Translating Between Words and Expressions

Return to table of contents

List words that indicate addition

List words that indicate subtraction

List words that indicate multiplication

List words that indicate division

List words that indicate equals

Be aware of the difference between "less" and "less than".

For example:"Eight less three" and "Three less than Eight" are

equivalent expressions. So what is the difference in wording?

Eight less three: 8 - 3Three less than eight: 8 - 3

When you see "less than", you need to switch the order of the numbers.

As a rule of thumb, if you see the words "than" or "from" it means you have to reverse the order

of the two items on either side of the word.

Examples: ·8 less than b means b - 8·3 more than x means x + 3·x less than 2 means 2 - x

_______________

_______________click to reveal

_______________

The many ways to represent multiplication...

How do you represent "three times a"?

(3)(a) 3(a) 3 a 3a

The preferred representation is 3a

When a variable is being multiplied by a number, the number (coefficient) is always written in front of the variable.

The following are not allowed:3xa ... The multiplication sign looks like another variablea3 ... The number is always written in front of the variable

Representation of division...

How do you represent "b divided by 12"?

b ÷ 12

b ∕ 12

b12

When choosing a variable, there are some that are often avoided:

l, i, t, o, O, s, S

Why might these be avoided?

It is best to avoid using letters that might be confused for numbers or operations. In the case above (1, +, 0, 5)

Three times j

Eight divided by j

j less than 7

5 more than j

4 less than j

1

2 3

4 5

6 7

8 9

0+

-

÷

TRANSLATE THE WORDS INTO AN

ALGEBRAIC EXPRESSION

j

÷÷÷

---

++

23 + m

The sum of twenty-three and m

Write the expression for each statement.Then check your answer.

d - 24

Twenty-four less than d

Write the expression for each statement.Then check your answer.

4(8-j)

Write the expression for each statement.Remember, sometimes you need to use parentheses for a quantity.

Four times the difference of eight and j

7w12

The product of seven and w, divided by 12

Write the expression for each statement.Then check your answer.

(6+p)2

Write the expression for each statement.Then check your answer.

The square of the sum of six and p

100 The quotient of 200 and the quantity of p times 7

A 200 7p

B 200 - (7p)

C 200 ÷ 7p

D 7p 200

101 35 multiplied by the quantity r less 45

A 35r - 45

B 35(45) - r

C 35(45 - r)

D 35(r - 45)

102 Mary had 5 jellybeans for each of 4 friends.

A 5 + 4 B 5 - 4

C 5 x 4

D 5 ÷ 4

103 If n + 4 represents an odd integer, the next larger odd integer is represented by

A n + 2B n + 3C n + 5D n + 6

From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

104 a less than 27

A 27 - a

B a 27

C a - 27

D 27 + a

105 If h represents a number, which equation is a correct translation of:“Sixty more than 9 times a number is 375”?

A 9h = 375B 9h + 60 = 375C 9h - 60 = 375D 60h + 9 = 375

From the New York State Education Department. Office of Assessment Policy, Development and Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.

Using Numerical and Algebraic Expressions and

Equations

Return to table of contents

We can use our algebraic translating skills to solve other problems.

We can use a variable to show an unknown.A constant will be any fixed amount.

If there are two separate unknowns, relate one to the other.

The school cafeteria sold 225 chicken meals today. They sold twice the number of grilled chicken sandwiches than chicken tenders. How many of each were sold?

2c + c = 225

chickensandwiches

chickentenders

total meals

c + 2c = 225 3c = 225 3 3 c = 75

The cafeteria sold 150 grilled chicken sandwiches and 75 tenders.

Julie is matting a picture in a frame. Her frame is 9 inches wide and her picture is 7 inches wide. How much matting should she put on either side?

2m + 7 = 92m + 7 = -7 -7 2m = 2 2 2 m = 1Julie needs 1 inches on each side.

14

12

12

14

9

both sides of the mat

size ofpicture

size of frame

12

12

Many times with equations there will be one number that will be the same no matter what (constant) and one that can be changed based on the problem (variable and coefficient).

Example: George is buying video games online. The cost of the video is $30.00 per game and shipping is a flat fee of $7.00. He spent a total of $127.00. How many games did he buy in all?

George is buying video games online. The cost of the video is $30.00 per game and shipping is a flat fee of $7.00. He spent a total of $127.00. How many games did he buy in all?

Notice that the video games are "per game" so that means there could be many different amounts of games and therefore many different prices. This is shown by writing the amount for one game next to a variable to indicate any number of games.

30g

cost ofone videogame

number of games

George is buying video games online. The cost of the video is $30.00 per game and shipping is a flat fee of $7.00. He spent a total of $127.00. How many games did he buy in all?

Notice also that there is a specific amount that is charged no matter what, the flat fee. This will not change so it is the constant and it will be added (or subtracted) from the other part of the problem.

30g + 7

cost ofone videogame

number of games

the cost of the shipping

George is buying video games online. The cost of the video is $30.00 per game and shipping is a flat fee of $7.00. He spent a total of $127.00. How many games did he buy in all?

"Total" means equal so here is how to write the rest of the equation.

30g + 7 = 127

cost ofone videogame

numberof games

the total amount

the cost of the shipping

George is buying video games online. The cost of the video is $30.00 per game and shipping is a flat fee of $7.00. He spent a total of $127.00. How many games did he buy in all?

Now we can solve it.

30g + 7 = 127-7 -7

30g = 120 30 30

g = 4 George bought 4 video games.

106 Lorena has a garden and wants to put a gate to her fence directly in the middle of one side. The whole length of the fence is 24 feet. If the gate is 4 feet, how many feet should be on either side of the fence?

12

107 Lewis wants to go to the amusement park with his family. The cost is $12.00 for parking plus $27.00 per person to enter the park. Lewis and his family spent $147. Which equation shows this problem?

A 12p + 27 = 147 B 12p + 27p = 147 C 27p + 12 = 147 D 39p = 147

108 Lewis wants to go to the amusement park with his family. The cost is $12.00 for parking plus $27.00 per person to enter the park. Lewis and his family spent $147. How many people went to the amusement park WITH Lewis?

109 Mary is saving up for a new bicycle that is $239. She has $68.00 already saved. If she wants to put away $9.00 per week, how many weeks will it take to save enough for her bicycle? Which equation represents the situation?

A 9 + 68 = 239B 9d + 68 = 239C 68d + 9 = 239D 77d = 239

110 Mary is saving up for a new bicycle that is $239. She has $68.00 already saved. If she wants to put away $9.00 per week, how many weeks will it take to save enough for her bicycle?

111 You are selling t-shirts for $15 each as a fundraiser. You sold 17 less today then you did yesterday. Altogether you have raised $675.

Write and solve an equation to determine the number of t-shirts you sold today.

Be prepared to show your equation!