Introduction to Worded Problems

Sample of words used to represent mathematical operations:

ADD	SUBTRACT	MULTIPLY	DIVIDE
add	subtract	multiplied by	divided by
sum	difference	product of	quotient
increased by	decreased by	times	per
more than*	less than*	double	split equally
exceeds	minus	triple	ratio of
plus	take away	twice of	divided among
total	reduced by	grouped	each
gain	loss		out of
deposit	withdraw

Note: Phrases like “less than” and “more than” require reversing the usual order of terms in translation. For example: “5 less than $x$” means $x - 5$.

Sample Sentences with Corresponding Algebraic Expressions

Statement	Algebraic Expression
Seven increased by five times a number.	$$7 + 5x$$
Ten less than three times a number.	$$3x - 10$$
Six times a number, increased by 4.	$$6x + 4$$
The product of 2, and a number decreased by 6.	$$2(x - 6)$$
A number used as a factor of itself 4 times.	$$x^4$$
Four times a number, divided by 8 equals 12.	$$\frac{4x}{8} = 12$$
12 less than the quotient of a number and 3 is zero.	$$\frac{x}{3} - 12 = 0$$
15 more than twice the product of a number and 5 is 55.	$$2 \cdot 5x + 15 = 55$$
A fourth of the sum of a number and 3.	$$\frac{x + 3}{4}$$

Problem 1:

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Problem 2:

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Problem 3:

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Problem 4:

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Problem 5:

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Problem 6:

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Problem 7:

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Problem 8:

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