common source of errors.
What real-world problems use multiplication by multiples of 10?
Calculating the total number of items in cases of 10, 20, or 100; finding distances traveled at 60 mph for several hours; computing costs when buying in bulk; and scaling recipes all require multiplying by multiples of 10.