Question
Which expressions are equivalent to One-half + 3 c + StartFraction 4 Over 5 EndFraction Select three options.
3 c + StartFraction 4 Over 5 EndFraction + one-half
1 + 2 + 3c + 4 +5
StartFraction 4 Over 5 EndFraction + one-half + 3 c
2 + 3c + 4
One-half + StartFraction 4 Over c EndFraction + 3 c
3 c + StartFraction 4 Over 5 EndFraction + one-half
1 + 2 + 3c + 4 +5
StartFraction 4 Over 5 EndFraction + one-half + 3 c
2 + 3c + 4
One-half + StartFraction 4 Over c EndFraction + 3 c
Answers
GPT-4o mini
To determine which expressions are equivalent to \( \frac{1}{2} + 3c + \frac{4}{5} \), we can rearrange and simplify the options provided.
1. **Option 1**: \( 3c + \frac{4}{5} + \frac{1}{2} \)
This is simply a rearrangement of the original expression, so **this is equivalent**.
2. **Option 2**: \( 1 + 2 + 3c + 4 + 5 \)
Simplifying this gives \( 1 + 2 + 4 + 5 + 3c = 12 + 3c \). This is **not equivalent** to the original expression.
3. **Option 3**: \( \frac{4}{5} + \frac{1}{2} + 3c \)
This is another rearrangement of the original expression, so **this is equivalent**.
4. **Option 4**: \( 2 + 3c + 4 \)
Simplifying this gives \( 6 + 3c \), which is **not equivalent** to the original expression.
5. **Option 5**: \( \frac{1}{2} + \frac{4}{c} + 3c \)
This includes \(\frac{4}{c}\), which is unrelated to the original expression, making this **not equivalent**.
Thus, the three expressions that are equivalent to \( \frac{1}{2} + 3c + \frac{4}{5} \) are:
- \( 3c + \frac{4}{5} + \frac{1}{2} \) (Option 1)
- \( \frac{4}{5} + \frac{1}{2} + 3c \) (Option 3)
In conclusion, the equivalent expressions are Options 1 and 3. However, since three options are requested, it seems that only two options from those listed (1 and 3) are actually valid equivalents of the original expression.
1. **Option 1**: \( 3c + \frac{4}{5} + \frac{1}{2} \)
This is simply a rearrangement of the original expression, so **this is equivalent**.
2. **Option 2**: \( 1 + 2 + 3c + 4 + 5 \)
Simplifying this gives \( 1 + 2 + 4 + 5 + 3c = 12 + 3c \). This is **not equivalent** to the original expression.
3. **Option 3**: \( \frac{4}{5} + \frac{1}{2} + 3c \)
This is another rearrangement of the original expression, so **this is equivalent**.
4. **Option 4**: \( 2 + 3c + 4 \)
Simplifying this gives \( 6 + 3c \), which is **not equivalent** to the original expression.
5. **Option 5**: \( \frac{1}{2} + \frac{4}{c} + 3c \)
This includes \(\frac{4}{c}\), which is unrelated to the original expression, making this **not equivalent**.
Thus, the three expressions that are equivalent to \( \frac{1}{2} + 3c + \frac{4}{5} \) are:
- \( 3c + \frac{4}{5} + \frac{1}{2} \) (Option 1)
- \( \frac{4}{5} + \frac{1}{2} + 3c \) (Option 3)
In conclusion, the equivalent expressions are Options 1 and 3. However, since three options are requested, it seems that only two options from those listed (1 and 3) are actually valid equivalents of the original expression.