Estimate The Sum Of $\frac{9}{10}+\frac{7}{8}$.A. About $\frac{1}{2}$B. About 1C. About 0D. About 2

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Introduction

Estimating the sum of fractions is an essential skill in mathematics, particularly in algebra and geometry. It involves approximating the value of a fraction by rounding it to a nearby whole number or decimal value. In this article, we will explore how to estimate the sum of two fractions, specifically $\frac{9}{10}+\frac{7}{8}$.

Understanding the Fractions

Before we can estimate the sum, we need to understand the fractions involved. The first fraction is $\frac{9}{10}$, which means 9 tenths. The second fraction is $\frac{7}{8}$, which means 7 eighths.

Estimating the Sum

To estimate the sum, we need to find a common denominator for both fractions. The least common multiple (LCM) of 10 and 8 is 40. We can rewrite both fractions with a denominator of 40:

910=3640\frac{9}{10} = \frac{36}{40}

78=3540\frac{7}{8} = \frac{35}{40}

Now, we can add the fractions:

3640+3540=7140\frac{36}{40} + \frac{35}{40} = \frac{71}{40}

Rounding the Sum

To estimate the sum, we can round the fraction to a nearby whole number or decimal value. Let's round $\frac{71}{40}$ to the nearest tenth:

7140≈1.775\frac{71}{40} \approx 1.775

Rounding to the nearest tenth gives us an estimate of 1.8.

Comparing the Estimate to the Options

Now that we have estimated the sum, let's compare it to the options:

A. About $\frac{1}{2}$ B. About 1 C. About 0 D. About 2

Our estimate of 1.8 is closest to option B, which is "About 1".

Conclusion

Estimating the sum of fractions is an essential skill in mathematics. By understanding the fractions involved and finding a common denominator, we can estimate the sum. In this article, we estimated the sum of $\frac{9}{10}+\frac{7}{8}$ and found that it is approximately 1.8, which is closest to option B, "About 1".

Tips and Tricks

Here are some tips and tricks for estimating the sum of fractions:

  • Find a common denominator: To add fractions, you need to find a common denominator. The least common multiple (LCM) of the denominators is the smallest number that both denominators can divide into evenly.
  • Round to a nearby whole number or decimal value: To estimate the sum, you can round the fraction to a nearby whole number or decimal value.
  • Use a calculator: If you have a calculator, you can use it to find the exact sum of the fractions.

Common Mistakes

Here are some common mistakes to avoid when estimating the sum of fractions:

  • Not finding a common denominator: If you don't find a common denominator, you may end up with an incorrect estimate.
  • Rounding incorrectly: If you round the fraction incorrectly, you may end up with an incorrect estimate.
  • Not using a calculator: If you don't use a calculator, you may end up with an incorrect estimate.

Real-World Applications

Estimating the sum of fractions has many real-world applications, including:

  • Cooking: When cooking, you may need to estimate the sum of fractions to measure ingredients.
  • Building: When building, you may need to estimate the sum of fractions to measure materials.
  • Science: When conducting scientific experiments, you may need to estimate the sum of fractions to measure data.

Conclusion

Introduction

Estimating the sum of fractions is an essential skill in mathematics, particularly in algebra and geometry. In our previous article, we explored how to estimate the sum of two fractions, specifically $\frac{9}{10}+\frac{7}{8}$. In this article, we will answer some frequently asked questions about estimating the sum of fractions.

Q: What is the purpose of estimating the sum of fractions?

A: The purpose of estimating the sum of fractions is to approximate the value of a fraction by rounding it to a nearby whole number or decimal value. This is useful in real-world applications, such as cooking, building, and science.

Q: How do I find a common denominator for two fractions?

A: To find a common denominator for two fractions, you need to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators can divide into evenly.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest number that two or more numbers can divide into evenly. For example, the LCM of 10 and 8 is 40.

Q: How do I round a fraction to a nearby whole number or decimal value?

A: To round a fraction to a nearby whole number or decimal value, you can use the following steps:

  1. Determine the decimal value: Convert the fraction to a decimal value by dividing the numerator by the denominator.
  2. Round to the nearest tenth: Round the decimal value to the nearest tenth.
  3. Round to the nearest whole number: If the decimal value is greater than or equal to 0.5, round up to the nearest whole number. Otherwise, round down to the nearest whole number.

Q: What are some common mistakes to avoid when estimating the sum of fractions?

A: Some common mistakes to avoid when estimating the sum of fractions include:

  • Not finding a common denominator: If you don't find a common denominator, you may end up with an incorrect estimate.
  • Rounding incorrectly: If you round the fraction incorrectly, you may end up with an incorrect estimate.
  • Not using a calculator: If you don't use a calculator, you may end up with an incorrect estimate.

Q: How do I use a calculator to estimate the sum of fractions?

A: To use a calculator to estimate the sum of fractions, follow these steps:

  1. Enter the fractions: Enter the fractions into the calculator.
  2. Add the fractions: Add the fractions using the calculator.
  3. Round the result: Round the result to the nearest whole number or decimal value.

Q: What are some real-world applications of estimating the sum of fractions?

A: Some real-world applications of estimating the sum of fractions include:

  • Cooking: When cooking, you may need to estimate the sum of fractions to measure ingredients.
  • Building: When building, you may need to estimate the sum of fractions to measure materials.
  • Science: When conducting scientific experiments, you may need to estimate the sum of fractions to measure data.

Conclusion

Estimating the sum of fractions is an essential skill in mathematics. By understanding the fractions involved and finding a common denominator, we can estimate the sum. In this article, we answered some frequently asked questions about estimating the sum of fractions. We hope this article has been helpful in understanding the concept of estimating the sum of fractions.

Tips and Tricks

Here are some tips and tricks for estimating the sum of fractions:

  • Use a calculator: If you have a calculator, use it to find the exact sum of the fractions.
  • Round to a nearby whole number or decimal value: To estimate the sum, round the fraction to a nearby whole number or decimal value.
  • Find a common denominator: To add fractions, you need to find a common denominator.

Common Mistakes

Here are some common mistakes to avoid when estimating the sum of fractions:

  • Not finding a common denominator: If you don't find a common denominator, you may end up with an incorrect estimate.
  • Rounding incorrectly: If you round the fraction incorrectly, you may end up with an incorrect estimate.
  • Not using a calculator: If you don't use a calculator, you may end up with an incorrect estimate.

Real-World Applications

Estimating the sum of fractions has many real-world applications, including:

  • Cooking: When cooking, you may need to estimate the sum of fractions to measure ingredients.
  • Building: When building, you may need to estimate the sum of fractions to measure materials.
  • Science: When conducting scientific experiments, you may need to estimate the sum of fractions to measure data.