Question

Use this information to answer the following questions.
Three expressions are shown.
Expression 1
StartFraction 576 Over 112 EndFraction
Expression 2
7 left parenthesis 8 x minus 4 right parenthesis
Expression 3
negative four halves left parenthesis 16 x minus 8 right parenthesis
Question content area bottom
Part 1
Which number is equivalent to expression 1
A.StartFraction 7 Over 36 EndFraction
StartFraction 7 Over 36 EndFraction
B.StartFraction 11 Over 576 EndFraction
StartFraction 11 Over 576 EndFraction
C.StartFraction 36 Over 7 EndFraction
StartFraction 36 Over 7 EndFraction
D.StartFraction 58 Over 112 EndFraction
StartFraction 58 Over 112 EndFraction

Answer 1

To find out which number is equivalent to Expression 1, we need to simplify Expression 1:

Expression 1 is:

\[
\frac{576}{112}
\]

To simplify this fraction, we find the greatest common divisor (GCD) of 576 and 112.

1. **Find the GCD:**
- The factors of 576 are: \( 1, 2, 3, 4, 6, 8, 9, 12, 16, 24, 36, 48, 64, 72, 144, 192, 288, 576 \)
- The factors of 112 are: \( 1, 2, 4, 7, 8, 14, 16, 28, 56, 112 \)
- The GCD of 576 and 112 is 16.

2. **Divide both the numerator and denominator by the GCD:**
\[
\frac{576 \div 16}{112 \div 16} = \frac{36}{7}
\]

So, Expression 1 simplifies to:

\[
\frac{36}{7}
\]

Now we can find the equivalent option from the choices given:

A. \(\frac{7}{36}\)
B. \(\frac{11}{576}\)
C. \(\frac{36}{7}\)
D. \(\frac{58}{112}\)

The correct answer is:

**C. \(\frac{36}{7}\)**.