1. Section 1.6 Using Properties in Computation
Integrated Math
Section 1.6
Using Properties in Computation

2. Can you multiply this problem in your head?
(without paper or a calculator)
5(85)(2)= ?

3. If it is rewritten as 5(2)(85), is it easier?
What property did we use to make the problem easier?
5(85)(2) → 5(2)(85)

4. If you were adding this group of numbers, would rearranging them make the problem easier?
= ?
= ?

5. When using order of operations, consider this problem
(42×4)×25
Changing the parentheses makes this easier!
42 ×(4×25)
What property did we apply?

6. What is the definition of a term?

7. Definitions
Term- a number or variable or a product of numbers and variables
Coefficient- the number in front of a variable
Like terms- two or more terms with the same variable(s) raised to the same power(s).

8. Like Terms
Unlike terms
3x, 5x
3x, 5
2 𝑥 2 , 5 𝑥 2
2 𝑥 2 , 5x
3xy, 5xy
3xy, 5x
6a, 5a
6a, 5b

9. Combining Like Terms When adding or subtracting like terms,
The coefficients are combined
The variable part doesn’t change
3 𝑥 2 +5 𝑥 2 = 8 𝑥 2

11. Think of combining like terms this way:
You can combine apples with apples and oranges with oranges but DON’T MAKE A FRUIT BOWL!!!!

12. Multiplying terms
If you need to multiply (3x)(2y) This says 3∙𝑥∙2∙𝑦 Commutative property says that equals 3∙2∙𝑥∙𝑦 𝑤ℎ𝑖𝑐ℎ 𝑒𝑞𝑢𝑎𝑙𝑠 6𝑥𝑦 WHEN MULTIPLYING, THE VARIABLE PART DOES NOT HAVE TO BE THE SAME!

13. Be able to discern the difference between operations
5x + 2y addition
(5x)(2y) multiplication
Which one can be simplified?

14. When adding or subtracting terms, every term has a coefficient!
What is the coefficient if there is nothing preceding a variable?

15. Don’t forget about invisible 1’s
4x + x + 3x = 8x

16. Dividing terms 55𝑥𝑦 5 Think of this like reducing a fraction
Consider the problem-
55𝑥𝑦 Think of this like reducing a fraction
5×11×𝑥×𝑦 5

17. If you have a numerator with several terms, every term must be divided by the denominator.
−10 𝑥 2 +6𝑥 = −5 𝑥 2 +3x+12

18. Distributive property
Always use distributive property before trying to combine like terms
4 3𝑥+2 −6(5𝑥−7)
12𝑥+8−30𝑥+42
−18𝑥+50

19. A negative outside parentheses changes all the signs of the terms inside the parentheses.
This is the same as multiplying by a negative 1.
−1 6 =−6
− 6𝑥−2 =−6𝑥+2
4𝑥+2 − 3𝑥+7 =4𝑥+2−3𝑥−7