Division is a fundamental operation in mathematics that can sometimes seem daunting, especially when dealing with decimals. However, with the right approach and understanding, even complex divisions can be simplified. The problem at hand is dividing 158.8 by 39.7. To tackle this, we'll go through the steps of division, focusing on accuracy and simplicity.
Understanding Division with Decimals
When dividing numbers, especially decimals, it’s crucial to align the decimal points properly and perform the division as if the numbers were whole, then adjust the decimal point in the quotient accordingly. In the case of 158.8 divided by 39.7, we first ensure that both numbers have their decimal points aligned. Since both numbers have one decimal place, we can proceed with the division.
Performing the Division
To simplify the division, let’s first convert both numbers into whole numbers by multiplying each by 10, which shifts the decimal point one place to the right. This gives us 1588 and 397. Now, we divide 1588 by 397.
| Operation | Result |
|---|---|
| 1588 ÷ 397 | 4 |
The result of dividing 1588 by 397 is approximately 4. This is because 397 multiplied by 4 equals 1588. However, since our original numbers were decimals, we must consider the placement of the decimal point in our result. Given that we multiplied both numbers by 10 to remove the decimals, our quotient remains 4, but we need to adjust for the original decimal places.
Final Calculation and Adjustment
Considering the original problem, 158.8 divided by 39.7, and our simplified calculation, the quotient is approximately 4.0. This is because the adjustment for the decimal places was inherently accounted for in our method of simplification. The result directly provides the simplified form without needing further adjustment for decimal placement.
Verification
To verify our calculation, let’s perform a quick multiplication using the quotient we found: 4 * 39.7 = 158.8. This confirms that our division result is correct and that our method of simplifying the division by temporarily removing the decimal points was effective.
| Verification Operation | Result |
|---|---|
| 4 * 39.7 | 158.8 |
This verification step is crucial as it ensures the accuracy of our division result. It's always a good practice to verify mathematical operations, especially when dealing with decimals or complex numbers.
How do I simplify division with decimals?
+To simplify division with decimals, multiply both the dividend and divisor by a power of 10 that removes the decimals, perform the division with the whole numbers, and then adjust the decimal point in the quotient if necessary. Verification through multiplication can confirm the result's accuracy.
Why is verifying division results important?
+Verifying division results is important because it ensures accuracy. By multiplying the quotient by the divisor, you can confirm that the product equals the original dividend, thus validating your division result.
In conclusion, dividing 158.8 by 39.7 can be simplified by converting the numbers to whole numbers, performing the division, and then considering the decimal placement. The result of this division is approximately 4.0, which has been verified through multiplication to ensure accuracy. This method and approach can be applied to various division problems involving decimals, making division easier and more accessible.
