Which is smaller?
`2(35)/(42)or7(32)/(40)`

Answer

To determine which fraction is smaller between \( \frac{235}{42} \) and \( \frac{732}{40} \), we can follow these steps:

### Step 1: Simplify the Fractions
First, we simplify both fractions.

1. **For \( \frac{235}{42} \)**:
- The numerator is already in its simplest form, so we keep it as \( 235 \).
- The denominator is \( 42 \).

Thus, \( \frac{235}{42} \) remains as it is.

2. **For \( \frac{732}{40} \)**:
- The numerator \( 732 \) can be simplified by dividing both the numerator and denominator by their greatest common divisor (GCD).
- The GCD of \( 732 \) and \( 40 \) is \( 4 \).
- So, \( \frac{732 \div 4}{40 \div 4} = \frac{183}{10} \).

Now we have:
- \( \frac{235}{42} \)
- \( \frac{183}{10} \)

### Step 2: Find a Common Denominator
To compare the two fractions, we need a common denominator. The denominators are \( 42 \) and \( 10 \).

- The least common multiple (LCM) of \( 42 \) and \( 10 \) is \( 210 \).

### Step 3: Convert Both Fractions to Have the Same Denominator
Now we convert both fractions to have the denominator of \( 210 \).

1. **For \( \frac{235}{42} \)**:
- Multiply both the numerator and denominator by \( 5 \) (since \( 42 \times 5 = 210 \)):
\[ \frac{235 \times 5}{42 \times 5} = \frac{1175}{210} \]

2. **For \( \frac{183}{10} \)**:
- Multiply both the numerator and denominator by \( 21 \) (since \( 10 \times 21 = 210 \)):
\[ \frac{183 \times 21}{10 \times 21} = \frac{3843}{210} \]

### Step 4: Compare the Two Fractions
Now we compare \( \frac{1175}{210} \) and \( \frac{3843}{210} \).

Since both fractions have the same denominator, we can compare the numerators directly:
- \( 1175 < 3843 \)

### Conclusion
Thus, \( \frac{235}{42} \) is smaller than \( \frac{732}{40} \).

### Final Answer
The smaller fraction is \( \frac{235}{42} \).

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