WHATS THE MISSING LETTER Or How to solve

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WHAT’S THE MISSING LETTER? Or How to solve Algebraic Equations 4 y + 4

WHAT’S THE MISSING LETTER? Or How to solve Algebraic Equations 4 y + 4 – y + 3 + = y + 28 (they really won’t be this long)

But what’s this Algebra stuff?

But what’s this Algebra stuff?

ALGEBRA n ALGEBRA means: Reduction and comparison (using numbers and letters).

ALGEBRA n ALGEBRA means: Reduction and comparison (using numbers and letters).

It’s all about BALANCE In math, what you do to one side you have

It’s all about BALANCE In math, what you do to one side you have to do to the other.

The Mystery “person” in Algebra is the… n VARIABLE (S): A letter(s) or symbol

The Mystery “person” in Algebra is the… n VARIABLE (S): A letter(s) or symbol that represents a number in an algebraic expression. In y + 5 = 9 the variable is y.

What’s the opposite operation? n INVERSE OPERATION: Two operations that undo each other. Addition

What’s the opposite operation? n INVERSE OPERATION: Two operations that undo each other. Addition and subtraction undo each other. Multiplication and division undo each other.

Let’s do some work. But first… n n n n The inverse of division

Let’s do some work. But first… n n n n The inverse of division is ______. MULTIPLICATION The inverse of subtraction is ______. ADDITION The inverse of multiplication is ______. DIVISION The inverse of addition is ______. SUBTRACTION

Solving Subtraction Equations x – 150 = 180 X – 150 + 150 =

Solving Subtraction Equations x – 150 = 180 X – 150 + 150 = 180 + 150 (-150 +150 =0) x = 330

X – 150 + 150 = 180 + 150 (-150 +150 =0) x =

X – 150 + 150 = 180 + 150 (-150 +150 =0) x = 330 n Try this on your whiteboard. Balance yours using the inverse operation. n y – 11 = 3 n y – 11 + 11 = 35 + 11 n y = 46 The inverse operation was ______ ADDITION n 2) n n x + 8 = 27 x + 8 – 8 = 27 – 8 x = 19 The inverse operation was ____ SUBTRACTION

What’s next? . . . Multiplication! 150 x = 180 (Remember…if a number and

What’s next? . . . Multiplication! 150 x = 180 (Remember…if a number and a variable are stuck together, that means they are going to be… +, -, x or ÷ ?

What’s next? . . . Multiplication! 150 x = 180 n n (Remember…if a

What’s next? . . . Multiplication! 150 x = 180 n n (Remember…if a number and a variable are stuck together, that means they are going to be… +, -, x or ÷ ?

150 x = 180 150 150 180 x = 1. 2

150 x = 180 150 150 180 x = 1. 2

Try some. Use the Inverse Operation. n n 4 b = 32 4 4

Try some. Use the Inverse Operation. n n 4 b = 32 4 4 b=8 (4 • 8 = 32) n n 48 = 6 y 6 6 Y=8 6 48 (6 • 8 = 48)

The inverse of multiplication is… DIVISION!!! n

The inverse of multiplication is… DIVISION!!! n

And finally, Division n The inverse of Division is… n MULTIPLICATION. n X ÷

And finally, Division n The inverse of Division is… n MULTIPLICATION. n X ÷ 150 = 180

X ÷ 150 = 180 X ÷ 150 • 150 = 180 • 150

X ÷ 150 = 180 X ÷ 150 • 150 = 180 • 150 n (÷ 150 • 150 cancel out) n X = 27000 n

Two more examples. Remember to show the inverse operation. c÷ 3=9 n c ÷

Two more examples. Remember to show the inverse operation. c÷ 3=9 n c ÷ 3 • 3 = 9 • 3 n C = 27 (9 • 3 ) n 2. 5 = z ÷ 4 n 2. 5 • 4 = z ÷ 4 • 4 n 10 = z (2. 5 • 4) n

One more step…Combining like terms n n n n m + 6 + 12

One more step…Combining like terms n n n n m + 6 + 12 = 38 Combine the numbers first +6 + 12 = 18 M +18 = 38 Now do the inverse operation M + 18 – 18 = 38 – 18 M = 20

What if…? n n n n 3 + y – 7 = 45 You

What if…? n n n n 3 + y – 7 = 45 You can do each inverse as you go. 3 – 3 + y – 7 +7 = 45 – 3 + 7 Y = (45 -3) + 7 Order of operations Y = 42 + 7 Y = 49 3 + 49 – 7 = 45

n 4 + p + 8 = 19

n 4 + p + 8 = 19