1-1: Writing Expressions and Equations

? Lesson Opener ? represents a number. That number plus ten equal 14. How do we represent the number algebraically? ?

WHAT YOU’LL LEARN Translate words into algebraic expressions and equations.

BUILD YOUR VOCABULARY (pages 2–3) An algebraic expression contains numbers and variables along with +, -, x, and/or ÷. A variable is a symbol used to represent an unknown number. A numerical expression contains numbers along with +, -, x, and/or ÷.

BUILD YOUR VOCABULARY (pages 2–3) A factor is a quantity that is being multiplied. A product is the result of numbers that are multiplied. An equation is a mathematical sentence that contains an equals sign (=).

ORGANIZE IT In your notes, write several words or phrases for each of the operations, addition, subtraction, multiplication, and division.

Addition Subtraction plus the sum of increased by more than added to The total of minus the difference of decreased by less than fewer than subtracted from

Multiplication Division Times The product of Multiplied by At Of Divided by The quotient of The ratio of per

Write an algebraic expression for each verbal expression. EXAMPLES Write an algebraic expression for each verbal expression. 1 the sum of p and 12 p + 12 2 the product of k and q k  q or kq

Your Turn Write an algebraic expression for each verbal expressions a) b decreased by 6 b) the product of 9 and z b – 6 9  z or 9z

A python eats 4 pounds of meat each month. EXAMPLES A python eats 4 pounds of meat each month. 3 Write a numerical expression to represent the amount it eats in 5 months. The numerical expression is 4  5 or 4(5). 4 Write an algebraic expression to represent the amount it eats in d months. The algebraic expression is 4  d or 4d.

Write a verbal expression for each algebraic expression. EXAMPLES Write a verbal expression for each algebraic expression. 5 the sum of 37 and s . 37 + s 37 increased by s. 6 5 (b – 3) 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 a) x ÷ 7 b) 4 + (2n) X divided by 7 the sum of 4 and the product of 2 and n.

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. Equality Equals Is Is equivalent to Is equal to Is the same as Is as much as Is identical to

Write an expression for each sentence. EXAMPLES Write an expression for each sentence. 7 The quotient of t and 8 equals 20. t ÷ 8 = 20 or t/8 = 20 8 Seven less than three times g is 31. 3g - 7 = 31

Write an expression for each sentence. Your Turn Write an expression for each sentence. a) A number x increased by 12 is the same as 27. b) The product of 8 and d decreased by 9 equals 23. X + 12 = 27 8d – 9 = 23

Write a sentence for each equation. EXAMPLES Write a sentence for each equation. 9 j + 4 = 21 Four more than j is equal to 21. 10 3z – 12 = 11 The product of 3 and z decreased by 12 equals 11.

Your Turn Ten less than r is equal to 5. Write a sentence for each equation. a) r - 10 = 5 b) Ten less than r is equal to 5. The quotient of n and 3 increased by 6 equals 30.