Math 010: Verbal expressions & Intro to Equations October 9, 2013.

Math 010: Verbal expressions & Intro to EquationsOctober 9, 2013

Pre-test on Verbal ExpressionsFirst page of worksheet

5.7 Verbal -> Variable Expressions

•Verbal means words, variable means algebraic/math language•Memorize terms, also understand meaning in context

Addition Terms• “added to”• “more than” – adding numbers makes

them more• Except when negatives are involved• “the sum of”• “increased by” – adding will create an

increased quantity• “the total of” – to find a total, add all

quantities together

Subtraction Terms• “minus”• “the difference between”• “decreased by” – subtracting will create a

decreased quantity• “less than” • Note: 5 less than y means y - 5• “subtract… from”• Note: 2 subtracted from x means x - 2

Multiplication Terms• “times”• “twice” means two times• “of” – used with fractions• “ of x” means times x or x• “the product of” • “multiplied by”

Division Terms

• “divided by”• “the quotient of”• “the ratio of” • ratios can be division problems or fractions

“t increased by 9”

• A study published by the Nature Climate Change journal last year predicted that by the year 2100, the global temperature will be increased by 9 degrees Fahrenheit. • Let t represent the current global temperature. • Write an expression for the predicted future temperature.• Current global temperature, plus 9 degrees• t + 9

“twice w”

• According to the Wall Street Journal, a waiter working in San Francisco makes twice as much as a waiter working in New York City.

• Let w be the wages of a waiter working in New York City.• Write an expression for the wages of a waiter in San Francisco.• twice as much means two times as much• 2w – remember, no symbol means multiplication.

“the product of y and z”• The amount of gas money used on a trip is the product of the

number of gallons of gas used and the price of gas per gallon.• Let y be the number of gallons used, and let z be the price of

gas per gallon.• Write a formula for the amount of gas money used.• Product means multiply!• yz

“7 less than t”• What operation?• Subtraction.• With subtraction, always ask “Does the order of numbers stay

the same or get reversed?• In the case of less than, it gets reversed.• t - 7

“the difference between y and 4”• Difference means subtraction.• Reverse or stay the same?• Order stays the same.• y - 4

“the quotient of y and z”

• Speed is defined as the quotient of distance and time. Let y represent distance and z represent time.

• Write an expression for speed.• Quotient means division!• y ÷ z• Can also write as a fraction:

“the fifth power of a”• A decateron, or 5-cube, is a hypercube that exists in five

dimensions. The 5-dimensional volume of a decateron with side length a is defined as the fifth power of a.

• Power means exponent.• - that means a · a · a · a · a

“x minus 2”• Pretty obvious here• But ask: Does order stay the same or reverse?• Stays the same.• x - 2

“x divided by 12”

•Another obvious one

•Or write as a fraction:

“8 more than x”• I don’t remember our test scores, but I know I got 8 more

points than you did.• Let x represent your test score. • Write an expression for my test score.• More means addition• x + 8

“the total of 5 and y”• I went to a restaurant and ordered one item for 5 dollars, and

another item for y dollars.• Write an expression to represent the total of the bill.• Total means addition• 5 + y

“y multiplied by 11”• Just a note here on order…• Dictated word for word, you get y · 11• In multiplication, constant terms come first• 11y

“the sum of x and z”

•Sum means addition.•x + z

“6 added to y”

• Obvious, but note order again…• Dictated: 6 + y• In addition, variable terms come before

constant terms.• y + 6

“m decreased by 3”

•Decreased by means minus.•Order stays the same or reverses?•Same•m - 3

“the cube of r”

• The volume of a cube with side length r is defined as the cube of r.• • That means

“subtract 9 from z”

•We know the operation is subtraction…•But does the order stay the same or reverse?•It reverses.•z - 9

“10 times t”

•Dictated: 10 · t•10t

“one-half of x”

•In fractions, of means…•Multiply• =

“the ratio of t and 9”• For every t pairs of shoes in my closet,

I have 9 pairs of socks.• Find the ratio of shoes to socks.•Ratio means division•Can write t ÷ 9 or

“the square of x”

• The area of a square with side length x is defined as the square of x.

Adding more layers• Translate “three times the sum of c

and five” into math.• “3 times the sum of c and 5”•3 is not just multiplied by one object,

it is multiplied by the sum.• So we need parentheses around the

sum: (c + 5)•3 (c + 5)

“The difference between four times w and nine”

•Two parts to the difference: “four times w” minus “nine”•Difference means subtract, order stays the same•4w - 9

“Five less than the product of n and eight”

•Less than means subtraction, order reverses…•So it’s “the product of n and eight” minus 5•8n - 5

“The quotient of r and the sum of r and four”• Quotient is the blanket term here –

applies to the rest of the sentence• Use a fraction• r is the numerator• “the sum of r and four” is the denominator

“Twice x divided by the difference between x and 7”• Think of the division problem as a fraction.• “divided by” is the fraction bar.• “Twice x” is the numerator.• “The difference between x and 7” is the denominator.

Do your homework for 5.7

• Recommended to work ahead. Check your answers to odd #s in the back of the book• Send me an email before midnight on

Sunday with at least 3 verbal -> variable expressions from the 5.7 HW you want me to go over next Wednesday• YOUR EMAIL MESSAGE WILL COUNT AS

TODAY’S QUIZ GRADE

Review: Multiplying Fractions

• Evaluate •Multiplication is the easiest fraction

operation.•Multiply numbers across the top and

across the bottom

Dividing Fractions

• Evaluate • Flip the second fraction!!• Then multiply

Adding fractions

=

If denominators are the same, keep the denominator and add across the top only.

Adding fractions

Evaluate

Subtracting fractions

•Evaluate

Simplify fractions

• Simplify • Do 4 and 10 share a common factor?• Ask starting with 2.• Yes, they are both divisible by 2.

6.1 Intro to Equations

• In an equation, goal is to get the variable (letter) by itself.•Ask “What operation is being done to x?” then do the opposite.•Perform the same operation on both sides OF THE EQUALS SIGN

x – 6 = -11. Solve for x.

•What operation is being done on x?• Subtraction of 6.• So add 6 to both sides.

6 + t = 14. Solve for t.

• What operation is being done to t?• Addition of 6. • 6 comes first, OK because addition is

commutative.• Subtract 6 from each side.

2x = -26. Solve for x.

•What operation is being performed on x?•Multiplication by 2.• So divide each side by 2.

-7m = 56. Solve for m.

•What operation is being performed on m?•Multiplication by -7.• So divide each side by

-7.

. Solve for y.•What operation is

being done on y?• Fraction bar

means…•Division by 8.• So multiply each

side by 8.

. Solve for x.

•What operation is being done to x?• Division by 7.• So multiply each side by 7.

Goodnight

• Don’t forget to email me before midnight on Sunday with at least 3 verbal -> variable expressions from the 5.7 HW you want me to go over next Wednesday• kianxie@gmail.com• See you next Wednesday