Translating Algebraic and Verbal Expressions

Warm Up Answer the following problems 1.(5+2-6) - (1-5+12) + (6-3+11)= 2.2(5-3) 2 + (15÷3x2) - (5+2 x 1-4)= Let a=5 b=7 c=-9 3.2a + (b-c) + a 2 = 4.a+c - (2 x a ÷ 5) + c 2 = 12/18/2015www.numberbender.com

WRITING EXPRESSIONS AND EQUATIONS 12/18/2015www.numberbender.com3

Algebraic Expression ? represents a number. That number plus ten equal 14. How do we represent the number algebraically? 12/18/2015www.numberbender.com4

What You’ll Learn 12/18/2015www.numberbender.com5

Build Your Vocabulary numbers variables An algebraic expression contains numbers and variables along with +, -, x, and/or ÷. symbol A variable is a symbol used to represent an unknown number. numbers A numerical expression contains numbers along with +, -, x, and/or ÷. 12/18/2015www.numberbender.com6

DIFFERENCE is for SUBTRACTION. SUM is for ADDITION. PRODUCT is for MULTIPLICATION. QUOTIENT is for DIVISION. Build Your Vocabulary 12/18/2015www.numberbender.com7

ADDITION plus the sum of increased by more than added to The total ofSUBTRACTION minus the difference of decreased by less than fewer than subtracted from Other Terminologies 12/18/2015www.numberbender.com8

DIVISION divided by the quotient of the ratio of perMULTIPLICATION times the product of multiplied by at of Other Terminologies 12/18/2015www.numberbender.com9

Examples Write an algebraic expression for each verbal expression. 12/18/2015www.numberbender.com10 the sum of p and 12 the product of k and q

Your Turn Write an algebraic expression for each verbal expression. 12/18/2015www.numberbender.com11

Examples A python eats 4 pounds of meat each month. Write a numerical expression to represent the amount it eats in 5 months. Write an algebraic expression to represent the amount it eats in d months. 12/18/2015www.numberbender.com12 4 × 54(5) The numerical expression is 4 × 5 or 4(5). 4 × d4d The algebraic expression is 4 × d or 4d.

Examples Write a verbal expression for each algebraic expression. 12/18/2015www.numberbender.com s 5 (b – 3) the sum of 37 and s. 37 increased by s. 5 times the difference of b and 3. 5 multiplied by the difference of b and 3.

Your Turn Write a verbal expression for each algebraic expression. 12/18/2015www.numberbender.com14 x ÷ (2n) x divided by 7 the sum of 4 and the product of 2 and n

What is an Equation? An equation is a mathematical sentence that contains an equals sign (=). Words are used to indicate the equals sign. An equation may contain numbers, variables, or algebraic expressions. 12/18/2015www.numberbender.com15 Equality equals is is equivalent to is equal to is the same as is as much as is identical to

Examples Write an expression for each sentence 12/18/2015www.numberbender.com16 t ÷ 8 = 20 3g – 7 = 31 The quotient of t and 8 equals 20. Seven less than three times g is 31. t/8 = 20

Your Turn Write an expression for each sentence 12/18/2015www.numberbender.com17 8d – 9 = 23 A number x increased by 12 is the same as 27. The product of 8 and d decreased by 9 equals 23. x + 12 = 27

Examples Write a sentence for each equation 12/18/2015www.numberbender.com 3z – 12 = more than j is equal to 21 j + 4 = 21 The product of 3 and z decreased by 12 equals 11

Your Turn Write a sentence for each equation 12/18/2015www.numberbender.com less than r is equal to 5 r – 10 = 5 The quotient of n and 3 increased by 6 equals 30.