To determine if the improper fraction \( \frac{45}{32} \) converts to the mixed number \( 1 \frac{13}{3} \):
1. Convert the improper fraction to a mixed number:
- An improper fraction is a fraction in which the numerator (top number) is greater than or equal to the denominator (bottom number).
- To convert an improper fraction to a mixed number, divide the numerator by the denominator.
- The quotient is the whole number part.
- The remainder is the numerator of the fractional part.
- The denominator remains the same.
Let's do the calculation:
- Divide \( 45 \) (numerator) by \( 32 \) (denominator):
[tex]\[
45 ÷ 32 = 1 \text{ remainder } 13
\][/tex]
- Therefore, the improper fraction \( \frac{45}{32} \) can be expressed as:
[tex]\[
1 \frac{13}{32}
\][/tex]
2. Check the given mixed number:
- The given mixed number is \( 1 \frac{13}{3} \).
3. Compare the converted mixed number with the given mixed number:
- \( 1 \frac{13}{32} \) is not the same as \( 1 \frac{13}{3} \).
4. Conclusion:
Since \( \frac{45}{32} \) converts to \( 1 \frac{13}{32} \) and not \( 1 \frac{13}{3} \), the statement is false.
So, the answer to the question is:
False
