# Math Signal Words

## 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.

• And
• Sum
• In excess
• Greater
• More than
• Increased by
• 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 = (?)

## Subtraction

### Words that signal subtraction:

• Decreased by
• Diminished by
• Subtract
• Reduce
• Difference
• Less than
• From
• Minus
• 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 = (?)

## Multiplication

### 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

## Division

### 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

## Equality

### 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) = (?)

## Inequality

### 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

### 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:

English words Algebraic Expression
Ten more than X X + 10
A number added to 5 5 + X
A number increased by 13 X + 13
5 less than 10 10 – 5
A number decreased by 7 X – 7
Difference between X and 3 X – 3
Twice a number 2X
Ten percent of X .10X
Ten times X 10X
Quotient of X and 3 3X
The product of 2 times a number is 10 2X = 10
5 times the sum of X and 2 5( X + 2 )
7 is greater than X 7 > X
The sum of two consecutive integers (X) + (X + 1)
The sum of two consecutive odd integers (X) + (X + 2)
The sum of two consecutive even integers (X) + (X + 2)