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

Pre-test on Verbal Expressions First 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

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”

“the fifth power of 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”

“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”

“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”

“the ratio of t and 9”

“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”

“Twice x divided by the difference between x and 7”

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 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 MESSAGE WILL COUNT AS TODAY’S QUIZ GRADE

Review: Multiplying Fractions

Dividing Fractions

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

Adding fractions

Subtracting fractions

Simplify fractions

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.

What operation is being done on y? Fraction bar means… Division by 8. So multiply each side by 8.

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

Goodnight Don’t forget to 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 See you next Wednesday