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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: \(18~-~3~\times~4~+~6\).
Your answer
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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

Apply operation priority

\[\text{multiplication}~\text{before}~\text{addition}~\text{or}~\text{subtraction}\]

The prompt expression contains multiplication, subtraction, and addition without grouping symbols. Multiplication has higher priority, so evaluate 3 × 4 before using either neighboring sign.

02

Evaluate the product

\[3~x~4~=~12\]

The factors 3 and 4 come directly from the multiplication in the original expression. Their product is 12.

03

Rewrite the entire expression

\[18~-~3~x~4~+~6~=~18~-~12~+~6\]

Replace only the completed product 3 × 4 with 12. Preserve the original 18, subtraction sign, addition sign, and final 6 so no term is lost or moved.

04

Work left to right

\[18~-~12~+~6~=~6~+~6~=~12\]

After multiplication, only subtraction and addition remain. They have equal priority, so compute from left to right: 18 - 12 = 6, then add the original final 6 to get 12.

05

Check by regrouping signed terms

\[18~+~(-12)~+~6~=~24~-~12~=~12\]

Treat subtraction as adding negative 12. Combining the positive terms gives 24, and 24 - 12 equals 12, confirming the result.

06

State the expression value

\[12\]

The expression 18 - 3 × 4 + 6 equals 12 after multiplication is completed first and the remaining operations are performed left to right. This matches choice B.

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Another way

  1. After multiplying, interpret 18 - 12 + 6 as the sum of signed terms 18, -12, and 6; combining them gives 12.

!

Common mistake

Do not evaluate every operation strictly from left to right at the start. Multiplication has priority, so 3 × 4 must become 12 before subtracting.

Solution walkthrough video