Often, working on word problems is a difficult task because a student doesn’t know how to translate words into mathematical symbols.

The following examples may help.

### Words that signal addition:

And

Sum

Add

Made larger

In excess

Greater

More than

Added to

Increased by

In addition

Plus

Raised by

#### Examples:

1. Thirty-five and eighty-six are what?

Translation: 35 + 86 = (?)

2. Three hundred sixteen increased by eight is what amount?

Translation: 316 + 8 = (?)

3. Ellen has sixteen candy bars to sell. If this amount is raised by twenty, how many will she have?

Translation: 16 + 20 = (?)

### Words that signal subtraction:

Decreased by

Diminished by

Subtract

Reduce

Difference

Less than

From

Minus

Made smaller by

Take away

#### Examples:

1. Eighty-nine is how much less than one hundred forty-seven?

Translation: 147 – 89 = (?)

2. Seventy-six decreased by sixteen is what?

Translation: 76 – 16 = (?)

3. Find the difference between 19 and 62.

Translation: 62 – 19 = (?)

4. Tommy has two hundred fifty-three baseball cards. If his collection is made smaller by thirty cards, how many will he have?

Translation: 253 – 30 = (?)

### Words that signal multiplication:

(The answer to a multiplication problem is called a product.)

Product

Times

Multiplied by

Doubled, tripled, etc.

Times as much

Percent of

Of

Interest on

#### Examples:

1. Susan runs around her block six times every day. If the distance around the block is ½ (.5) of a mile, how many miles a day does she run?

Translation: ½ x 6 = (?)

2. Seventeen tripled equals what?

Translation: 17 x 3 = (?)

3. What is the product of twenty, six and sixteen?

Translation: (?) = 20 x 6 x 16

4. What is 37% of 500?

Translation: (?) = .37 x 500

### Words that signal division:

(The answer to a division problem is called a quotient. The number being divided is called a dividend and the number doing the dividing is called the divisor.)

Per

Quotient

Go(es) into

How many

Divided by

Contained in

#### Examples:

1. How many times does 11 go into to 121?

121 ÷ 11 = (?) or 121/11

2. What is the quotient with a dividend of forty-four and the divisor of 4?

4 ÷ 44 = (?) or 4/44

3. How many gallons of oil are contained in 400 quarts? (Note: 4 quarts = a gallon.)

400 ÷ 4 = (?) or 400/4

### Words that signal equality:

Is

Will be

Equal

Was

Results

#### Examples:

1. How many of the 18 jobs will be left after reducing them by half?

18 – 18/2 = (?)

2. Seven percent of forty is what?

.07 (40) = (?)

### Words that signal inequality:

Greater than** >**

Greater than or equal to **≥**

Less than **<**

Less than or equal to **≤**

#### Examples:

1. Four plus a number is greater than seven.

4 + X > 7

2. Fourteen divided by a number is less than or equal to two.

14/X < 2

### Quantity is signaled by ( )

#### Example:

1. Four times the quantity seven plus X is equal to 40.

4 ( 7 + X ) = 40

### Translating English words into algebraic expressions:

Ten more than X

A number added to 5

A number increased by 13

5 less than 10

A number decreased by 7

Difference between X and 3

Twice a number

Ten percent of X

Ten times X

Quotient of X and 3

The product of 2 times a number is 10

5 times the sum of X and 2

7 is greater than X

The sum of two consecutive integers

The sum of two consecutive odd integers

The sum of two consecutive even integers

X + 10

5 + X

X + 13

10 – 5

X – 7

X – 3

2X

.10X

10X

3X

2X = 10

5( X + 2 )

7 > X

(X) + (X + 1)

(X) + (X + 2)

(X) + (X + 2)