Decimals

Solving multiplication problems with decimals

Multiplying decimal numbers is a lot like multiplying larger numbers. If you divide the large problem into a few smaller ones, it will be easier to solve. Let's see how this works by solving this problem: 2.3 x 4.

Click through the slideshow to learn how to multiply decimals.

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  To solve our problem, we'll use a familiar tool: the times table.

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  When multiplying stacked numbers, start with the right digit on the bottom. The bottom number only has one digit: 4.

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  We'll multiply 4 by the top number, 2.3. Since there's no 2.3 in the times table, we'll have to multiply one digit at a time.

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  As usual, we'll solve the problem from right to left. So, we'll multiply 4 by the digit on the top right. Here, that's 3.

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  Now it's time to solve 4 x 3. We can use the times table.

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  4 x 3 is 12, but there's no room to write both digits underneath the 4 and 3.

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  Remember, this means we'll have to carry. We learned about carrying numbers in the lesson on multiplying larger numbers.

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  We'll write the right digit, 2, under the line...

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  We'll write the right digit, 2, under the line...then we'll carry the left digit, 1, up to the next set of digits in the problem.

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  Now it's time for the next step. We'll multiply 4 x 2.

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  4 x 2 = 8. But we won't write 8 under the line yet. Remember, there's one more step.

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  We need to make sure we add the number we carried: 1.

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  We'll set up our addition problem.

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  1 + 8 = 9.

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  We'll write 9 beneath the line.

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  In our problem, we multiplied a decimal number: 2.3. This means our answer will also need to be a decimal number.

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  Let's figure out where to put the decimal point (.).

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  In the problem, 2.3 has one digit to the right of the decimal point.

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  This means our answer will also have one digit to the right of the decimal point.

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  We'll place the decimal point so that only one digit is to the right: the 2.

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  Our problem is solved. The total is 9.2. We know that 2.3 x 4 = 9.2. We can read this answer as nine and two-tenths.

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  Let's try another problem. This time we'll multiply money: $3.05 x 2.

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  First, we'll multiply the bottom number, 2, by the digit on the top right. That's 5.

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  2 x 5 = 10.

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  We'll write the 0 under the line...

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  We'll write the 0 under the line...and carry the 1. We'll place it above the next digit.

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  The next digit is 0.

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  Anything times zero is zero, so we know that 2 x 0 = 0.

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  Remember, we need to make sure we add the 1 that we carried.

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  0 + 1 = 1. We'll write 1 beneath the line.

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  Finally, we'll multiply 2 and 3.

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  2 x 3 = 6, so we'll write 6 beneath the line.

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  It's time to place our decimal point. We need to count the digits to the right of the decimal point in our problem.

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  3.05 has two digits to the right of the decimal point. They're 0 and 5.

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  This means our answer will need to have two digits to the right of the decimal point.

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  We'll place the decimal point so that two digits are to the right: the 1 and the 0.

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  Finally, we'll write a dollar sign ($) to the left of the number.

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  We've solved the problem. $3.05 x 2 = $6.10. We can read this as six dollars and ten cents.

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Now you try it. Solve these multiplication problems. Remember, you can always use a times table to help.