Proportional relationships
Two quantities are proportional if y = kx, where k is the constant of proportionality. If 3 notebooks cost $6, then k = 2, so 5 notebooks cost $10.
Try it: If 4 pencils cost $3, how much do 12 pencils cost?
Show answer
$9.
Lessons by subject. Read the lesson, try the question, then check your answer.
Topics follow the Georgia Standards of Excellence, the state's current standards (they replaced the older Common Core Georgia Performance Standards). This is an unofficial study aid, not a Coffee County Schools resource. Your teacher's pacing guide and textbook come first. Official standards: georgiastandards.org.
Two quantities are proportional if y = kx, where k is the constant of proportionality. If 3 notebooks cost $6, then k = 2, so 5 notebooks cost $10.
Try it: If 4 pencils cost $3, how much do 12 pencils cost?
$9.
A 20% discount takes 20% off the price. For a $40 item, 20% is $8, so the sale price is $32.
Try it: A $50 jacket is 30% off. What is the sale price?
$35.
Use a number line. Subtracting a number is the same as adding its opposite: 4 − (−2) = 4 + 2 = 6.
Try it: What is −3 + 5?
2.
Same signs give a positive result. Different signs give a negative result. (−4)(−3) = 12 and (−4)(3) = −12.
Try it: What is (−6) ÷ 2?
−3.
The Sahara is the world's largest hot desert, in northern Africa. The Nile flows north to the Mediterranean Sea and has long supported farming in Egypt.
Try it: Which direction does the Nile flow?
North.
South of the Sahara are savannas and rain forests. Mount Kilimanjaro in Tanzania is the highest mountain in Africa.
Try it: Where is Mount Kilimanjaro?
In Tanzania, in Africa.
Much of Southwest Asia, also called the Middle East, is dry. The Arabian Peninsula and Persian Gulf region hold some of the world's largest oil reserves.
Try it: Why is oil important to the region's economy?
Many countries earn income by selling oil to the world.
The Tigris and Euphrates Rivers flow through Iraq and nearby countries. Water is scarce in much of the region, so it is very valuable.
Try it: Name one river in Southwest Asia.
The Tigris or the Euphrates.
A theme develops over a whole text. A good summary states the main ideas without your personal opinion.
Try it: Should a summary include your personal opinion?
No.
The setting can shape the plot, and the narrator's point of view affects what the reader learns.
Try it: How does a first-person narrator limit what we know?
We only learn what that narrator sees, thinks, and feels.
A clause has a subject and a verb. An independent clause can stand alone. A dependent clause cannot: because it rained.
Try it: Is because it rained a complete sentence?
No. It is a dependent clause.
Use a semicolon to join two related independent clauses: I studied; I passed. Use a colon before a list or explanation.
Try it: Which punctuation mark joins two related independent clauses without a conjunction?
A semicolon.