Embed Size (px)
Citation preview
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…
Words that mean Add or SubtractCOPY THIS!COPY THIS!
Addition Subtraction
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
Words that mean Multiply or DivideCOPY THIS!COPY THIS!
Multiply Divide
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)
Translating Verbal PhrasesCOPY THIS!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
StrategiesCOPY THIS!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 ∙ h This 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 add3. 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 variable2. The sum of 6 and m means to add3. Two less than means to subtract 24. 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 variable2. Decreased means to subtract3. The sum means to add4. 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 + y2)
Verbal Sentences into Equations and InequalitiesCOPY THIS!COPY THIS!
The words for equal are: is, are, was, were, is, are, was, were, will be, gives, yields, sold forwill be, gives, yields, sold for
The words for inequalities are as follows:
Less thanLess than <<
Less than or equal to, at most Less than or equal to, at most ≤≤
Greater thanGreater than >>
Greater than or equal to, at leastGreater 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 93. “is” means equal4. 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…
Your TurnCOPY THIS!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
Your TurnCOPY THIS!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 3.5
8.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 answersTranslate 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
52 – x
Check your answersWrite 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 3.5
8.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) = 10
35 / 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 4GRID 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 5GRID IN
If 11 is less than 7 times a certain number is 7 more than 4 times the number, what is the number?
