**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