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Chapter 1: Problem 89

\(132.1+(-25.45)\)

Short Answer

Expert verified
The result is \(106.65\).

Step by step solution

01

Identify the numbers to be added

Given numbers are \(132.1\) and \(-25.45\). Since second number is negative, this addition is practically subtraction. So, it will be \(132.1\) subtracted by \(25.45\).
02

Align the decimal point

In the subtraction operation, align the numbers as per the decimal places. So it should be: \n 132.10\n- 25.45
03

Perform the subtraction

Subtract the bottom number from the top number column by column. If the bottom number in column is greater than the top number, then borrow from the next left column. Once all columns subtracted, result is: \(106.65\)

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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 numbers less than zero. They are usually represented with a minus sign (-) in front. When dealing with expressions like \(132.1 + (-25.45)\), the presence of a negative number hints towards subtraction. Converting this to a subtraction operation results in \(132.1 - 25.45\), changing the problem from addition to subtraction.

Understanding how negative numbers work is crucial, especially when they are involved in addition or subtraction.
  • When you add a negative number, you're essentially subtracting.
  • Conversely, when you subtract a negative number, you're actually adding.
Learning to interpret negative numbers correctly can help simplify calculations and lead to correct results.
Decimal Subtraction
Decimal subtraction involves subtracting numbers with decimal points. To perform it correctly, align the numbers using their decimal points. This ensures that each digit is in the correct column:
  • The decimal points should be vertically aligned.
  • If necessary, add zeros to match the length of the numbers.
Let's apply this to \(132.1 - 25.45\). Align the numbers:
\[ \begin{array}{c} 132.10 \ - 25.45 \ \end{array} \]

Now, subtract each column starting from the rightmost side, just as you would in regular subtraction. Dealing with decimals accurately is critical, as any misalignment could lead to incorrect results.
Borrowing in Subtraction
Borrowing becomes essential when a digit being subtracted is larger than the digit directly above it. In our example, observe the subtraction step:
\[ \begin{array}{c} 132.10 \ - 25.45 \ \hline 106.65 \ \end{array} \]

In the tenths column, you'll need to borrow because \(1 - 5\) isn't possible directly. You borrow 1 from the next leftward column, turning \(1\) into \(11\), allowing you to subtract 5 from 11 to get 6.
  • Borrowing adjusts the values, allowing proper subtraction.
  • It's important to use borrowing when needed to ensure accurate answers.
Mastering borrowing provides confidence to tackle more complex subtraction problems, including those with decimals.

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Most popular questions from this chapter

\(\frac{8-6}{2} \neq 4-6\)

\(6(-3)=-3(6)\)

Determining Order of Operations Using the established order of operations, which of the following expressions has a value of 72 ? For those that do not, decide whether you can insert parentheses into the expression so that its value is 72 . (a) \(4+2^{3}-7\) (b) \(4+8 \cdot 6\) (c) \(93-25-4\) (d) \(70+10 \div 5\) (e) \(60+20 \div 2+32\) (f) \(35 \cdot 2+2\)

. \(11-\frac{3^{3}-30}{8+1}+1\)

\(7\left(\frac{1}{7}\right)=1\)
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