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Pre-Algebra

Translating Words to Expressions and Equations

Lesson

Turning English into algebra is one of the most important skills in the whole subject. Most “word problems” really break down into finding the variable and writing the relationship.

Step 1: Decide what the unknown is and name it (usually xx). Step 2: Translate the sentence into math.

Keyword cheat sheet

  • Sum, plus, more than, increased by → ++
  • Difference, minus, less than, decreased by → −-
  • Product, times, twice, of → ×\times
  • Quotient, divided by, per → ÷\div
  • Is, equals, results in → ==

Tricky: “less than”

“5 less than x” means x−5x - 5, NOT 5−x5 - x. The phrase flips the order.

Worked example 1

“Three more than a number.”

x+3x + 3

Worked example 2

“Twice a number, decreased by 4.”

2x−42x - 4

Worked example 3 — full equation

“The sum of a number and 7 is 15.”

x+7=15x + 7 = 15

How to type your answer

Use x as the variable. Use +, -, *, /, and parentheses. Write multiplication implicitly when possible: 2x instead of 2*x.

Practice

Work through these. Stuck? Click Get a hint.

Warm-Up

Quick problems to get going.

Problem 1

The sum of x and 7.\text{The sum of } x \text{ and 7.}

Problem 2

Twice a number x.\text{Twice a number } x.

Problem 3

5 less than x.\text{5 less than } x.

Problem 4

The quotient of x and 3.\text{The quotient of } x \text{ and 3.}

Practice

Standard problems matching the lesson.

Problem 5

4 more than a number x.\text{4 more than a number } x.

Problem 6

8 less than twice x.\text{8 less than twice } x.

Problem 7

Three times the sum of x and 5.\text{Three times the sum of } x \text{ and 5.}

Problem 8

The product of 6 and x.\text{The product of 6 and } x.

Problem 9

Half of x.\text{Half of } x.

Problem 10

x decreased by 9.x \text{ decreased by 9.}

Problem 11

x increased by 12.x \text{ increased by 12.}

Problem 12

4 times a number, plus 1.\text{4 times a number, plus 1.}

Problem 13

The sum of x and 6 is 14.\text{The sum of } x \text{ and 6 is 14.}

Problem 14

Twice x equals 10.\text{Twice } x \text{ equals 10.}

Problem 15

x minus 4 is 9.x \text{ minus 4 is 9.}

Problem 16

One third of x is 7.\text{One third of } x \text{ is 7.}

Problem 17

5 times a number x.\text{5 times a number } x.

Problem 18

x plus 12.x \text{ plus 12.}

Challenge

Harder problems — edge cases, trickier numbers, multiple steps.

Problem 19

Two times the difference of x and 7.\text{Two times the difference of } x \text{ and 7.}

Problem 20

5 more than three times x is 20.\text{5 more than three times } x \text{ is 20.}

Problem 21

The sum of x and 4, divided by 2.\text{The sum of } x \text{ and 4, divided by 2.}

Problem 22

7 less than x4.\text{7 less than } \frac{x}{4}.

Problem 23

2 dollars per item for x items, plus 3 dollars fee.\text{2 dollars per item for } x \text{ items, plus 3 dollars fee.}

Problem 24

8 dollars per visit for x visits plus 25 dollars join fee equals 81 dollars.\text{8 dollars per visit for } x \text{ visits plus 25 dollars join fee equals 81 dollars.}

Problem 25

Perimeter of rectangle with length x and width 7 is 30.\text{Perimeter of rectangle with length } x \text{ and width 7 is 30.}

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Quiz

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