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All courses Math Foundations · MF.NS.3 3 of 60
Evaluate multi-step numerical expressions using order of operations, including grouping symbols and exponents.

Evaluate without grouping symbols

Problem
Evaluate: 18 - 3 × 4 + 6.
Your answer

Hint

Find the multiplication in the original expression. Compute \(3\times4\) before doing either \(18-3\) or \(4+6\).

Multiplication comes before addition and subtraction. After the multiplication is replaced by its value, addition and subtraction have equal priority and are completed from left to right.

Solution walkthrough

01

Choose the first operation

\[18-3\times4+6\]

The expression contains subtraction, multiplication, and addition. Multiplication has higher priority, so \(3\times4\) must be evaluated before either neighboring operation.

02

Multiply

\[3\times4=12\]

Three groups of four make \(12\). This value replaces the complete multiplication part \(3\times4\).

03

Rewrite the whole expression

\[18-12+6\]

Keep every untouched number and operation in its original order. Only \(3\times4\) changes to \(12\), giving \(18-12+6\).

04

Subtract from left to right

\[18-12=6\]

Now only subtraction and addition remain. They have equal priority, so begin with the leftmost operation: \(18-12=6\).

05

Add the remaining six

\[6+6=12\]

The first \(6\) is the result of the subtraction. Add the final \(6\) from the original expression to get \(12\).

06

State the final number

\[18-3\times4+6=12\]

After completing multiplication first and then subtraction and addition from left to right, the value of the entire expression is \(12\). Choose the option showing \(12\).

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Another way

  1. After multiplying, subtraction may be written as addition of a negative: \(18-12+6=18+(-12)+6\). Because these are now addition terms, regroup them as \(18+6-12=24-12=12\).

!

Common mistake

Do not work across the original line as \(18-3\), then multiply; that produces \(66\). Do not turn \(18-12+6\) into \(18-(12+6)\), which produces \(0\). The plus six remains a separate left-to-right addition.