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

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

3. 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

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

6. 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.

7. #1 − 9 is the opposite of 9. True or False
#2 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦 − −9 9
#3 What would −[− −8 ] equal? -8

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!

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

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

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

12. 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)

13. 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)

14. #1 (−6)(−2)
#2 (8) (−3)
#3 (−3)(−2)(−4)

15. 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→ → −7→ −1 7

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

17. 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

18. 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!

19. 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 − (change to improper fractions)

21. Assignment #3
Pg. 28 # multiples of 3