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Chapter 1: Problem 5

Simplify each numerical expression. (Objective 2) $$16+5 \cdot 7$$

Short Answer

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51

Step by step solution

01

Understand the Order of Operations

The expression to simplify is \(16 + 5 \cdot 7\). To solve this correctly, we need to apply the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). Multiplication comes before addition in this sequence.
02

Multiply First

In the expression \(16 + 5 \cdot 7\), the multiplication should be done first. So we calculate \(5 \cdot 7\). This gives us \(35\).
03

Add the Results

Now that we have calculated the multiplication, the expression simplifies to \(16 + 35\). Next, we perform the addition: \(16 + 35 = 51\).

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Key Concepts

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

PEMDAS
Understanding the order of operations is crucial when simplifying mathematical expressions. Imagine you have a sequence of operations to perform, and there is a specific order in which they must be executed. This is where PEMDAS comes into play. PEMDAS is an acronym that helps us remember the sequence we should follow:
  • Parentheses \((P)\)
  • Exponents \((E)\)
  • Multiplication \((M)\) and Division \((D)\), left to right
  • Addition \((A)\) and Subtraction \((S)\), left to right
The key is to follow this order precisely. A common mistake is to overlook the priority of operations, leading to incorrect results. For example, in the expression \(16 + 5 \cdot 7\), if addition is performed before multiplication, the outcome will be wrong. PEMDAS ensures consistent and correct calculations every time.
Numerical Expressions
A numerical expression is like a math phrase consisting of numbers, operations, and in some cases, parentheses. It doesn't include an equals sign like an equation.

An expression such as \(16 + 5 \cdot 7\) asks us to perform certain operations to get a numerical result.
  • Numerical expressions require you to perform operations following the rules of PEMDAS.
  • No equation or inequality is involved, so their primary goal is simplification to arrive at a single value.
Playing around with numerical expressions can make math exciting! It challenges your understanding of numbers and operations, sharpening your skills as you learn to simplify them accurately.
Simplification Steps
Simplifying expressions involves reducing them to the simplest form possible, which is often a single number. To simplify, follow clear and sequential steps for calculation.

Take the expression \(16 + 5 \cdot 7\) as an example:
  • First, identify operations that require immediate action based on PEMDAS. In this expression, multiplication precedes addition.
  • Calculate \(5 \cdot 7\), resulting in \(35\).
  • With multiplication complete, the expression turns into \(16 + 35\).
  • Finally, perform the addition to arrive at \(51\).
Following a systematic approach ensures that you effectively simplify expressions without missing any critical operations. Simplification is not about skipping essential steps but about making the process as smooth and accurate as possible.

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Most popular questions from this chapter

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \((x-6)-(x+12)\) for \(x=-3\)

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(5(x-y)-9(x+y)\) for \(x=4\) and \(y=-4\)

Simplify each algebraic expression and then evaluate the resulting expression for the given values of the variables. \(-(n+2)-3(n-6)\) for \(n=10\)

Simplify each algebraic expression by combining similar terms. $$8 x+9+14 x-3 x-14$$

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