Lesson 1.2

Translating Complex Phrases

Some English phrases sneak in a twist — "less than" and "subtracted from" reverse the order. Master these tricky "turn-around words" and you'll never be fooled again.

Introduction

In Lesson 1.1 every key word placed the numbers in left-to-right order. Now we meet turn-around words — phrases where the subtraction or division order reverses.

Past Knowledge

You can translate simple phrases using sum, difference, product, and quotient.

Today's Goal

Correctly translate phrases with "less than," "subtracted from," and "divided into."

Future Success

Word problems in every future unit require flawless translation — especially with subtraction order.

Key Concepts

1. Normal-Order vs. Turn-Around Words

Type	Phrase	Result
Normal	"A number minus 4"
Turn-Around	"4 less than a number"
Turn-Around	"4 subtracted from a number"

2. The Golden Rule

"Less than" and "subtracted from" mean:
write the second thing first, then subtract the first thing.

3. Turn-Around Words List

Subtraction Turn-Arounds

less than
subtracted from
fewer than

Division Turn-Arounds

divided into

Worked Examples

Example 1: "Less Than"

Basic

Translate: "7 less than a number."

Spot the Turn-Around

"Less than" reverses the order. The gets subtracted.

Reverse the Order

Example 2: "Subtracted From" with Two Operations

Intermediate

Translate: "Twice a number, subtracted from 10."

Translate Each Piece

"Twice a number" →

Apply Turn-Around

"Subtracted from 10" → goes first.

Example 3: Multi-Step with Turn-Arounds

Advanced

Translate: "5 fewer than the product of 3 and a number."

Inner Part

"Product of 3 and a number" →

Apply Turn-Around

"5 fewer than" → subtract from .

Common Pitfalls

"5 less than x" ≠ "5 − x"

"5 less than " = , not .

Confusing "less" with "less than"

"A number less 4" → (normal). "4 less than a number" → (reversed). Same answer, different logic!

Real-Life Applications

Budgeting is full of turn-around language. "Your expenses are $200 less than your income" translates to . Getting the order wrong could make your budget look like you have extra money when you don't!