Algebra: Translating Words to Equations

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Correctly translating words to equations is the key to solving math word problems. Recognizing some key words and phrases may help you in the translation.

Keywords that involve Addition

sum
total
altogether
more than
greater than
consecutive
increased by
plus
gained
added
grew by
older than
farther than

Example:

The sum of the length and width is 30.	l + w = 30
The length is 4 more than the width.	l = w + 4
The length is greater than the width by 5.	l = w + 5
The consecutive integer after the integer n is 20.	n + 1 = 20
Jane is two years older than Alice.	j = a + 2
Alice ran 5 kilometers farther than Jane.	a = j + 5

Keywords that involve Subtraction

difference
diminished by br> fewer than
less than
decreased by
removed
taken away
lost
minus
subtracted from
younger than

Example:

The difference between Jane’s age and Alice’s age is 10.	|J - A| = 10
John has 10 fewer coins than Alice.	J = A - 10

Keywords that involve Multiplication

product
twice
doubled
tripled
times
multiplied by
of

Example:

The product of the length and the width is 50.	lw = 50
The length is twice the width.	l = 2w
John took half the number of marbles.

Keywords that involve Division

quotient
divided by
divided into
quotient of
shared equally
in
per

Example:

The length divided by the width is 5.
John traveled 100 miles in 2 hours.

The following video shows more keywords that can be used for algebra word problems

More examples and videos of algebra word problems.

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