Multiply a decimal by a one-digit whole number
Multiplying a decimal by a whole number is just like repeated addition. It's like buying 3 candy bars that cost $1.25 each. You can add $1.25 + $1.25 + $1.25, or you can use this simple multiplication trick!
Do this: Read the concept below, then try the quiz or activity.
Concept
There are a few great ways to think about multiplying a decimal by a whole number.
Method 1: The "Ignore and Place" Method This is the fastest method for getting an answer.
1. Ignore the decimal point and multiply the numbers as if they were both whole numbers. 2. Count how many decimal places were in your original decimal number. 3. Place the decimal point back into your answer so it has the same number of decimal places.
Example: 3.5 x 4
1. Ignore & Multiply: 35 x 4 = 140. 2. Count: The number 3.5 has one decimal place. 3. Place: Put one decimal place in your answer: 14.0. * Result: 14.0 or just 14.
Example 2: 1.25 x 3
1. Ignore & Multiply: 125 x 3 = 375. 2. Count: The number 1.25 has two decimal places. 3. Place: Put two decimal places in your answer: 3.75. * Result: 3.75
Method 2: Repeated Addition This helps you understand *why* it works.
* 3.5 x 4 is the same as adding 3.5 four times:
3.5 + 3.5 + 3.5 + 3.5 = 14.0* 1.25 x 3 is the same as adding 1.25 three times:
1.25 + 1.25 + 1.25 = 3.75Method 3: Think About Money This is very intuitive for decimals with one or two places.
* Problem: 0.75 x 4 * Think: 0.75 is like 75 cents (three quarters). * Four groups of three quarters is twelve quarters. * Twelve quarters is equal to $3.00. * So, 0.75 x 4 = 3.00 or 3.
Key Idea: All three methods give you the same answer! Use the "Ignore and Place" method for speed, and use the other two methods to check your work and make sure it makes sense.
Try it
Practice multiplying decimals by whole numbers!
Use any method to solve: 1. 2.5 x 3 = ? 2. 4.2 x 5 = ? 3. 8.1 x 7 = ? 4. 0.5 x 6 = ?
Problems with two decimal places: 5. 3.25 x 2 = ? 6. 1.50 x 4 = ? 7. 0.25 x 5 = ? 8. 6.08 x 3 = ?
Word Problems: 9. A pencil costs $0.45. How much would 5 pencils cost? 10. A bottle of juice holds 2.5 liters. How many liters are in 6 bottles? 11. If you run 1.8 miles every day, how many miles will you run in one week (7 days)?
Challenge Problems: 12. A bag of apples weighs 3.5 pounds. You buy 3 bags. You also buy a bag of oranges that weighs 4.2 pounds. What is the total weight of all the fruit? (This is a multi-step problem!) 13. Which is greater: 0.25 x 8 or 0.5 x 3?