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Chapter 1: Problem 72

Write a mathematical expression for each and simplify. The sum of \(-7\) and 20.

Short Answer

Expert verified
The simplified mathematical expression for the sum of \(-7\) and \(20\) is \(13\).

Step by step solution

01

Identify the operation

Since we need to find the sum of -7 and 20, we are dealing with addition.
02

Perform the operation

Add the two numbers together: \(-7 + 20\).
03

Write the expression

The mathematical expression for the sum is: \(( -7 ) + ( 20 )\)
04

Simplify the expression

When simplifying the expression, the result will be: \( -7 + 20 = 13 \) So the sum of -7 and 20 is 13.

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Key Concepts

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

Addition
Addition is one of the four fundamental arithmetic operations in math. It involves combining two or more numbers to find their total. Whenever you see words like "sum" or "add," you are looking at an operation that requires addition.

To perform addition in any mathematical expression, simply align your numbers and add them together. For example, in the expression \(-7 + 20\), you start with the first number, \(-7\), and add \(20\) to it.
  • The first number, \(-7\), acts as the starting point.
  • Then, you increase that amount by the second number, \(20\).


When you calculate \(-7 + 20\), you're essentially adding \(20\) to \(\-7\). This gives you the result of \(13\). It's like hopping 20 steps forward from \(-7\) on a number line to reach 13.
Integer Operations
Integer operations involve working with whole numbers which can be positive, negative, or zero. Different rules apply based on whether you are adding, subtracting, multiplying, or dividing integers.

With addition of integers, here are some simple guidelines:
  • When both integers have the same sign, add them normally and keep the sign.
  • If the integers have different signs, subtract the smaller absolute value from the larger absolute value and use the sign of the larger absolute value.


For our exercise, adding \(-7\) and \(20\), the numbers have different signs.

So, we subtract the smaller absolute value from the larger:\( |20| - |-7| = 20 - 7 = 13\). The result takes the sign of the larger number, which is positive.
Simplifying Expressions
Simplifying expressions means reducing them to their simplest form. This often involves performing operations and combining like terms. In arithmetic, it makes complex expressions easier to understand and solve.

To simplify an expression like \(( -7 ) + ( 20 )\), follow these steps:
  • Identify and understand the operation within the expression.
  • Perform any calculations needed. In this case, adding \(-7\) and \(20\) gives \(13\).
  • Ensure that there are no further operations or terms that can be combined or reduced.


Once simplified, expressions become clearer and more straightforward. For example, in this scenario, our simplified expression results in the number \(13\), with all calculations complete and no additional reduction possible.

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Most popular questions from this chapter

Objectives 3 and 4 A study conducted in 2000 indicated that about \(\frac{3}{5}\) of the full-time college students surveyed had consumed alcohol sometime during the 30 days preceding the survey. If 400 students were surveyed, how many of them drank alcohol within the 30 days before the survey? (Alcohol Research \& Health, The Journal of the Nat 1 Institute on Alcohol Abuse \& Alcoholism, Vol. 27, No. \(1,2003\) )

Use the order of operations to simplify. $$10-2(1-4)^{3} \div 9$$

Objectives 3 and 4 A welder must construct a beam with a total length of \(32 \frac{7}{8}\) in. If he has already joined a \(14 \frac{1}{6}\) -in. beam with a \(10 \frac{3}{4}-i n .\) beam, find the length of a third beam needed to reach the total length.

Write a mathematical expression for each and simplify. \(-25\) less than \(-19\).

Rewrite each expression using the distributive property. Simplify if possible. $$(8-2) 4$$
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