Math 010: Verbal expressions & Intro to Equations
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Transcript of Math 010: Verbal expressions & Intro to Equations
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Math 010: Verbal expressions & Intro to EquationsOctober 9, 2013
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Pre-test on Verbal ExpressionsFirst page of worksheet
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5.7 Verbal -> Variable Expressions
•Verbal means words, variable means algebraic/math language•Memorize terms, also understand meaning in context
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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
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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
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Multiplication Terms• “times”• “twice” means two times• “of” – used with fractions• “ of x” means times x or x• “the product of” • “multiplied by”
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Division Terms
• “divided by”• “the quotient of”• “the ratio of” • ratios can be division problems or fractions
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“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
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“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.
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“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
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“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
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“the difference between y and 4”• Difference means subtraction.• Reverse or stay the same?• Order stays the same.• y - 4
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“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:
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“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
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“x minus 2”• Pretty obvious here• But ask: Does order stay the same or reverse?• Stays the same.• x - 2
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“x divided by 12”
•Another obvious one
•Or write as a fraction:
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“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
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“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
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“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
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“the sum of x and z”
•Sum means addition.•x + z
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“6 added to y”
• Obvious, but note order again…• Dictated: 6 + y• In addition, variable terms come before
constant terms.• y + 6
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“m decreased by 3”
•Decreased by means minus.•Order stays the same or reverses?•Same•m - 3
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“the cube of r”
• The volume of a cube with side length r is defined as the cube of r.• • That means
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“subtract 9 from z”
•We know the operation is subtraction…•But does the order stay the same or reverse?•It reverses.•z - 9
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“10 times t”
•Dictated: 10 · t•10t
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“one-half of x”
•In fractions, of means…•Multiply• =
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“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
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“the square of x”
• The area of a square with side length x is defined as the square of x.
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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)
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“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
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“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
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“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
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“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.
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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
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Review: Multiplying Fractions
• Evaluate •Multiplication is the easiest fraction
operation.•Multiply numbers across the top and
across the bottom
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Dividing Fractions
• Evaluate • Flip the second fraction!!• Then multiply
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Adding fractions
=
If denominators are the same, keep the denominator and add across the top only.
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Adding fractions
Evaluate
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Subtracting fractions
•Evaluate
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Simplify fractions
• Simplify • Do 4 and 10 share a common factor?• Ask starting with 2.• Yes, they are both divisible by 2.
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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
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x – 6 = -11. Solve for x.
•What operation is being done on x?• Subtraction of 6.• So add 6 to both sides.
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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.
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2x = -26. Solve for x.
•What operation is being performed on x?•Multiplication by 2.• So divide each side by 2.
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-7m = 56. Solve for m.
•What operation is being performed on m?•Multiplication by -7.• So divide each side by
-7.
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. Solve for y.•What operation is
being done on y?• Fraction bar
means…•Division by 8.• So multiply each
side by 8.
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. Solve for x.
•What operation is being done to x?• Division by 7.• So multiply each side by 7.
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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• [email protected]• See you next Wednesday