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All courses Algebra I · A-SSE.1.b 14 of 76
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

Identify the grouped scope

\[3(12~+~5)~->~\text{inside}~12~+~5~\text{applies}~\text{to}~\text{one}~\text{person};~\text{outside}~3~\text{counts}~\text{people}\]

The parentheses package the ticket and snack costs into one person's subtotal before the outside factor repeats that group.

02

Interpret and evaluate the inside

\[12~\text{dollars}~\text{ticket}~+~5~\text{dollars}~\text{snack}~=~17~\text{dollars}~\text{for}~\text{one}~\text{person}\]

Both inside terms are per-person dollar costs, so their sum is a 17-dollar per-person subtotal.

03

Distinguish subtotal from grand total

\[\text{one}-\text{person}~\text{subtotal}~=~17~\text{dollars}/\text{person};~\text{all}-\text{three}~\text{total}~=~3(17)~=~51~\text{dollars}\]

The requested subexpression is only the inside quantity. Multiplying by 3 produces a different quantity: the total for all three people.

04

Report every subexpression field

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

The expression, role, scope, evaluated value, and unit all describe the grouped inside quantity rather than the outside total.

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Another way

  1. Rewrite 3(12 + 5) as (12 + 5) + (12 + 5) + (12 + 5); each repeated addend is one person's $17 subtotal.

!

Common mistake

Do not call 12 + 5 the total for three people. The parentheses describe one person's costs; the outside 3 creates the three-person total.

Solution walkthrough video