Section 1.3 Operations on the Set of Real Numbers Integrated Math Section 1.3 Operations on the Set of Real Numbers

Sum- answer when adding Difference- answer when subtracting Product- answer when multiplying Factors- numbers that are multiplied Quotient- answer when dividing

Absolute value- a number’s distance from zero on a number line 5 means how far is 5 from 0? 5 units −5 means how far is -5 from 0? 5 units

To remove a number from absolute value bars, find its distance from zero. −7 =? − −9 =? −4 +4=? 4 =? − 10 =?

Opposite numbers- two numbers on opposite sides of zero that have the same absolute value. 7 𝑎𝑛𝑑 −7 both have an absolute value of 7 7 and −7 are opposites.

#1 − 9 is the opposite of 9. True or False #2 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦 − −9 9 #3 What would −[− −8 ] equal? -8

Adding integers- - Treat the numbers like they are players on a team for tug-of war! -Think of a football game with the team gaining and losing yards! -Think of a piggy bank where you take some money out and put money in!

All positive numbers are on the same team- add them All negative numbers are on the same team –add them

If there are positive and negative numbers, the team with the most members wins (+ or −) and the excess number of players is the score!

#1 −6 + −5 = −11 #2 6 + 4 = 10 #3 −11+8 = −3 #4 14 + (−11) = 3

Keep-add a line –change the sign All subtraction problems are changed to addition problems! Add the opposite of the second number to the first number! ADD! 4 – 7 = 4 + (− 7) 11− 8 = 11 + (− 8) − 6 – 10 = − 6 + (− 10) − 3 – (− 5) = − 3 + (+5)

To multiply TWO numbers together- SAME SIGNS→ Positive answer (positive)(positive) = (positive) (negative)(negative) = (positive) Numbers get multiplied all the time!!! DIFFERENT SIGNS→ Negative answer (negative)(positive) = (negative) (positive)(negative) = (negative)

#1 (−6)(−2) #2 (8) (−3) #3 (−3)(−2)(−4)

Reciprocal- for every non-zero number, the reciprocal is 1 ÷ the non-zero number. If there is a fraction, the reciprocal can be found by flipping the fraction! 3→ 1 3 5 8 → 8 5 −7→ −1 7

For every non-zero real number- (the number)(the reciprocal) = 1 Sometimes the reciprocal is called the multiplicative inverse. 4 1 4 = 1

Terms for division- 𝑑𝑖𝑣𝑖𝑑𝑒𝑛𝑑 𝑑𝑖𝑣𝑖𝑠𝑜𝑟 = quotient Division can be changed to multiplication by multiplying the dividend by the reciprocal of the divisor. 24 4 = 24÷ 4 = 24 × 1 4

Division by zero is undefined. Think of dividing a pie into pieces. 1/1 = no cut or a whole pie 1/ 2 = divide pie into two pieces 1/3 = divide pie into three pieces etc. YOU CAN’T CUT BY ZERO!

Operations with fractions Some fractions are decimal-friendly Denominators of 2,4,5,8 and 10 You can divide to get a decimal If you divide up, your grade will go down For non-decimal-friendly fractions, use the calculator Try 2/7 + 3/5 Try −3 1 2 +2 1 3 (change to improper fractions)

https://www.youtube.com/watch?v=kOLfvdEv0yM

Assignment #3 Pg. 28 #3-126 multiples of 3