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Translating Words into Math The four basic operations used to combine numbers can be expressed in various ways. Below are some equivalent words can be useful in translating the written word into mathematical symbols: Addition: Synonym more than sum plus increased by Example 3 more than 5 the sum of 2 and 6 6 plus 9 7 increased by 3 Translation 5+3 2+6 6+9 7+3 Subtraction: Synonym less than difference minus decreased by Example 3 less than 5 difference of 6 and 2 9 minus 6 7 decreased by 3 Translation 5–3 6–2 9–6 7–3 Multiplication: Note: The symbol * is used for multiplication to avoid confusion with the variable x. Synonym Example Translation times 3 times 5 3*5 product product of 2 and 6 2*6 of one-half of 8 ½*8 Division: Note: The symbol / is used for division. If either the numerator or denominator of a fraction contains more than one term or factor, it must be enclosed in a set of parentheses for grouping. Synonym Example Translation per, a gas is $3 per gallon $3/gallon gas is $3 a gallon ratio, quotient ratio of 7 and 3 7/3 Quotient of 7 and 3 Equals: Synonym is, gives, yields Example 3 times x is 5 3 times x gives 5 3 times x yields 5 Translation 3x = 5 Translating Words into Math Examples (Solutions provided at bottom of page) Write each of the following algebraic expressions symbolically. 1. 9 is added to m 2. 5 times the sum of 8 and b 3. Four-fifths of the sum of 5 and d 4. 3 less than 5 times d 5. 4 times m 6. y divided by 5 7. Subtract one-third from 5 times w 8. Five-sixths of h is added to 5 9. Product of 4 and b 10. 7 minus f Write each of the following equations symbolically. 11. One-third of the sum of x and 5 is 3 times the sum of 2 and m. 12. b minus 3 is n added to 6. 13. 6 times x is three-fifths of the sum of 7 and f. 14. Subtracting 8 from 4 times x gives 5 divided by m. 15. Subtracting four-fifths from 9 times m yields the difference of one-sixth of b and 2 Solutions: 1. 4. 7. 10. 13. 9+m 5d – 3 5w – 1/3 7–f 6x = 3/5(7 + f) 2. 5. 8. 11. 14. 5(8 + b) 4m 5/6h + 5 1/3(x + 5) = 3(2 + m) 4x – 8 = 5/m 3. 6. 9. 12. 15. 4/5(5 + d) y/5 4b b–3=n+6 9m – 4/5 = 1/6b – 2 Worksheet 1 Algebraic Expressions Write each of the following algebraic expressions symbolically. 1. 4 is subtracted from one-half of f 2. 8 divided by b 3. Add 9 to 2 times f 4. Five-sixths of b is added to 7 5. Product of 8 and c Write each of the following equations symbolically. 6. The sum of h and 5 is equal to 8 less than 6 times y. 7. One-sixth of the sum of x and 5 is 4 minus y. 8. 7 divided by x is 5 less than 8 times y. 9. The sum of 9 and w is the sum of 3 and 7 times h. 10. The product of 7 and w is 8 times the sum of 2 and x.