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Chapter 1: Problem 39

Find each sum. $$ [-3+(-4)]+[5+(-6)] $$

Short Answer

Expert verified
-8

Step by step solution

01

- Handle the first set of brackets

Calculate the sum inside the first set of brackets. Add -3 + (-4). This can be visualized simply as adding two negative numbers together: -3 + (-4) = -7.
02

- Handle the second set of brackets

Next, calculate the sum inside the second set of brackets. Add 5 + (-6). This can be visualized as adding a positive number to a negative number: 5 + (-6) = -1.
03

- Add the results of the two brackets

Sum the results obtained in Step 1 and Step 2: -7 + (-1) = -8.

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Key Concepts

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

Understanding Negative Numbers
Negative numbers are simply numbers less than zero. They are written with a minus sign in front of them. For example, -3 is a negative number. In many real-life situations, negative numbers are used: such as temperatures below freezing, debts, and elevations below sea level.
Integer Addition Made Easy
When adding integers, there are a few simple rules to follow. Integers include both positive and negative whole numbers.

Here are some rules to remember when adding integers:
  • When adding two positive integers, the result is always positive. For example, 3 + 4 = 7.
  • When adding two negative integers, the result is always negative. For example, -3 + (-4) = -7.
  • When adding a positive and a negative integer, subtract the smaller absolute value from the larger absolute value and keep the sign of the larger absolute value. For example, 5 + (-6) is like 6 - 5, which equals -1.
Another trick is to think about adding negative numbers like moving to the left on a number line, and adding positive numbers like moving to the right.
Mastering the Order of Operations
The order of operations is crucial when solving math problems. To ensure you get the correct answer, follow these steps:
1. Solve expressions inside parentheses first.
2. Simplify exponents (if any).
3. Perform multiplication and division from left to right.
4. Finally, perform addition and subtraction from left to right.
In our example, \([-3+(-4)]+[5+(-6)]\), we first handle the calculations inside the brackets: -3 + (-4) and 5 + (-6). Then we add the results: -7 + (-1). By following the order of operations, we ensure accurate results鈥攅nding up with a final answer of -8.

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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 6 if it is divisible by both 2 and \(3,\) and not otherwise. Show that (a) \(1,524,822\) is divisible by 6 and \((b) 2,873,590\) is not divisible by 6

Find each difference. $$ \frac{1}{2}-\left(-\frac{1}{4}\right) $$

Perform each indicated operation. $$ -7.6247-[(-3.9928+1.42773)-(-2.80981)] $$

A manufacturer has fixed costs of \(\$ 1000\) to produce widgets. Each widget costs \(\$ 5\) to make. The fixed cost to produce gadgets is \(\$ 750,\) and each gadget costs \(\$ 3\) to make. Write an expression for the cost to make \(y\) gadgets.

Find each difference. $$ \frac{9}{10}-\left(\frac{1}{8}-\frac{3}{10}\right) $$
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