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Chapter 1: Problem 67

Perform each indicated operation. $$ \frac{-5(-6)}{9-(-1)} $$

Short Answer

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Step by step solution

01

Simplify the Numerator

Multiply the numbers in the numerator \( -5(-6) \). Remember that multiplying two negative numbers results in a positive number: \( -5 \times -6 = 30 \).
02

Simplify the Denominator

Simplify the expression in the denominator \( 9 - (-1) \). Subtracting a negative is the same as adding a positive: \( 9 - (-1) = 9 + 1 = 10 \).
03

Divide the Simplified Numerator by the Simplified Denominator

Now, divide the simplified numerator by the simplified denominator: \( \frac{30}{10} = 3 \).

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Key Concepts

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

simplifying fractions
Understanding how to simplify fractions will make working with them much easier. The goal is to express the fraction in its simplest form, meaning the numerator and denominator have no common factors other than 1. Start by finding the greatest common divisor (GCD) of the numerator and the denominator. Here's a simple approach:
  • List the factors of both the numerator and the denominator.
  • Identify the largest factor that both lists have in common.
  • Divide both the numerator and the denominator by this common factor.
For example, if you have the fraction \(\frac{30}{10}\), the GCD of 30 and 10 is 10. Dividing the numerator and denominator by 10 gives: \[\frac{30}{10} = \frac{30 \text{ 梅 } 10}{10 \text{ 梅 } 10} = \frac{3}{1} = 3 \] . By simplifying fractions, you make calculations easier and more straightforward.
multiplying integers
Multiplying integers might seem tricky at first, but it's quite simple with some practice. Remember these key points:
  • Multiplying two positive numbers results in a positive number: \(2 \times 3 = 6\).
  • Multiplying two negative numbers also results in a positive number: \(-2 \times -3 = 6\). The negatives cancel each other out.
  • Multiplying a positive number by a negative number results in a negative number: \(2 \times -3 = -6\).
In the given solution, we multiply \(-5(-6)\). Since both integers are negative, their product is positive: \(-5 \times -6 = 30\).
dividing integers
Dividing integers follows similar rules to multiplying them, with special attention to the signs:
  • Dividing a positive number by a positive number gives a positive result: \(12 \text{ 梅 } 3 = 4\).
  • Dividing a negative number by a negative number also results in a positive number, like with multiplication: \(-12 \text{ 梅 } -3 = 4\).
  • Dividing a positive number by a negative number, or vice versa, results in a negative number: \(12 \text{ 梅 } -3 = -4\) and \(-12 \text{ 梅 } 3 = -4\).
For example, in the exercise, the simplified division was \(\frac{30}{10}\). Both numbers are positive, so the result is positive: \[\frac{30}{10} = 3 \]. Remember the rules, and practice to build confidence in dividing integers.

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Most popular questions from this chapter

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

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. When 6 is added to a number, the result is \(-3\)

Simplify each expression. $$ -5(8 x+2)-(5 x-3)-3 x+17 $$

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

Write each sentence as an equation, using \(x\) as the variable. Then find the solution from the set of integers between \(-12\) and \(12,\) inclusive. The quotient of a number and 4 is \(-1\)
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