Chapter 1.1.1-1.1.2: Integers & Fractions

What are the magnitude/weights and opposites?

magnitudes/weights: of a number is the distance it is from 0 on the number line

opposites: numbers on opposite sides of zero, but the same distance away from zero

What is sum, difference, product, and quotient?

sum: the result of adding two or more numbers
difference: the result of subtracting two or more numbers
product: the result of multiplying two or more numbers
quotient: the result of dividing two or more numbers

What are two opposite numbers called?

a zero-pair, because adding them
always results in 0.

How do you add integers of the same signs? different signs?

-To add two numbers of the same sign, add their weights and place it
after the sign

-To add two numbers of opposite signs, find the difference of their
weights and place it after the sign of the number with the greater
weight.

What are the two ways “-” is used?

When it is between two expressions, it means subtract (e.g., 3 − 4)

. Otherwise, it

means ’opposite’ or ’negative’ (e.g., −3 + 4).

What is Subtraction as Addition of the Opposite?

instead of performing a subtraction operation, you can rewrite the problem as an addition problem by changing the sign of the number being subtracted (making it its "opposite") and then adding that number instead

What are the rules of multiplying and dividing integers?

-If the signs of the two numbers are the same, then the sign of the answer is positive.

-If the signs of the two numbers are different, then the sign of the

answer is negative.

What are rational numbers?

Any rational number looks like p/q where p and q are integers and q is not zero

What are the Prime Factorization Rules?

1. Divide by the smallest prime (start with 2).

2. Continue dividing by primes until the result is prime.

3. Express as a product of primes.

How do you Multiply, divide, Add, & Subtract Fractions?

• Multiply: Multiply numerators and denominators.

• Divide: Multiply by the reciprocal.

• Add/Subtract: Find the LCD, adjust fractions, then add/subtract numerators.