Math 010: Word problems & Exam Review Part IOctober 16, 2013

Verbal expressions – Key points

“Less than” and “subtracted from” are REVERSE ORDER SUBTRACTION

Order matters with subtraction and division

Know all the basic terms by heart – use list to test yourself and p. 354 in the book

Write all quotients as fractions to be safeExample “The quotient of r and the

sum of r and four” becomes

Layered verbal expressions

Look at the first part of the expression, up to the first “math term”

That will be the “outside”/”main” operation, all others go “inside”

Example: “Six times the difference between y and eight”

Six times the difference between y and eight

So multiplying by 6 is the “outside” operation

y-8 goes on the inside

6(y-8)

“Twice the sum of three and w”

First math term is TwiceMultiplying by 2 is the “outside”

operation“Sum of three and w” is on the

inside2(3+w)

“The quotient of nine times k and seven”

First math term is quotient – division is “outside”

A quotient must have two components, what two things are being divided?

“nine times k” and “seven”

Could write (9k)÷(7)

Preferred:

“The total of twice q and five”

First math term is totalAddition must contain two

terms, what two things are being added together?

“twice q” and “five”2q + 5

“Seven subtracted from the product of eight and d”

First math term is “subtracted from”

“Product of eight and d” = 8d on the “inside”

Don’t forget it’s reverse order8d - 7

“five less than the product of n and eight”

First math term is less thanFive less than something – what?“the product of n and eight” = 8nREVERSE ORDER!8n - 5

“the quotient of r and the sum of r and four”

First math term: quotient = division

A quotient must have two components.

What is divided by what?

r is divided by “the sum of r and four”.

sum of r and four = (r + 4)

Can write: r ÷ (r + 4) NEED PARENTHESES

Preferred to write:

FRACTIONS REVIEW

#31-33 on practice test

When multiplying fractions, multiply across top and bottom.

= Simplify?

Both 2 and 6 divisible by 2 -> =

14+13

When adding fractions, you need a common denominator. What is the common denominator?

12

Relationship to each denominator: 12 = 4 · 3; 12 = 3 · 4

= =

34+(−

15)

Adding a negative number is the same as subtracting.

Need a common denominator

20

=

Squaring fractions: #29-30 on practice test

Remember, squared means….

Multiplied by itself.

So = · Just multiply across top and bottom!

= · = = = · = =

Word problem #2 on practice test One-fifth of the freshman class at RIC is taking Math 010

this semester. Out of the students taking Math 010, one-fifth of them are asking for extra help in the class from their professors. What fraction of the entire freshman class is asking for extra help in Math 010?

This problem is asking “What is one-fifth of one-fifth?”

Of means times.

· = =

#6

A campground is charging $14 for each RI resident and $18 for each out-of-state resident.

Write a variable expression that shows the total amount charged, letting x represent the number of RI residents and y represent the number of out-of-state residents.

What operation to calculate cost at the each rate?

Multiply $14 by number of RI residents -> $14x

Multiply $18 by number of out-of-state -> $18y

Now add the two costs together

$14x + $18y

Don’t forget the dollar signs – worth 1 point on exam

#7

Use the expression you wrote in the last problem to calculate the total amount charged for two RI residents and three out-of-state residents.

$14x + $18y

x = 2; y = 3

Plug in each value

$14(2) + $18(3)

Order of operations: multiply first

$28 + $54 = $82

Don’t forget the dollar signs

#11

I bought three concert tickets, all equally priced. I paid $63.60 for all three tickets.

What was the cost of each ticket? Write an equation, and solve.

3 concert tickets = $63.60

Let x represent the cost of one ticket

3x = $63.60

To solve, get x alone

Divide each side by 3

x = $21.20

Don’t forget the dollar sign.

#21

I want to buy an empty lot. The owner told me the lot is a perfect square, and the area of the lot is 144 square yards. What is the length of the lot on one side?

Area of a square = where s is the length of one side

= 144 sq. yd.

To get s alone, undo the “squared” operation

Take the square root of both sides

s = 12 yards

Remember units in answer: Yards is a measure of LENGTH

144 square yards

#23

Shawn was checking out at Old Navy when he noticed his receipt total was $46.61, which was more than he thought he was spending. He realized he had been charged for an extra item, which was $7.99. With the extra item taken out, what was Shawn’s actual total?

(There is no sales tax on any items.) Set up the problem correctly and solve.

The extra item must be removed from the total.

Removed means SUBTRACTED

$46.61 - $7.99 = $38.62

Work on the practice test alone or in pairs. See me if you have not gotten your Exam #1 back

Look over all questions, ask for help if you need it

Use the powerpoints from previous classes to review at home

For your quiz grade, AFTER you have looked over all problems, rate your confidence out of 5 on the following topics (5 best, 1 worst): Fractions

Simplifying algebraic expressions

Verbal -> variable expressions

Graphing inequalities

Decimals

Word problems