Algebra Ii By Monica Yuskaitis

Algebra Ii By Monica Yuskaitis - Transcript

Algebra II
By Monica Yuskaitis

Definitions
• Equation – A mathematical
sentence stating that 2
expressions are equal.
• 12 – 3 = 9
• 8 + 4 = 12

Definitions
• Equation – A mathematical
sentence with an equals sign.
• 16 – 5 = 11
• 14 + 3 = 17

Definitions
• Equals Sign (=) Means that the amount is the same on both sides.
• 4 + 2 = 6
• 5 – 2 = 3

An Equation is like a balance scale. Everything must be equal on both sides.
10 5 + 5
=

When the amounts are equal on both sides it is a true equation.
12 6 + 6
=

When the amounts are unequal on both sides it is a false equation.
8 2 + 2
=

When an amount is unknown on one side of the equation it is an open equation.
7 n + 2
=

When you find a number for n you change the open equation to a true equation. You solve the equation.
7 n + 2
=
5

Are these equations true, false or
open?
• 11 - 3 = 5
• 13 + 4 = 17
• N + 4 = 7
• 12 – 3 = 8
• 3 + v = 13
• 15 – 6 = 9
false
true
open
false
open
true

Definitions
• Inverse operation – the opposite
operation used to undo the first.
• 4 + 3 = 7 7 – 4 = 3
• 6 x 6 = 36 36 / 6 = 6

How to solve an addition
equation
• Use the inverse operation for
addition which is subtraction
• m + 8 = 12 12 - 8 = 4
• m = 4 4 + 8 = 12

How to solve a subtraction
equation
• Use the inverse operation for
subtraction which is addition
• m - 3 = 5 5 + 3 = 8
• m = 8 8 - 3 = 5

Solve these equations using the
inverse operations
• n + 4 = 7
• n – 5 = 4
• n + 4 = 17
• n – 6 = 13
• n + 7 = 15
• n – 8 = 17
3
9
13
19
8
9

Commutative Property
• 5 + 4 = 9 4 + 5 = 9
• a + b = c b + a = c
• 6 + 3 = 9 3 + 6 = 9
• x+ y = z y + x = z
• 3 + 4 + 1 = 8 1 + 3 + 4 = 8

Solve these equations using the
commutative property
• n + 7 = 7 + 4
• m + 2 = 2 + 5
• z + 3 = 3 + 9
• g + 6 = 6 + 11
• s + 4 = 4 + 20
• c + 8 = 8 + 32
n = 4
m = 5
z = 9
g = 11
s = 20
c = 32

The Identity Property of Addition
• 7 + 0 = 7
• a + 0 = a
• 8 + 0 = 8
• c + 0 = c
• 2 + 0 = 2

Use the Identity Property of
addition to solve these problems
• n + 0 = 8
• b + 0 = 7
• m + 0 = 3
• v + 0 = 5
• w + 0 = 4
• r + 0 = 2
n = 8
b = 7
m = 3
v = 5
w = 4
r = 2

Subtraction Rules of zero
• 7 – 7 = 0
• n – n = 0
• 4 – 0 = 4
• n – 0 = n

Find the value of n using the rules
of subtraction
• n - 8 = 0
• n – 9 = 0
• n – 0 = 7
• n – 0 = 9
• n – 7 = 0
• n – 0 = 5
n = 8
n = 9
n = 7
n = 9
n = 7
n = 5

Write an equation for these
problems using a variable
• Timothy got 72 right on his timed test in July. He got 99 right on this same test in November.
• Jasmin runs 15 minutes before school and 30 minutes after school.
• One zinger costs 25 cents. Issak bought 4.
72 + n = 99 or 99 – 72 = n
15 + 30 = n
4 x 25 = n