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Chapter 1: Problem 78

Perform each indicated operation. \(\frac{-40(3)}{-2-3}\)

Short Answer

Expert verified
24

Step by step solution

01

Simplify the numerator

Multiply the numbers in the numerator: \ \ \( -40 \times 3 = -120 \)
02

Simplify the denominator

Add the numbers in the denominator: \ \ \( -2 - 3 = -5 \)
03

Divide the results

Divide the simplified numerator by the simplified denominator: \ \ \( \frac{-120}{-5} = 24 \)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying the Numerator
The numerator of a fraction is the top part, and simplification means performing operations to make it as simple as possible. In this exercise, the numerator is originally written as \(-40 \times 3\). Simplifying this involves multiplying these numbers together.

When we calculate \(-40 \times 3\), the result is \(-120\). So, the simplified numerator here is \(-120\).

Performing this multiplication step first helps to ensure that the next stages of simplification work smoothly and correctly.
Simplifying the Denominator
The denominator of a fraction is the bottom part, and like the numerator, it also needs to be simplified for easy division. The exercise starts with a denominator written as \(-2 - 3\).

We simplify this by adding the two numbers together. Since both numbers are negative, their sum is
\(-2 - 3 = -5\). Now, the denominator is simplified to \(-5\).

It's crucial to correctly carry out this operation to move on to the next step without errors.
Dividing the Results
After simplifying both the numerator and the denominator, the next task is to divide these results. You should now have a fraction that looks like this: \(\frac{-120}{-5}\).

When both the numerator and the denominator are negative, dividing them results in a positive number. Therefore, \(\frac{-120}{-5}\) simplifies to \24\.

This final step is straightforward but important. Make sure the signs are right, and perform this straightforward division.

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Most popular questions from this chapter

Write a numerical expression for each phrase, and simplify the expression. The product of -9 and \(2,\) added to 9

Write a numerical expression for each phrase, and simplify the expression. The product of 12 and the difference of 9 and -8

Write each phrase as a mathematical expression using \(x\) as the variable, and simplify. Nine times a number added to \(6,\) subtracted from triple the sum of 12 and 8 times the number

Twice the product of -1 and \(6,\) subtracted from -4

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) \(\left(\frac{5}{6} x+\frac{3}{2} y\right)\left(-\frac{1}{3} a\right)\)
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