Language of Algebra

Introduction

• Translating from English to math language.
• Focus on common keywords and math operations: addition, subtraction, multiplication, and division.

Common Math Operations & Keywords

• Addition: sum, plus, added to
• Subtraction: difference, minus, subtract, less than
• Multiplication: product, times, multiply
• Division: quotient, divide, per

Important Keywords

• Addition: Sum
• Subtraction: Difference
• Multiplication: Product
• Division: Quotient

Notation Recommendations

• Sum: ( ) +
• Difference: ( ) -
• Product: ( ) •
• Quotient: ( ) ÷ (numerator/denominator)

Exercises

Example 1

• Statement: A number increased by five
  • Translation: x + 5

Example 2

• Statement: Twice a number minus four
  • Translation: 2x - 4

Example 3

• Statement: 7 divided by a number
  • Translation: 7 ÷ x or 7/x

Subtraction Keywords

• Subtraction is not commutative
• Keywords: less than, subtracted from, taken from
• Write the expression backwards.

Example: Subtraction Keywords

• Statement: Five taken from a number
  • Translation: x - 5
• Statement: A number less than two
  • Translation: 2 - x
• Statement: Five less a number
  • Translation: 5 - x (no need to write backwards)

Complex Statements

Example 4

• Statement: Four subtracted from twice a number
  • Translation: 2x - 4

Expressions With Main Keywords

Example 1

• Statement: The sum of five and a number
  • Translation: 5 + x

Example 2

• Statement: The product of a number and eight
  • Translation: 8x (simplified from x • 8)

Example 3

• Statement: Twice the difference of a number and seven
  • Translation: 2(x - 7)

Example 4

• Statement: Twice the number decreased by ten
  • Translation: 2x - 10

Setting Up Equations

• Importance of recognizing keywords that represent the equal sign.

Example 1

• Statement: Three times a number added to four is 16
  • Translation: 3x + 4 = 16

Example 2

• Statement: The sum of negative five and a number is equal to eight
  • Translation: -5 + x = 8

Example 3

• Statement: Twice a number less than four gives us ten
  • Translation: 4 - 2x = 10

Summary

• Translate expressions and equations using keywords.
• Practice with exercises and handouts to become proficient in translating.

Next Steps

• Complete exercises in the provided handout.