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Chapter 1: Problem 69

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

Short Answer

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Step by step solution

01

Simplify the numerator

First, evaluate the expression in the numerator. The numerator is \( -5(-6) \). Multiplying -5 by -6 gives 30. So, the numerator simplifies to 30.
02

Simplify the denominator

Next, evaluate the expression in the denominator. The denominator is \( 9 - (-1) \). Subtracting -1 from 9 is the same as adding 9 and 1. Thus, the denominator simplifies to 10.
03

Perform the division

Now, divide the simplified numerator by the simplified denominator: \( \frac{30}{10} \). Performing the division, we get 3.

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Key Concepts

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

multiplication of integers
Multiplication of integers involves a few basic rules. Most students know that multiplication is repeated addition. But what happens when you multiply negative numbers? Here are some simple rules:
  • A positive number times a positive number gives a positive result. For example,
    \(5 \times 6 = 30\).

  • A positive number times a negative number gives a negative result. For example,
    \(5 \times -6 = -30\).

  • A negative number times another negative number gives a positive result. For example,
    \(-5 \times -6 = 30\).
In our exercise, the numerator is \(-5(-6)\). Following the third rule,
\(-5 \times -6\) simplifies to 30, because two negatives cancel each other out.
simplifying fractions
Simplifying fractions means reducing them to their simplest form. In the exercise,
we have \(\frac{30}{10}\) after evaluating both the numerator and denominator.
To simplify a fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).
This simplifies \(\frac{30}{10}\) to 3. Let's look at it in detail:
  • The GCD of 30 and 10 is 10.

  • So, divide both 30 and 10 by 10. This gives us:
    \(\frac{30 \div 10}{10 \div 10} = \frac{3}{1} = 3\).
It's crucial to understand that simplifying fractions
can often make problems more manageable.
integer addition and subtraction
Integer addition and subtraction follow specific rules too.
These operations are involved in simplifying our denominator \(9 - (-1)\):
  • Subtracting a negative number is the same as adding its positive counterpart.
    So, subtracting -1 from 9 is the same as adding 9 and 1.

  • In our case, 9 - (-1) turns into 9 + 1, which equals 10.
Understanding these rules can help you solve problems faster and
avoid mistakes in basic arithmetic operations involving integers.

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Most popular questions from this chapter

The operation of division is used in divisibility tests. A divisibility test allows us to determine whether a given number is divisible (without remainder) by another number. An integer is divisible by 2 if its last digit is divisible by \(2,\) and not otherwise. Show that (a) \(3,473,986\) is divisible by 2 and (b) \(4,336,879\) is not divisible by 2 .

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. A number multiplied by \(-7,\) subtracted from the sum of 13 and six times the number

Bruce Buit also enjoys playing Triominoes. On five successive turns, his scores were \(-13,15,-12,24,\) and \(14 .\) What was his total score for the five turns?

Explain how the procedure of changing \(\frac{3}{4}\) to \(\frac{9}{12}\) requires the use of the multiplicative identity element, 1

Write a numerical expression for each phrase and simplify. The quotient of \(-20\) and the sum of \(-8\) and \(-2\)
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