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Chapter 1: Problem 71

Write a mathematical expression for each and simplify. The sum of \(-21\) and 13.

Short Answer

Expert verified
The simplified mathematical expression for the sum of -21 and 13 is \(-21 + 13 = -8\).

Step by step solution

01

Write the mathematical expression

The sum of two numbers can be represented as an addition. So, we write the sum of -21 and 13 as a mathematical expression: \(-21 + 13\)
02

Simplify the expression

Now, we will simplify the expression by finding the sum of the two numbers: \(-21 + 13 = -8\) So, the sum of -21 and 13 is -8.

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Key Concepts

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

Addition of Integers
Adding integers involves finding the total or sum of two numbers in a set of whole numbers that can be positive or negative. It's crucial to understand that integers include not only positive numbers, like 1 or 4, but also negative numbers, such as -2 or -15, and zero. When you add integers,
  • If both integers have the same sign, you add their absolute values, and keep the common sign. For instance, -4 + (-5) becomes -9.
  • If the integers have different signs, subtract the smaller absolute value from the larger absolute value, and take the sign of the number with the larger absolute value. For example, in -21 + 13, subtract 13 from 21, which equals 8, and since 21 has the larger absolute value, the result is negative, giving us -8.
Understanding these rules helps you simplify problems involving integer addition efficiently.
Integer Operations
Integer operations encompass several basic math operations that can be performed on integers: addition, subtraction, multiplication, and division. Each operation has simple rules to follow. Let's break them down:
  • Addition and Subtraction: These can often intertwine when it comes to integers, and similar rules apply. For subtraction, it is helpful to think "add the opposite". For example, when you see 5 - (-3), it translates to 5 + 3, resulting in 8.
  • Multiplication and Division: When multiplying or dividing integers, if both numbers have the same sign, the result is positive. If the signs differ, the result is negative. For instance, -2 multiplied by -3 equals 6, whereas -2 multiplied by 3 equals -6.
These rules are fundamental guidelines to resolve and simplify expressions and equations involving integers.
Basic Algebra Skills
Basic algebra involves understanding how numbers and their operations behave and interact through expressions and equations. One key aspect is the manipulation and simplification of expressions:
  • Expression Formation: Forming expressions helps set up problems for solving. In our example, to express "the sum of -21 and 13," we write -21 + 13.
  • Simplification: This involves performing operations to convert expressions into their simplest form. It means reducing expression complexity without changing its value. For example, simplifying -21 + 13 to -8.
  • Translating Words to Symbols: Often, real-life problems are described in words, and understanding how to translate this into mathematical symbols is a critical skill. Knowing that "sum" means addition helps you form the correct equation initially.
Mastering these skills forms a strong framework for solving more complex algebraic problems later on.

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Most popular questions from this chapter

Write an expression for each and simplify. Answer the question with a complete sentence. During one offensive drive in the first quarter of Super Bowl XXXVIII, the New England Patriots ran for 7 yd, gained 4 yd on a pass play, gained 1 yd on a running play, gained another 6 yd on a pass by Tom Brady, then lost 10 yd on a running play. What was the Patriots' net yardage on this offensive drive?

Rewrite each expression using the distributive property. Simplify if possible. $$(-10+3) 5$$

Rewrite each expression using the distributive property. Simplify if possible. $$-(6+1)$$

Write a mathematical expression for each and simplify. Twice the difference of \(-5\) and \(-15\)

Write a mathematical expression for each and simplify. Twice the sum of 18 and \(-31\)
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