Pregunta
- How does multiplying both the dividend and the divisor by a
factor of 10 sometimes make a problem easier to solve?
factor of 10 sometimes make a problem easier to solve?
Ask by Bolton Salazar. in the United States
Jan 30,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
Multiplying both the dividend and divisor by 10 turns decimals into whole numbers, making the division easier to solve without changing the result.
Solución
Multiplying both the dividend and the divisor by a factor of 10 (or any power of 10) can simplify a division problem by eliminating decimals, making the numbers easier to work with. Here’s how and why this works:
Understanding the Concept
-
No Change in the Quotient:
- When you multiply both the dividend (the number being divided) and the divisor (the number you are dividing by) by the same factor, the ratio between them remains unchanged. This means the quotient (the result of the division) stays the same.
- Example:
- Original Problem:
- Multiply both by 10:
- Both
and equal 6.
- Original Problem:
-
Eliminating Decimals:
- Dividing numbers with decimals can be cumbersome, especially without a calculator. Multiplying both numbers by a factor of 10 (or 100, 1000, etc.) moves the decimal point to the right, converting them into whole numbers.
- Example:
- Original Problem:
- Multiply both by 10:
- Multiply again by 10 if needed:
simplifies to or 8.5.
- Original Problem:
-
Simplifying Mental Math or Manual Calculations:
- Whole numbers are generally easier to divide mentally or by hand compared to numbers with decimals.
- Example:
- Original Problem:
- Multiply both by 10:
- Original Problem:
Benefits
- Ease of Calculation: Whole numbers reduce the complexity of division.
- Reduced Errors: Eliminating decimals minimizes the chances of making mistakes in manual computations.
- Consistency: This method can be consistently applied to various division problems involving decimals.
Conclusion
Multiplying both the dividend and the divisor by a factor of 10 (or another power of 10) is a strategic way to simplify division problems, especially those involving decimals. By converting them into whole numbers, the calculations become more straightforward, faster, and less prone to error.
Example for Clarity:
Let’s take the division problem
.
-
Original Division:
-
-
Multiply Both by 10:
-
So,
.
This method made the division simpler by removing the decimal points.
Answer Summary:
Because multiplying both numbers by 10 shifts decimals and turns them into whole numbers without changing the quotient, it simplifies the division by making the dividend and divisor easier to work with.
Respondido por UpStudy AI y revisado por un tutor profesional
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Beyond the Answer
Multiplying both the dividend and the divisor by 10 is a clever trick that simplifies the numbers you’re working with! For example, if you’re dividing 50 by 5, changing it to 500 divided by 50 may help visualize the problem more clearly—especially when dealing with decimals. Bigger numbers can sometimes be easier to manipulate, especially when they align with our base-10 number system!
Additionally, this method aligns nicely with our everyday experiences. Think about money; when you’re calculating prices, it’s common to convert cents into dollars. By scaling up your numbers, you can avoid fractions and arrive at a solution more efficiently while keeping your calculations neat and tidy!
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