Multiply 8 by (-7/2). Write your answer in simplest form.
Understand the Problem
The question is asking to multiply the number 8 by the fraction (-7/2) and to present the final answer in its simplest form.
Answer
$-28$
Answer for screen readers
The final answer is $-28$.
Steps to Solve
- Convert the whole number to a fraction
Convert the number 8 into a fraction by expressing it as $\frac{8}{1}$.
- Multiply the fractions
Now we will multiply the two fractions. This can be done by multiplying the numerators together and the denominators together: $$ \frac{8}{1} \cdot \frac{-7}{2} = \frac{8 \cdot (-7)}{1 \cdot 2} $$
- Calculate the numerator and denominator
Calculating the numerator and the denominator gives: $$ \frac{-56}{2} $$
- Simplify the fraction
To simplify $\frac{-56}{2}$, divide both the numerator and the denominator by their greatest common divisor (GCD), which is 2: $$ \frac{-56 \div 2}{2 \div 2} = \frac{-28}{1} = -28 $$
The final answer is $-28$.
More Information
The multiplication of a whole number by a fraction results in a simplified fraction. In this case, multiplying 8 by $-\frac{7}{2}$ produced a negative integer, which illustrates that multiplying positive and negative numbers results in a negative product.
Tips
- Not converting the whole number to a fraction: Some might forget to express 8 as $\frac{8}{1}$ before multiplying.
- Incorrectly simplifying the fraction: Make sure to divide both the numerator and denominator by their GCD to get the simplest form.
