Math 6H (Period 3)

Writing Equations 5.2

An equation is a mathematical sentence; a statement that uses an equal sign to separate two equal expressions     expression = expression

An equation has two sides à a left side and a right side!

For example    x + 5 = 7

A solution of an equation involving one variable is a value of the variable that makes the equation true.  For example 2 is a solution of x + 5 = 7 because  2 + 5 = 7  is a TRUE statement.

Finding all the solutions of an equation is called solving the equation.

Some equations are simple enough to solve using mental math.  We will use those simple equations to build our understanding of the algebraic method of solving equations.

A phrase does not usually contain a verb but a sentence MUST contain a verb. The verb in an equation is usually either “is”, equals”  or “is equal to”

We practiced translating several sentences into algebraic equations, such as:

The sum of a number and 8 is 17à n + 8 =17

Five less than a number is 9 à  x - 5 = 9

Fourteen equals 8 times a number à 14 = 8m

The quotient of 12 and a number is 4 à 12/y = 4

Sometimes it is a good idea to break down the verbal sentences when translating to an algebraic equation.  Circle the operation  and place the algebraic sign for that operation.  We wrote out our verbal sentences and below the “is” we wrote +. Then we took each part and translated it carefully.

Another method is the following  example:
The sum ( write +) of 3 ( write 3 before the +) and a number (write n after the +) is (write =) 10 ( write 10 after the =)

Explain why the equations x + 3 = 5 and 3 + x = 5 have the same solutions but the equations x – 3 = 5 and 3 – x = 5 do not.

Math 6H (Period 3)

Writing Expressions 5.1

To use algebra in solving real-life problems, you need to translate words, phrases and sentences into mathematical symbols. Fist look for the words that indicate operations.

We went through several examples for each operation:

Translating Addition Phrases:

Ten more than a number     à x + 10

The sum of -8 and a number à -8 + y

A number plus 3 à n + 3

Translating Subtraction Phrases

Five minus a number à 5 - x

The difference of 3 and a number à  3 – n

Nine less than a number à  y – 9

Translating Multiplication Phrases

Five times a number à  5y

The product of 7 and a number à  7x

A number multiplied by -2 à -2m

Translating Division Phrases

The quotient of a number and 6 à x/6

Five divided by a number à  5/n

REMEMBER: Subtraction and division are NOT commutative. the order in which you write the numbers and variables changes the meaning of the variable expression.  

We then discussed the problem in our textbook on page 218

You join a health club that has a membership fee and a tennis court fee. According to the sign in the textbook, the membership is $25 a month and the court fee is $5 per use. We had to write an expression for your total  monthly cost.

MEMBERSHIP FEE   + COURT FEE · NUMBER OF TIMES YOU USED THE COURT

Let n = the number of times you use a court.

25 + 5n

We went through Problems # 24-27 on Page 219

A truck traveled 65 miles per hour for a number of hours, To find the number of miles traveled... youà multiply. The distance traveled equals the product of the rate of travel and the time traveled.

Your regular paycheck is increased by $65 for working overtime. To find the total amount of your paycheck... youà add; “increased by” indicated addition.

Sixty-five fewer people came than the number expected. To find the number of people who came ...you à subtract; “fewer” indicates subtraction

Your grandmother is 5 years younger than her brother. To find your grandmother’s age ...youà subtract; “younger than” indicates subtraction.

Math 6A (Periods 2 & 4)

Although we saw this You Tube video in class, several of you asked to see it again... so