Master the Art of Multiplying 7.8 by 5.1: Long and Shortcut Methods Explained

7.8 X 5.1

39.78

To multiply 7.8 by 5.1, you can use either the long method or the shortcut method (which involves mental math and estimation).

Using the Long Method:
1. Write the two numbers vertically, lining up the decimal points:
7.8
x 5.1
——-
2. Multiply the ones place (8 x 1), which equals 8. Write 8 in the ones column.

7.8
x 5.1
——-
8
3. Multiply the tenths place (8 x 5), which equals 40.

7. 8
x 5.1
——-
4 0
8
4. Multiply the decimal places (7 x 1), which equals 7. Write 7 in the hundredths column.

7. 8
x 5.1
——-
3 9 .
8
5. Multiply the whole numbers (7 x 5), which equals 35. Write 35 in the tens column and carry over the 3 to the next column.

7. 8
x 5.1
——-
3 9 . 7
3 5
6. Add up the products in each column to get the final answer:

39.78

Using the Shortcut Method:
1. Round each number to one decimal place, ignoring the multiplication sign:

7.8 ≈ 8
5.1 ≈ 5
2. Multiply the rounded numbers mentally:

8 x 5 = 40
3. Adjust the final answer for the difference in rounding from the actual numbers:

To adjust for the rounding, you can either add or subtract the difference between the rounded numbers and actual numbers in a percentage form or by estimation. Estimation can be done by adding or subtracting 1 for every tenth of difference. In this case, the difference in rounding is 0.3, so we can add 1 to the product:

40 + 1 = 41
4. The final answer is 41.

Therefore, 7.8 x 5.1 ≈ 39.78 (long method) or 41 (shortcut method).

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