Question

Multiply 4 by -5/8. Write the answer as a mixed number in simplest form. (1 point)

Answer 1

To multiply \( 4 \) by \( -\frac{5}{8} \), follow these steps:

1. Convert the whole number \( 4 \) to an improper fraction with a denominator of \( 1 \), so it becomes \( \frac{4}{1} \).
2. Multiply the numerators and then the denominators of the two fractions:

\[ \frac{4}{1} \times -\frac{5}{8} = -\frac{4 \times 5}{1 \times 8} = -\frac{20}{8} \]

3. Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is \( 8 \) in this case:

\[ -\frac{20}{8} = -\frac{20 \div 8}{8 \div 8} = -\frac{2 \times 1}{1 \times 1} = -\frac{2}{1} \]

Since \( -\frac{2}{1} \) is an improper fraction where the numerator is a multiple of the denominator, we can simplify it to a whole number:

\[ -\frac{2}{1} = -2 \]

Thus, the product of \( 4 \) and \( -\frac{5}{8} \) is \( -2 \).

Since the result is a whole number and not a mixed number, the answer is just \( -2 \), not in mixed number form. Mixed numbers are typically used to represent numbers between two whole numbers, consisting of a whole number part and a proper fraction part. In this case, since the result is a whole number, there is no proper fraction part, so it is just \( -2 \).