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Word Problems Involving & NUMBERS
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Before We Start Recall How we can change
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WORDS I N T O MATH
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The following slides show how many words in word problems can be translated into Math Symbols.
The translations shown are not always the only translations and there may be others more appropriate for each word problem you encounter. However, the examples in the next slides typify the most common translations of words into Math Symbols.
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MATH WORDS = is
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MATH WORDS = is of
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MATH WORDS + more
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MATH WORDS + more less
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MATH WORDS product
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MATH WORDS product quotient FRACTION
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MATH WORDS sum
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MATH WORDS sum difference
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MATH WORDS twice
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MATH WORDS Twice as many
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MATH WORDS Twice as many Three times as many
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MATH WORDS Twice as many Three times as many Triple
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MATH WORDS Half of
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MATH WORDS Half of Half as many
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MATH WORDS One third of
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MATH WORDS One third of A third as many
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In the following slides you will find several different types of word problems.
If you wish to see how to solve the problem, click on the problem and you will be taken to the solution.
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Seven is 3 less than twice a number. Find the number
NUMBER PROBLEMS 1 Seven is 3 less than twice a number. Find the number 2 One-fourth of a number is 5 less than the number itself Find the number Four times a number, increased by 25, is 13 less than six times the number Find the number 3
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AGE PROBLEMS Mark is 11 years older than his sister. In 8 years he will be twice as old as she will be then. How old are they now? 4 Mrs. Ford is 48 and Mrs. Lincoln is How many years ago was Mrs. Ford exactly twice as old as Mrs. Lincoln? 5
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1 Example #1
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Seven is 3 less than twice a number
Click to go To List of Problems Find the Number
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Seven is 3 less than twice a number
7 Find the Number
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7 Seven is 3 less than twice a number Let x represent the number
Find the Number
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7 Symmetric Prop. Of Equality Not Absolutely Necessary but it’s nice to have the unknown variable on the left side Find the Number
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Clearly shows that you are adding the same thing to both sides
7 Clearly shows that you are adding the same thing to both sides Find the Number
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Clearly shows that you are dividing by the same thing on both sides
7 Clearly shows that you are dividing by the same thing on both sides Find the Number
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Go back and read the problem
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Seven is 3 less than twice a number
Let x represent the number Seven is 3 less than twice a number Click to go To List of Problems Find the Number
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2 Example #2
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One-fourth of a number is 5 less than the number itself
Click to go To List of Problems Find the Number
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One-fourth of a number is 5 less than the number itself
Find the Number
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Let x represent the number
One-fourth of a number is 5 less than the number itself Find the Number
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Let x represent the number
One-fourth of a number is 5 less than the number itself Find the Number
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Let x represent the number
One-fourth of a number is 5 less than the number itself Find the Number
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Let x represent the number
One-fourth of a number is 5 less than the number itself Find the Number
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Say goodbye to the fraction
Clearly shows that you are multiplying by the same thing on both sides Say goodbye to the fraction
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Clearly shows that you are subtracting the same thing from both sides
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Clearly shows that you are dividing by the same thing on both sides
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Go back and read the problem
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Let x represent the number
One-fourth of a number is 5 less than the number itself
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Let x represent the number
One-fourth of a number is 5 less than the number itself Click to go To List of Problems
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3 Example #3
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Four times a number, increased by 25, is
13 less than six times the number. Find the number Click to go To List of Problems
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Let x represent the number
Four times a number, increased by 25, is 13 less than six times the number. Find the number
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Let x represent the number
Four times a number, increased by 25, is 13 less than six times the number. Find the number
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Let’s Proceed by using the Properties of Equality to get an equivalent equation with all of the variables on one side
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Clearly shows that you are subtracting the same thing from both sides
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Clearly shows that you are subtracting the same thing from both sides
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Clearly shows that you are dividing by the same thing on both sides
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Go back and read the problem
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Let x represent the number
Four times a number, increased by 25, is 13 less than six times the number. Find the number Click to go To List of Problems
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4 Example #4
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We don’t know Mark’s Age or his Sister’s Age!!!!
Let x represent Mark’s age now Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? How do we start ? We don’t know Mark’s Age or his Sister’s Age!!!! Let’s go with Mark’s Age Click to go To List of Problems
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW Mark’s Age Sister’s Age
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age
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Please Excuse My Dear Aunt Sally
Simplify First Please Excuse My Dear Aunt Sally Parenthesis Exponents Multiply or Divide Add or Subtract
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Optional Let’s Proceed by using the Reflexive Property
to get an equivalent equation with all of the variables on one side with no negative signs
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Clearly shows that you are subtracting the same thing from both sides
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Clearly shows that you are adding the same thing to both sides
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Go back and read the problem
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age Substitute
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age
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Let x represent Mark’s age now
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age
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Check out the Ages in 8 Years
Mark is 11 years older than his sister In 8 years he will be twice as old as she will be then. How old are they now? NOW 8 Years from Now Mark’s Age Sister’s Age Click to go To List of Problems
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5 Example #5
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Mrs. Ford is 48 and Mrs. Lincoln is 35. How many years ago was Mrs
Mrs. Ford is 48 and Mrs. Lincoln is How many years ago was Mrs. Ford exactly twice as old as Mrs. Lincoln? NOW Mrs. Ford Mrs. Lincoln Click to go To List of Problems
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Let x represent the number of years ago
Mrs. Ford is 48 and Mrs. Lincoln is How many years ago was Mrs. Ford exactly twice as old as Mrs. Lincoln? NOW x years Ago Mrs. Ford Mrs. Ford Mrs. Lincoln Mrs. Lincoln
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Let x represent the number of years ago
Mrs. Ford is 48 and Mrs. Lincoln is How many years ago was Mrs. Ford exactly twice as old as Mrs. Lincoln? NOW x years Ago Mrs. Ford Mrs. Lincoln
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Let x represent the number of years ago
Mrs. Ford is 48 and Mrs. Lincoln is How many years ago was Mrs. Ford exactly twice as old as Mrs. Lincoln? NOW x years Ago Mrs. Ford Mrs. Lincoln
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Let x represent the number of years ago
Mrs. Ford is 48 and Mrs. Lincoln is How many years ago was Mrs. Ford exactly twice as old as Mrs. Lincoln? NOW x years Ago Mrs. Ford Mrs. Lincoln
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Please Excuse My Dear Aunt Sally
Let’s Simplify before starting Please Excuse My Dear Aunt Sally Parenthesis Exponents Multiply or Divide Add or Subtract
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Let’s Proceed by using the Properties of Equality to get an equivalent equation with all of the variables on one side
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Clearly shows that you are adding the same thing to both sides
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Clearly shows that you are subtracting the same thing from both sides
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Go back and read the problem
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Let x represent the number of years ago
Mrs. Ford is 48 and Mrs. Lincoln is How many years ago was Mrs. Ford exactly twice as old as Mrs. Lincoln? NOW x years Ago Mrs. Ford Mrs. Lincoln
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Let x represent the number of years ago
Let's Check Mrs. Ford is 48 and Mrs. Lincoln is How many years ago was Mrs. Ford exactly twice as old as Mrs. Lincoln? NOW x years Ago Mrs. Ford Mrs. Lincoln
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Let x represent the number of years ago
Mrs. Ford is 48 and Mrs. Lincoln is How many years ago was Mrs. Ford exactly twice as old as Mrs. Lincoln? NOW x years Ago Mrs. Ford Mrs. Lincoln Click to go To List of Problems
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