More English to Algebra Translating word problems

Translating Verbal Phrases The key to translating verbal phrases it to know what the English words mean mathematically… It’s expected that you know the words that mean add, subtract, multiply and divide Here are some more terms for the following…

COPY THIS! Words that mean Add or Subtract COPY THIS! AdditionSubtraction Plus Increased by In all More than Sum Total Minus Subtract Decreased by Less Difference between/of Less than (reverses the order of subtraction) combined together Fewer than

COPY THIS! Words that mean Multiply or Divide COPY THIS! MultiplyDivide Times Product of Multiplied by Each Of Factors Divided Quotient of A, An, in, or per Rate Ratio of Separate by a factor of Out of Percent (divide by 100)

COPY THIS! Translating Verbal Phrases COPY THIS! The starting point to translate verbal phrases is to identify the variable first… Most often you will know what the variable is by the phrase “a number”… It doesn’t matter which order you add or multiply…you will get the same results; however, when subtracting or dividing it DOES matter which order you place the numbers

Example # 1 Five years older than her brother 1.First identify the variable…in this case the variable is her brother’s age…lets call that a 2. The term “older than” means to add 3. Five years means the number 5 So the above expression can be written as: 5 + a

COPY THIS! Strategies COPY THIS! Some strategies that you can use when working with this concept are: Read the expression or sentence more than once… Underline, circle, or box each of the terms as you identify them Lets look at some more examples….

Example # 2 Six dollars an hour times the number of hours 1. Hour is the variable …let’s call it h 2. Times means to multiply 3. Six dollars means the number 6 The algebraic expression is: 6 ∙ hThis can also be written as 6h

Example # 3 Three more than the quantity five times a number 1. 5 times a number is the variable …let’s call it 5n 2. More than means to add 3. Three means the number 3 The algebraic expression is: 5n + 3

Example # 4 Two less than the sum of 6 and a number m 1. A number m is the variable 2. The sum of 6 and m means to add 3. Two less than means to subtract 2 4. In this instance you have to add before you subtract…so the sum of 6 and m would go in parenthesis The algebraic expression is: (6 + m) – 2

Example # 5 A number x decreased by the sum of 10 and the square of a number y 1. A number x is the variable 2. Decreased means to subtract 3. The sum means to add 4. In this instance you have to add the sum of 10 and the square of a number y. Since you have to perform this function first before you subtract …10 and the square of y would go in parenthesis The algebraic expression is: x – ( 10 + y 2 )

COPY THIS! Verbal Sentences into Equations and Inequalities COPY THIS! is, are, was, were, will be, gives, yields, sold for The words for equal are: is, are, was, were, will be, gives, yields, sold for The words for inequalities are as follows: Less than< Less than or equal to, at most ≤ Greater than> Greater than or equal to, at least≥

Example # 6 Nine less than the product of ten and a number d is eleven 1. The variable is 10 and a number d, which is written as 10d 2. Nine less means to subtract 9 3. “is” means equal 4. The total is 11 The algebraic expression is: 10d – 9 = 11

Comments On the next couple of slides are some practice problems…The answers are on the last slide… Do the practice and then check your answers…If you do not get the same answer you must question what you did…go back and problem solve to find the error…

COPY THIS! Your Turn COPY THIS! Translate the verbal phrase into an algebraic expression. Use x for the variable in your expression 1. Nine more than an number 2. Three more than ½ a number 3. The quotient of a number and two tenths 4. The difference of ten and a number 5. Five squared minus a number

COPY THIS! Your Turn COPY THIS! Write each sentence as an algebraic equation or inequality 6. Nine is greater than three times a number 7. Twenty-five is the quotient of a number y and Three times the quantity two less than a number x is ten 9. The quotient of thirty-five and a number t is less than or equal to seven 10. A number q is equal to or greater than one hundred

Check your answers Translate the verbal phrase into an algebraic expression. Use x for the variable in your expression 1. Nine more than an number 2. Three more than ½ a number 3. The quotient of a number and two tenths 4. The difference of ten and a number 5. Five squared minus a number 9 + x or x + 9 ½x + 3 or 3 + ½x x  2/10 10 – x 5 2 – x

Check your answers Write each sentence as an algebraic equation or inequality 6. Nine is greater than three times a number 7. Twenty-five is the quotient of a number y and Three times the quantity two less than a number x is ten 9. The quotient of thirty-five and a number t is less than or equal to seven 10. A number q is equal to or greater than one hundred 9 > 3x 25 = y / 3.5 3(x – 2) = / t ≤ 7 q ≥ 100

SAT Word Problem example 1 If 4 less than x is 1 more than y, what is x in terms of y? A. Y – 3 B. Y + 1 C. Y + 3 D. Y + 4 E. Y + 5

SAT Word Problem example 2 A number x is 3 less than 4 times the number y. Two times the sum of x and y is 9. Which of the following pairs of equations could be used to find the values of x and y? A. x = 4y – 3 2(x+y) = 9 B. y = 4x – 3 2(x+y) = 9 C. x = 4(y – 3)2(x+y) = 9 D. y = 4(x – 3)2x+y = 9 E. x = 4y – 3 2 (xy) = 9

SAT Word Problem example 3 Arthur has 3 times as many marbles as Scott. If Arthur gives Scott 6 marbles, Arthur will be left with 4 more marbles than Scott. What is the total number of marbles that Arthur and Scott have? A. 36 B. 32 C. 30 D. 24 E. 21

SAT Word Problem example 4 GRID IN Half the difference of two positive numbers is 10. If the smaller of the two numbers is 3, what is the sum of the two numbers?

SAT Word Problem example 5 GRID IN If 11 is less than 7 times a certain number is 7 more than 4 times the number, what is the number?