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Chapter 1: Problem 14

Simplify each numerical expression. (Objective 2) $$(15-6)(13-4)$$

Short Answer

Expert verified
The simplified expression is 81.

Step by step solution

01

Perform Subtraction in the First Parenthesis

Simplify inside the first parenthesis by subtracting: \(15 - 6\). Compute the result, which is \(9\).
02

Perform Subtraction in the Second Parenthesis

Next, simplify inside the second parenthesis by subtracting: \(13 - 4\). Compute the result, which is \(9\).
03

Multiply the Results from Both Parentheses

Multiply the results obtained from the first and second parentheses: \(9 \times 9\). The product is \(81\).

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Key Concepts

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

Numerical Expressions
Numerical expressions are mathematical phrases that include numbers and operations but do not have an equal sign. They illustrate calculations that need to be carried out in a step-by-step process. In algebra and arithmetic, simplifying these expressions helps in finding a single numerical value for complex calculations.
  • Think of numerical expressions as a way to "describe" a numerical operation without working it out straight away.
  • Follow the order of operations, PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right).
Understanding numerical expressions involves comprehending how these operations work together to simplify calculations effectively and accurately.
Subtraction in Parentheses
When dealing with expressions, parentheses indicate which operations should be completed first. In our given example, \[(15-6)(13-4),\] it's crucial to first solve the operations inside each parenthesis before proceeding. This follows the order of operations often remembered by the acronym PEMDAS, where parentheses come first.
  • Within the first set of parentheses, subtract 6 from 15, giving us 9.
  • Within the second set, subtract 4 from 13, also giving us 9.
Remember, simplifying expressions within parentheses helps to organize the rest of the calculation, ensuring accuracy and clarity in solving mathematical problems.
Multiplication of Numbers
Multiplication is the mathematical operation of scaling one number by another. Once subtraction within each parenthesis is simplified, the next step is to multiply the results.
  • In our expression, after simplifying we have \(9 \times 9\).
  • This means you take one of the 9's and "scale" it by 9 times the size of the other.
The result is 81, which is the final simplified value of the expression.
Multiplication consolidates steps in a calculation into a singular product, making it indispensable in algebraic simplification.

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Most popular questions from this chapter

State whether the expressions in each problem are equivalent and explain why or why not. \(2 x-3 y+4 z\) and \(2 x-4 z+3 y\)

Simplify each numerical expression. Don't forget to take advantage of the properties if they can be used to simplify the computation. $$(-2)(18)(-12)(-5)$$

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \((a-b)-(a+b)\) for \(a=19\) and \(b=-17\)

State the property that justifies each statement. For example, \(3+(-4)=(-4)+3\) because of the commutative property for addition. $$[5(-8)] 4=5[-8(4)]$$

Simplify each algebraic expression by combining similar terms. $$-(x-6)+5(x-9)$$
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