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Chapter 1: Problem 47

Write the subtraction problem as a related addition problem. For example, \(19-6=13\) can be written as \(13+6=19\) $$102-75=27$$

Short Answer

Expert verified
27 + 75 = 102

Step by step solution

01

Identify the given subtraction problem

The given subtraction problem is \(102 - 75 = 27\).
02

Understand the relationship between subtraction and addition

Subtraction can be rewritten as an addition problem by adding the result (difference) to the subtrahend to get the minuend. For example, \(a - b = c\) can be rewritten as \(c + b = a\).
03

Rewrite the given subtraction problem as an addition problem

Using the relationship from Step 2, rewrite \(102 - 75 = 27\) as \(27 + 75 = 102\).

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Key Concepts

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

subtraction
Subtraction is one of the basic operations in arithmetic, used to find the difference between two numbers. It is often represented by the minus sign (-). For example, in the problem \(102 - 75 = 27\), 102 is the minuend, 75 is the subtrahend, and 27 is the difference.
When you subtract, you essentially take away the value of the subtrahend from the minuend.
Understanding how to manipulate subtraction problems forms a crucial part of developing arithmetic skills in prealgebra.
This exercise shows how subtraction relates to addition, making it easier for students to grasp inverse operations.
addition
Addition is the arithmetic operation of combining two or more numbers to find their total or sum. It is commonly represented by the plus sign (+).
While subtraction finds the difference between numbers, addition brings numbers together.
In the context of our exercise, rewriting subtraction as addition can make it easier for some students to understand the relationship between the two.
For example, the subtraction problem \(102 - 75 = 27\) can be seen as the addition problem \(27 + 75 = 102\).
This relationship highlights that adding the subtrahend back to the difference gives the original minuend.
inverse operations
Inverse operations are paired arithmetic operations that reverse the effect of each other. Addition and subtraction are inverse operations.
This means if you start with a number, add another number to it, and then subtract the same number you added, you'll end up with your starting number.
For instance, if we solve \(102 - 75 = 27\) and then look at its inverse operation in the form \(27 + 75 = 102\), the steps confirm both operations undoing each other.
Understanding this inverse relationship is key in solving many prealgebra problems and verifying your work.
prealgebra
Prealgebra is the foundation of algebra, focusing on arithmetic and introducing basic mathematical concepts and skills. These skills include:
  • Understanding and performing basic operations like addition, subtraction, multiplication, and division.
  • Recognizing the properties of numbers and operations.
  • Learning the relationships between operations.
This exercise of converting a subtraction problem into an addition problem helps build a strong foundation in these basic concepts.
It aids in developing number sense and prepares students for more complex algebraic problems they will encounter later on.

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Most popular questions from this chapter

Fill in the blank with the inequality symbol \(<\) or \(>\). $$48 \square 47$$

For each English sentence, write a mathematical expression and simplify. Find the quotient of 1890 and 45.

Perform the indicated operation by using a calculator. $$\begin{array}{r} 4,905,620 \\ -\quad 458,318 \\ \hline \end{array}$$

Perform the indicated operation by using a calculator. $$\begin{array}{r} 45,418 \\ 81,990 \\ 9,063 \\ +56,309 \\ \hline \end{array}$$

Three top television shows entertained the following number of viewers in one week: \(26,548,000\) for American Idol, \(26,930,000\) for Grey's Anatomy, and \(20,805,000\) for House. Find the sum of the viewers for these shows.
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