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Chapter 1: Problem 53

Perform each indicated operation. $$ -10-(-4)(2) $$

Short Answer

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Step by step solution

01

Identify Operations

First, identify the operations involved in the expression $$-10 - (-4)(2).$$ It includes subtraction and multiplication.
02

Perform Multiplication

Perform the multiplication \((-4) \times 2 = -8.\) Now the expression is $$-10 - (-8).$$
03

Rewrite Subtraction of Negative

Rewrite the subtraction of a negative number as addition. So $$-10 - (-8)$$ is the same as $$-10 + 8.$$
04

Perform Addition

Finally, add $$-10 + 8.$$ This equals $$-2.$$

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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 is one of the basic operations in algebra. When multiplying integers, we must consider both the numerical value and the signs (positive or negative).

The rules for multiplication of integers are simple:
  • A positive number times a positive number equals a positive number.
  • A positive number times a negative number equals a negative number.
  • A negative number times a negative number equals a positive number.


For instance, in step 2 of our exercise, we multiply \text{\((-4) \times 2\)} to get \text{\(-8\)}. We followed the rule that a negative times a positive equals a negative.
subtraction of integers
Subtraction of integers may seem tricky at first, but it's manageable once you understand the rules.
When subtracting integers, always remember:
  • Subtracting a positive number is the same as adding a negative number.
  • Subtracting a negative number is the same as adding a positive number.


For example, in Step 3, rewriting \text{\(-10 - (-8)\)} as \text{\(-10 + 8\)} makes the operation clearer. We're turning the subtraction of a negative into an addition.
Essentially, subtracting a negative reverses the sign and turns it into addition, enabling simpler calculations.
addition of integers
Addition of integers is another fundamental operation. When adding integers, you always combine their values. The sign (positive or negative) affects the result.
Here are basic rules to remember:
  • Adding positive numbers together gives a positive result.
  • Adding negative numbers together gives a negative result.
  • Adding a positive and a negative number involves subtracting their absolute values and taking the sign of the number with the larger absolute value.


In Step 4, we add \text{\(-10 + 8\)}. Here, we subtract 8 from 10 and keep the negative sign of the larger number in absolute value, getting a result of \text{\(-2\)}.
This rule helps simplify and solve problems involving integers.

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Most popular questions from this chapter

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ 5 x-2 y+3 a $$

To find the average (mean) of numbers, we add the numbers and then divide the sum by the number of terms added. For example, to find the average of \(14,8,3,9,\) and \(1,\) we add them and then divide by 5. $$ \frac{14+8+3+9+1}{5}=\frac{35}{5}=7 \leftarrow \text { Average } $$ Find the average of each group of numbers. $$ -15,29,8,-6 $$

Write a numerical expression for each phrase and simplify. The product of \(-\frac{2}{3}\) and \(-\frac{1}{5},\) divided by \(\frac{1}{7}\)

Translate each phrase into a mathematical expression. Use \(x\) as the variable. Combine like terms when possible. Six times a number added to \(-4,\) subtracted from twice the sum of three times the number and 4 (Hint: Twice means two times.)

Evaluate each expression for \(x=6, y=-4,\) and \(a=3\) $$ 5 x-4 a^{2} $$
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