Question
1. Which expressions are equivalent to \( 3 \frac{1}{4}-\left(-\frac{5}{8}\right) \) ? Select all that apply. A. \( 3 \frac{1}{4}-\left(\frac{5}{8}\right) \) B. \( 3 \frac{1}{4}+\left(\frac{5}{8}\right) \) C. \( 3 \frac{1}{4}+\left(-\frac{5}{8}\right) \) D. \( 3 \frac{1}{4}+\left(+\frac{5}{8}\right) \) E. \( -3 \frac{1}{4}+\left(-\frac{5}{8}\right) \) F. \( -3 \frac{1}{4}+\left(+\frac{5}{8}\right) \)
Ask by Chambers Howell. in the United States
Dec 24,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
Options B and D are equivalent to \( 3 \frac{1}{4} - \left(-\frac{5}{8}\right) \).
Solution
To determine which expressions are equivalent to \( 3 \frac{1}{4} - \left(-\frac{5}{8}\right) \), let's simplify the original expression first:
\[
3 \frac{1}{4} - \left(-\frac{5}{8}\right) = 3 \frac{1}{4} + \frac{5}{8}
\]
Now, let's evaluate each option:
**A.** \( 3 \frac{1}{4} - \left(\frac{5}{8}\right) \)
This simplifies to \( 3 \frac{1}{4} - \frac{5}{8} \), which is **not** equivalent to the original expression.
**B.** \( 3 \frac{1}{4} + \left(\frac{5}{8}\right) \)
This directly matches the simplified form \( 3 \frac{1}{4} + \frac{5}{8} \). **Equivalent.**
**C.** \( 3 \frac{1}{4} + \left(-\frac{5}{8}\right) \)
This simplifies to \( 3 \frac{1}{4} - \frac{5}{8} \), which is **not** equivalent to the original expression.
**D.** \( 3 \frac{1}{4} + \left(+\frac{5}{8}\right) \)
This also matches the simplified form \( 3 \frac{1}{4} + \frac{5}{8} \). **Equivalent.**
**E.** \( -3 \frac{1}{4} + \left(-\frac{5}{8}\right) \)
This expression has different signs and is **not** equivalent to the original expression.
**F.** \( -3 \frac{1}{4} + \left(+\frac{5}{8}\right) \)
This expression has a different sign for the whole number part and is **not** equivalent to the original expression.
**Therefore, the equivalent expressions are options B and D.**
**Answer:**
Both options **B** and **D** are equivalent to the original expression.
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Beyond the Answer
When you subtract a negative number, it’s the same as adding the positive version of that number. So, \( 3 \frac{1}{4} - (-\frac{5}{8}) \) transforms into \( 3 \frac{1}{4} + \frac{5}{8} \). Our correct choice is B! In mathematical expressions, be mindful of signs! One common mistake is confusing whether to add or subtract when dealing with negative numbers. Always remember that subtracting a negative is like giving a high-five to positivity – it’s an instant boost! So, keep that in mind to avoid unnecessary errors!
