Everyday Language —> Math Action
Basics
An algebraic expression is often a word problem.
A word problem requires you to translate Everyday Language into Math Action.
Addition language can flip-flop: y + 5 is the same as 5 + y
Subtraction language cannot flip-flop: y – 5 is not the same as 5 – y
Multiplication language can flip-flop: 5y is the same as y5
Division language cannot flip-flop: is not the same as
For the sake of order of operations, it is better to set up division language in form rather than x÷y form.
When a number is immediately adjacent to a letter or parenthesis, an invisible multiplication sign is in force.
3y = 3 × y
3(y) = 3 × y
3(5) = 3 × 5
Dictionary – Algebraic Expressions
The following table lists Everyday words under the Math actions that they represent.
Addition | Subtraction | Multiplication | Division |
add | subtract | multiply | divide |
sum | difference | product | quotient |
plus | minus | times | share |
more | less | compound | split |
increase | decrease | augment | fit |
greater | fewer | ||
Expressions |
Question
What is 4 more than y?
Answer
y + 4
or
4 + y
Answer Process
more means addition
addition language can flip-flop
Question
The number of dogs d in our neighborhood has increased by 7. Write an expression that represents this increase.
Answer
d + 7
or
7 + d
Answer Process
increase means addition
addition language can flip-flop
Question
What is 4 less than y?
Answer
y – 4
(but not 4 – y)
Answer Process
less means subtraction
subtraction language cannot flip-flop
Question
The number of cats c in our neighborhood has decreased by 7. Write an expression that represents this decrease.
Answer
c – 7
(but not 7 – c)
Answer Process
decrease means subtraction
subtraction language cannot flip-flop
Question
What is 4 multiplied by y?
Answer
4y
or
y4
Answer Process
multiply means multiplication
multiplication language can flip-flop
Question
The number of birds in our neighborhood is 7 times the number of birds b in any other neighborhood. Write an expression that represents the number of birds in our neighborhood.
Answer
7b
or
b7
Answer Process
times means multiplication
multiplication language can flip-flop
Question
What is 4 divided by y?
Answer
(but not )
Answer Process
divide means division
division language cannot flip-flop
Question
The number of hamsters h in our neighborhood will be shared among a total of 7 neighborhoods (including our own). Write an expression that represents the number of hamsters that each neighborhood will share.
Answer
(but not )
Answer Process
share means division
division language cannot flip-flop
Question
The number of cats c in our neighborhood is 7 more than 5 times the number of dogs d. Write an expression that represents the number of cats in relation to the number of dogs in our neighborhood.
Answer
c = 5d + 7
or
c = 7 + 5d
Answer Process
number of cats relates to 5 times number of dogs → 5d
cats are 7 more than 5 times dogs → 5d + 7
c = 5d + 7 or c = 7 + 5d
Question
The number of hamsters h in our neighborhood is 4 less than number of birds b in our neighborhood split among a total of 7 neighborhoods (including our own). Write an expression that represents the number of hamsters in relation to the number of birds in our neighborhood.
Answer
h = – 4
(but not h = 4 – )
Answer Process
number of hamsters relates to number of birds split among 7 neighborhoods →
hamsters are 4 less than birds split among 7 neighborhoods → – 4
h = – 4
Question
A full partner in a law firm charges $300.00 an hour. A junior associate in the law firm charges $50.00 an hour. The law firm bills a client for a case in which the junior associate worked 10 more hours than the full partner. Write an expression in terms of hours h worked.
Answer
300h + 50(h+10)
Answer Process
full partner’s hours → h
full partnerr’s part of bill → 300h
junior associate’s hours → h + 10
junior associate’s part of bill → 50(h + 10)
putting it all together —> 300h + 50(h + 10)
Question
A full partner in a law firm charges $300.00 an hour. A junior associate in the law firm charges $50.00 an hour. The law firm bills a client for a case in which the junior associate worked 10 more hours than the full partner. Write an expression that represents the total bill T in terms of hours h worked.
Answer
T = 300h + 50(h+10)
Answer Process
full partner’s hours → h
full partner’s part of bill → 300h
junior associate’s hours → h + 10
junior associate’s part of bill → 50(h + 10)
total bill → T
putting it all together —> T = 300h + 50(h + 10)
Question
A full partner in a law firm charges $300.00 an hour. A junior associate in the law firm charges $50.00 an hour. The law firm bills a client a total of $6000.00 for a case in which the junior associate worked 10 more hours than the full partner. Write an expression that represents the total bill in terms of hours h worked.
Answer
300h + 50(h+10) = 6000
Answer Process
full partner’s hours → h
full partner’s part of bill → 300h
junior associate’s hours → h + 10
junior associate’s part of bill → 50(h + 10)
total bill → 6000
putting it all together —> 300h + 50(h + 10) = 6000
Practice – Questions
1. What is 6 more than x?
2. What is 6 less than x?
3. What is 6 times x?
4. What is x divided by 6?
5. What is the difference between 6 times x and 7 divided by y?
6. The number of bottles in a drugstore is 4000 less than 3 times the number of pills. Write an expression that represents the number of bottles b in relation to the number of pills p in the drugstore.
7. The number of jars in the local food bank is 7 more than the number of cans in the local food bank shared among a total of 9 food banks (including the local food bank). Write an expression that represents the number of jars j in relation to the number of cans c in the local food bank.
8. A surgeon charges $2500.00 per service performed. A physician’s assistant charges $100.00 per service performed. A patient receives a bill in which a physician’s assistant performed 5 times as many services as a surgeon. Write an expression in terms of services s performed.
9. A hospital employs 100 registered nurses and 250 nurse’s assistants. A nurse’s assistant earns $2140.00 a month less than a registered nurse. Let y represent total nursing salaries in any given month and x represent the salary of a registered nurse in any given month. Write an expression that represents y in terms of x.
10. At the candy store, a customer purchased x buttercreams at $0.25 each, the same number of toffees as buttercreams at $0.62 each, and three times as many nougats as buttercreams at $0.88 each. The customer spent a total of $19.64. Write an expression that represents the customer’s purchase in terms of x.
Practice – Answers
1. x + 6 or 6 + x
2. x – 6
3. 6x or x6
4.
5. 6x –
6. b = 3p – 4000
7. j = + 7 or j = 7 +
8. 2500s + 100(5s)
9. y = 100x + 250(x – 2140)
10. 0.25x + 0.62x + 0.88(3x) = 19.64