To multiply decimals by whole numbers mentally, treat the decimal as a whole number during the multiplication, and then adjust the decimal place in the final answer. Here's a breakdown:
Steps for Mental Multiplication
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Ignore the decimal point: Pretend the decimal is a whole number and perform the multiplication. This simplifies the initial calculation.
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Multiply as Whole Numbers: Carry out the multiplication as you would with two whole numbers. This is usually the easier part of the mental calculation.
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Count Decimal Places: Determine the number of digits to the right of the decimal point in the original decimal number.
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Adjust the Decimal Point: In the product (your answer), count from right to left the same number of places as you found in step 3 and insert the decimal point there.
Examples
Let's illustrate with a few examples:
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Example 1: 2.5 x 3
- Step 1 & 2: Ignore the decimal and multiply: 25 x 3 = 75
- Step 3: There's one decimal place in 2.5.
- Step 4: Move the decimal point one place to the left in 75, resulting in 7.5. Therefore, 2.5 x 3 = 7.5
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Example 2: 0.12 x 4
- Step 1 & 2: Ignore the decimal and multiply: 12 x 4 = 48
- Step 3: There are two decimal places in 0.12.
- Step 4: Move the decimal point two places to the left in 48, resulting in 0.48. Therefore, 0.12 x 4 = 0.48
Tips for Mental Calculation
- Break Down Numbers: If the whole number is large, break it down into smaller, more manageable parts (e.g., multiply by 10 and then by 2 instead of by 12).
- Estimation: Before performing the exact calculation, estimate the answer. This helps you check if your final answer is reasonable.
- Practice Regularly: Mental math skills improve with practice. Try working through various examples to become more comfortable with the process.
Summary
Multiplying decimals by whole numbers mentally involves treating the decimal as a whole number during multiplication and then adjusting the decimal place in the final result based on the number of decimal places in the original decimal number. Estimation and breaking down larger numbers can make the process easier.
