Introduction to Algebra

• Terms:

1.) VARIABLES: Letters that represent UNKNOWN numbers. 2.) TERMS: Elements separated by the plus or minus sign3.) COEFFICIENT: The number before a variable in a

multiplication term4.) EXPRESSION: One or more algebraic term without an

equals sign5.) EQUATION: A statement that two amounts are EQUAL.

6.) FORMULA: A rule expressed in math symbols, such as

Introduction to Algebra

Introduction to Algebra

Introduction to Algebra

4x -7 = 5

Equation

Introduction to Algebra

• Distance equals rate of speed multiplied by the amount of time traveled.

Distance = Rate x TimeD = RT

Formula

Translating Equations

The sum of three times a number and eight is thirty-six

3r + 8 = 36

The words "the sum of" tell us we need a plus sign because we're going to add three times a number to eight. The words "three times" tell us the first term is a number multiplied by three.

Translating Equations

 A number decreased by two is equal to three.n – 2 = 3

The sum of eight and a number is twelve. 8 + x = 12Two less than a number is four.

y – 2 = 4Nine is equal to a number divided by four.

9 = t ÷ 4

Translating Equations• You try:A number divided by 2 is equal to 11

Four more than three times a number is thirteen. Three equals six times a number. Five less than the product of eight and a number

is thirty-five.

Translating Equations• You try:A number divided by 2 is equal to 11

d ÷ 2 = 11Four more than three times a number is thirteen. 3y + 4 = 13Three equals six times a number. 3 = 6zFive less than the product of eight and a number is

thirty-five.8r – 5 = 35

Common Formulas

SIMPLE INTEREST:Interest = Principle x Rate x Time

DISTANCE: Distance = Rate x Time

TOTAL COST:Total Cost = (number of units)x (price per unit)

Substituting in Formulas

If Sarah drove 390 miles at an average speed of 60 miles per hour, how long did it take her to complete her trip?

Substituting in Formulas

If Sarah drove 390 miles at an average speed of 60 miles per hour, how long did it take her to complete her trip?

1) Write the formula you need:Distance = Rate x Time

D = RT2) Substitute numbers for variables where

possible:390 = 60T

Substituting in Formulas

1) Write the formula you need:D = RT

2) Substitute numbers for variables where possible:390 = 60T

3) Solve the equation using your algebra skills 390 = 60T

÷60 ÷606.5 = T

It took Sarah 6.5 hours to complete her trip.

Substituting in Formulas1) If the total cost of a shipment of pet food cans was $350 and there were

875 cans, how much did each can cost?

2) Write the formula you need:Cost = # of Units x Price per unitC = UP

2) Substitute numbers for variables where possible:350 = 875P

3) Solve the equation using your algebra skills 350 = 875P

÷875 ÷875.4 = P

Each can costs .4 dollars – or 40 cents.

Algebra Translating and Formulas

• Try pages 24 and 25 in the GED Math Practice booklet and enter your answers on Blackboard.