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Part A Estimate 10/12−3/8 using benchmark values. Your equation must show the estimate for each fraction and the final estimate for the expression. (2 points) To estimate 10/12 minus 3/8 using benchmarks we round the fractions to the nearest values. For 10/12 the nearest benchmark is 9/12. For 3/8 it remains as is. Rewrite with a common denominator of 24: 9/1 x 2/2 is 18/24 and 3/8 x 3/3 is 9/24. Subtract 18 minus 9 over 24 to get 9/24. The estimate is 9/24. Question 2 Part B Solve 1012−38 . Show your solution as an equation. (2 points) 20/24​−9/24​=11/24​ Question 3 Part C Calculate the difference between your estimate in Part A and the actual value you calculated in Part B. Be sure to show this solution as an equation. Based on this difference, do you think your estimate for Part A was reasonable? Explain.

1 answer

Part A: Estimate 10/12 − 3/8 using benchmark values.

To estimate \( \frac{10}{12} - \frac{3}{8} \), we first round the fractions to nearby benchmark values.

  • For \( \frac{10}{12} \):

    • This fraction can be simply represented as \( \frac{5}{6} \) when simplified, but for estimating with benchmarks, we round it to \( 1 \) (or \( \frac{12}{12} \)) because it is close to 1.

  • For \( \frac{3}{8} \):

    • The nearest benchmark is \( \frac{1}{2} \) (or \( \frac{4}{8} \)) since \( 3/8 \) is closer to \( 1/2 \).

So, we can rewrite the estimation as follows:

\[ \frac{10}{12} \approx 1 \quad \text{(or \( \frac{12}{12} \))} \quad \text{and} \quad \frac{3}{8} \approx \frac{1}{2} \quad \text{(or \( \frac{4}{8} \))} \]

Now, we estimate:

\[ 1 - \frac{1}{2} = \frac{1}{2} \]

Final Estimate:

The estimate is \( \frac{1}{2} \).

Part B: Solve \( \frac{10}{12} - \frac{3}{8} \)

First, we rewrite both fractions with a common denominator. The least common multiple (LCM) of \( 12 \) and \( 8 \) is \( 24 \).

Convert \( \frac{10}{12} \) and \( \frac{3}{8} \) to have a denominator of \( 24 \):

  • For \( \frac{10}{12} \): \[ \frac{10}{12} \times \frac{2}{2} = \frac{20}{24} \]

  • For \( \frac{3}{8} \): \[ \frac{3}{8} \times \frac{3}{3} = \frac{9}{24} \]

Now we can subtract:

\[ \frac{20}{24} - \frac{9}{24} = \frac{11}{24} \]

Final Answer:

The exact value is \( \frac{11}{24} \).

Part C: Calculate the difference between your estimate and the actual value

The estimate from Part A is \( \frac{12}{24} \) (which is equivalent to \( \frac{1}{2} \) or \( \frac{12}{24} \)), and from Part B, the actual difference is \( \frac{11}{24} \).

To find the difference:

\[ \text{Difference} = \text{Estimate} - \text{Actual} \] \[ \text{Difference} = \frac{12}{24} - \frac{11}{24} = \frac{1}{24} \]

Reasonableness of the Estimate:

The difference between the estimate \( \frac{12}{24} \) and the actual value \( \frac{11}{24} \) is \( \frac{1}{24} \). This small difference suggests that the estimate was reasonable. It shows that our approximation method effectively captured the essence of the operation, despite not yielding the exact value. The estimate was close to the actual answer, indicating it provided a useful simplification for quick calculations.