Question

evaluate each expression. when the answer is not a whole number, write your answer as a fraction in the form a/b.
a. $-4 \cdot -6 = \square$
b. $-24 \cdot \frac{-7}{6} = \square$
c. $4 \div -6 = \square$
d. $\frac{4}{3} \div -24 = \square$
(lesson 5 - 11)

Explanation:

Part a

Step1: Recall sign rule for multiplication

When multiplying two negative numbers, the result is positive. So, \(-4 \cdot -6\) is the same as \(4 \cdot 6\).

Step2: Perform the multiplication

\(4\times6 = 24\)

Step1: Simplify the fraction and signs

First, note that \(-24\times\frac{-7}{6}\). The negative times negative is positive, and we can simplify \(24\) and \(6\) first. \(24\div6 = 4\).

Step2: Multiply the remaining numbers

So we have \(4\times7=28\) (since the two negatives make a positive and we simplified the fraction part)

Step1: Recall division rule for signs

A positive divided by a negative is negative. So, \(4\div - 6=-\frac{4}{6}\)

Step2: Simplify the fraction

Simplify \(\frac{4}{6}\) by dividing numerator and denominator by their greatest common divisor, which is \(2\). So \(-\frac{4\div2}{6\div2}=-\frac{2}{3}\)

Answer:

\(24\)

Part b