Write expressions and Equations 1.3 & 1.4 Write expressions and Equations

Writing Algebraic Expressions Phrases that describe how items or variables are related can be converted into algebraic expressions. Key words, such as "less than" or "five times" will determine which operation will be involved. The given phrase may give us the variable to use, or it may simply say "some number" in which case we will use "n."

Some examples of these phrases are: 5 more than a number 3 fewer than a number the sum of 7 and number

Fill in the chart with words that mean the same as the given math operation: Addition  Subtraction   Multiply Division plus sum more than minus difference less than times of product twice quotient ratio half third

Ex 1: Write an algebraic expression that describes each phrase given. the difference of a number and 4 6 times a number a number divided by 3 x – 4 6x x 3

d) the sum of 7 and number e) the product of 2 and a number f) the quotient of x and y 7 + x 2x x y

Flips the order of the numbers Than Flips the order of the numbers Ex 2: Write an algebraic expression that describes the phrase given.

a) 5 more than a number b) 3 fewer than a number c) 8 less than a number x + 5 x – 3 x – 8

Ex 3: Write an algebraic expression that describes the phrase given. a) The sum of a number and 12 b) 4 less than 5 times y c) The product of a number and 4 x + 12 5y – 4 4x

d) 6 fewer than x e) The difference of m and n f) One third of x x – 6 m – n

g) a less than b h) 7 times the sum of 3 and a number i) 4 more than the square of a number b – a 7(3 + x)

Quantity Group in parenthesis

Ex 4: Write the expression. a) 3 times the quantity a + b b) 5 times the quantity of the sum of x and 7 c) 2 less than 12 times the quantity of 3(a + b) 5(x + 7) 12(x + y) – 2

Ex 5: A piece of ribbon L feet long is cut from a ribbon that is 8 feet long. Write an expression for the length of the remaining piece of ribbon. 8 - L

Ex 6: You work a lemonade stand with two other friends and collect tips in a jar. You agree to pay your friend’s mom $2 out of the tip money to pay for all the cups and ice. If the amount of the tips is “M”, write an expression for how much each of you will get in tips after the mom is paid. M – 2 3

Equal = “is” Makes an equation

Ex 7: Write the equation that the given sentence represents.   a) The difference of twice a number k and 8 is 12. b) The product of 6 and a number n is 24.    c) 3 less than x is 12 2k – 8 = 12 6n = 24 x – 3 = 12

d) The sum of x and 7 is the same as twice y.      e) Twice the quotient of t and 7 is 20. f) 4 times the sum of n and 10 is 15. x + 7 = 2y 4(n + 10) = 15

Number opposite zero on number line. Changes the sign

Ex 8: Find the opposite value.

Distance a number is from zero. Absolute value Distance a number is from zero. Makes any number inside positive when taken out

Ex 8: Find the absolute values as indicated.

Ex 9: Evaluate the expression with the absolute value.

Ex9: Evaluate the expression with the absolute value.

Ex 10: Write the equation that the given sentence represents.   a) Twice the absolute value of the sum of x and 4 is 10. b) The absolute value of the difference of 7 and a number is equal to 13.