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All courses Math I · A-SSE.1.b 14 of 59
Interpret complex expressions by treating meaningful sub-expressions as single units.

Interpret a sub-expression inside parentheses

Problem
In 3(12+5), three people each pay $12 ticket plus $5 snack. For 12+5, identify role, scope, value/formula, and unit.
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Hint

Look inside the parentheses first. The sub-expression 12 + 5 describes one person's total before the outside 3 counts all three people.

An expression inside parentheses is one complete group. The outside coefficient tells how many identical groups there are.

Solution walkthrough

01

Read one complete group

\[12~+~5\]

The sub-expression adds the ticket cost and snack cost for one person.

02

Interpret the outside multiplier

\[3(12~+~5)\]

The 3 means there are 3 identical people, each with that same one-person cost.

03

Decide what the inside means

\[12~+~5~=~\text{one person's total}\]

Before multiplying by 3, the expression inside the parentheses describes what one person pays.

04

State the answer in context

\[\text{subexpression}~=~12+5;~\text{role}~=~\text{per}-\text{person}~\text{subtotal};~\text{scope}~=~\text{one}~\text{person};~\text{value}~=~\$17;~\text{unit}~=~\text{dollars}/\text{person}\]

The sub-expression 12 + 5 means the cost for one person before multiplying by 3.

+

Another way

  1. Rewrite as (cost for one person) + (cost for one person) + (cost for one person).

  2. Evaluate 12 + 5 first to see that it is a single person's combined ticket-and-snack cost.

!

Common mistake

Thinking 12 + 5 already represents all three people. The parentheses show one group, and the 3 is what repeats that group.