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Chapter 1: Problem 32

Find each sum. SEE EXAMPLE \(2 .\) (OBJECTIVE 2 ) \((-1.2)+(-5.3)\)

Short Answer

Expert verified
-6.5

Step by step solution

01

Identify the numbers

The numbers given are -1.2 and -5.3. Both are negative. The task is to add these two numbers.
02

Add the numbers

Add the absolute values of the numbers, i.e., 1.2 and 5.3, which equals to 6.5. Since the original numbers were both negative, the result will also be negative.
03

Write down the result

The result of \((-1.2)+(-5.3)\) is -6.5.

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Key Concepts

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

Absolute Value
When dealing with numbers, especially negative ones, the concept of absolute value is essential. Absolute value refers to how far a number is from zero on the number line, regardless of direction. It's always a positive number or zero. For instance:
  • The absolute value of 5 is 5.
  • The absolute value of -5 is also 5, since it's the distance away from zero.
Now, why do we talk about absolute values when adding numbers? Well, absolute values help us focus on the magnitude without worrying about the sign.
When adding \(-1.2\)and \(-5.3\), first consider their absolute values, \(1.2\) and \(5.3\). Together, they add up to \(6.5\).This value tells us the size of the result. Since both numbers being added are negative, the final result will also be negative.
Negative Numbers
Negative numbers are those less than zero and are shown with a minus sign. They might sound tricky at first glance, but they follow basic arithmetic rules, just like positive numbers. When you add two negative numbers, you essentially add their absolute values and attach a negative sign to the result. This is because negative numbers represent values below zero, and combining them takes you further below zero.
For example, with the expression \((-1.2) + (-5.3)\):
  • Adding absolute values 1.2 and 5.3 gives you 6.5.
  • Because both numbers are negative, the result of \(-6.5\) is obtained to reflect their negative nature.
So, when adding negative numbers, remember to keep the negative sign in the final answer.
Addition of Decimals
Adding decimals can seem a bit complex, but it becomes straightforward when you line up the decimal points. Just like whole numbers, decimals have their own place value system. Here鈥檚 a simple guide:
  • Align the numbers vertically so their decimal points are in a straight line.
  • Proceed with adding as you normally would, starting from the rightmost digit and moving left.
In the exercise \((-1.2) + (-5.3)\), treat the numbers as \(1.2 \ ext{and} \ 5.3\) initially:
  • Add them to get \(6.5\), respecting the decimal alignment.
  • Since both numbers were negative, the sum is -6.5, illustrating why the sign is crucial.
Addition of decimals requires attention to the decimal places, ensuring you accurately align and gather all values during calculation.

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Most popular questions from this chapter

Write each inequality as an equivalent inequality in which the inequality symbol points in the opposite direction. $$3+8>8$$

Two carpenters bid on a home remodeling project. The first bids \(\$ 9,350\) for the entire job. The second will work for \(\$ 27.50\) per hour, plus \(\$ 4,500\) for materials. He estimates that the job will take 150 hours. Which carpenter has the lower bid?

Consider the following sets: the integers, natural numbers, even and odd integers, positive and negative numbers, prime and composite numbers, and rational numbers. Find a number that fits in as many of these categories as possible.

Graph each set of numbers on a number line. Use brackets or parentheses where applicable. The even integers that are also prime numbers

Write each inequality as an equivalent inequality in which the inequality symbol points in the opposite direction. $$2 \cdot 3<3 \cdot 4$$
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