University of Phoenix Material
Translating Word Problems
One of the most challenging (and fear-inducing) concepts for math students is word problems. The key to translating these problems from words to math symbols is knowing the vocabulary.
The table below offers some keywords you might see in a word problem; these keywords give you the information you need to create a math formula.
Math Operators and Common Keywords
Operator
Keywords
Addition
Sum, more than, and, increase, plus, all together, total
Subtraction
Difference, less than, decreased by, fewer, take away, minus
Example 1
The sum of some number and 5 is 12.
The highlighted keywords correspond to addition and equals in the chart. We also know that the phrase
“some number” indicates an unknown variable. We can use n here to represent that, giving us:
[Some number] + 5 = 12 + 5 = 12
Example 2
A family purchased a 12-cut pizza, and there was enough pizza for 3 pieces per person. How many people are in the family?
The keywords here correspond to division and equals on the chart.
Currently, the number of individuals in the family is unknown, so we can use a variable x to represent that unknown. Using this information and the numbers given in the problem, we can create the following math sentence: 12 ÷ 3 =
Example 3
Twice as many kids attended camp this year compared with last year, and enrollment was 42 kids.
The keywords here correspond to multiplication and equals on the chart. The unknown quantity is the number of individuals attending camp last year. Let’s use y to represent this variable.
2 = 42
Example 4
Joe had 15 marbles and Sue had 12. What is the difference?
The keywords correspond to subtraction and equals on the chart. We can use a variable m to represent the unknown value.
15– 12 =
Basic Number Properties
Associative Property of Addition
Definition:
The associative property of addition states that the way in which the terms of a sum are grouped does not change the sum.
(a + b) + c = a + (b + c)
Example:
Both (3 + 4) + 5 and 3 + (4 + 5) are equal to 12.
Associative Property of Multiplication
Definition:
The associative property of multiplication states that the way in which the factors in a product are grouped does not change the product.
(ab)c = a(bc)
Example:
Both (2 · 3) · 4 and 2 · (3 · 4) are equal to 24.
Commutative Property of Addition
Definition:
The commutative property of addition states that the order in which the terms of a sum are added does not change the sum.
Translating Word Problems
MTH/208
a+b=b+a
Example:
Both 35 + 43 and 43 + 35 are equal to 78.
Commutative Property of Multiplication
Definition:
The commutative property of multiplication states that the order in which two factors in a product are multiplied does not change the product. ab = ba
Example:
Both 6 · 24 and 24 · 6 are equal to 144.
Distributive Property
Definition:
The distributive property states that for any numbers a, b, and c it is true that a(b + c) = ab + ac.
Example:
Both 2(3 + 4) and 2 · 3 + 2 · 4 are equal to 14.
Additive Identity
Definition:
The number 0 is the additive identity because when 0 is added to any number, the sum is that number.
Examples:
7+0=7 a+0=a Multiplicative Identity
Definition:
The number 1 is the multiplicative identity because when 1 is multiplied by any number, the product is that number.
Examples:
1 x 35 = 35 a·1=a Additive Inverse
Definition:
The additive inverse of a number is the number such that the sum of the given number and its additive
Translating Word Problems
MTH/208
inverse is 0 (the additive identity).
Example:
The numbers −5 and 5 are additive inverses because −5 + 5 = 0.
Multiplicative Inverse
Definition:
The multiplicative inverse of a number a/b is the number b/a . The product of any nonzero number and its multiplicative inverse is 1. The multiplicative inverse of a number is also called the reciprocal.
Example:
The multiplicative inverse of 3/5 is 5/3 because 3/5 x 5/3 = 1.
Like Terms
Definition:
Like terms are terms that have identical variables and exponents. Two or more constant terms are considered to be like terms.
Example:
In the expression 3c+ 2c²+ 5c²+ 4c, 3c and 4c are like terms, and 2c² and 5c² are like terms.
