The number line grows a left half this week, and every rule for it comes down to direction and distance. Area rides along: the space inside a figure, counted in squares.
What you have to be able to do
Add and subtract signed numbers
Give the opposite and the absolute value of any number
Find the area of a rectangle and a triangle
The procedures
Adding signed numbers
Same signs: add the sizes and keep the sign.
Different signs: subtract the sizes and keep the sign of the larger.
Zero is the balance point; opposites cancel to it.
Subtracting signed numbers
Subtracting is adding the opposite. Rewrite it that way, every time.
Then follow the addition rules above.
Two sign changes in a row put you back where you started.
Area
A rectangle is length times width.
A triangle is half of base times height.
Area answers come in square units.
Worked
WORKED
Compute −8 + 3 and −8 − 3. −8 + 3: different signs, subtract sizes, keep the minus. −8 − 3 is −8 + (−3): same signs, add the sizes. ANSWER: −5 and −11
WORKED
A triangle has base 10 and height 7. Find its area. Half of base times height. Half of 70. ANSWER: 35 square units
Terms
Term
Meaning
opposite
the number the same distance from zero on the other side
absolute value
a number’s distance from zero, never negative
area
the number of unit squares inside a figure
Check yourself
1. Compute −6 + 14
2. Compute |−9|
3. A rectangle is 8 by 5.5. Find the area.
reveal answers
8 · 9 · 44 square units
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.
-- THE UNKNOWN -- week 2, signed numbers and areaalgebra 1 · oda