Week 3: Multiplying signed numbers, order of operations, and unit multipliers

Field Book

9 to 12

Due

Test 1 due

Method

Paper first, every step

Multiplication picks up signs this week and the order of operations becomes law. Unit multipliers arrive too: fractions equal to one that trade a measurement into new units without changing its size.

What you have to be able to do

Multiply and divide signed numbers
Evaluate expressions in the correct order
Convert units, including square units, with unit multipliers

The procedures

Signs in multiplication and division

Same signs give a positive answer.
Different signs give a negative answer.
Count the negative factors: an even count is positive, an odd count is negative.

Order of operations

Grouping symbols first, from the inside out.
Then multiply and divide, left to right.
Then add and subtract, left to right.

Unit multipliers

A unit multiplier is a fraction equal to one, like 12 inches over 1 foot.
Multiply by it so the old unit cancels and the new unit stays.
Square units need two multipliers, one for each dimension.

Worked

WORKED

Compute (−4)(−6) − (−3)(5).
(−4)(−6) is 24, and (−3)(5) is −15.
24 − (−15) is 24 + 15.
ANSWER: 39

WORKED

Convert 2 square feet to square inches.
Two multipliers: 12 in1 ft twice, once per dimension.
2 × 12 × 12.
ANSWER: 288 square inches

Terms

Term	Meaning
order of operations	grouping first, then multiply and divide, then add and subtract, left to right
unit multiplier	a fraction equal to one that trades one unit for another
product	the answer to a multiplication

Check yourself

1. Compute (−7)(8)

2. Compute 20 − 3 × 4

3. Convert 5 yards to feet

reveal answers

−56 · 8 · 15 feet

This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.