Variable Expressions Vocabulary Words To Know Translating Words

Variable Expressions Vocabulary Words To Know

Translating Words to Variable Expressions 1. The SUM of a number and nine 2. The DIFFERENCE of a number and nine n+9 n– 9 3. The PRODUCT of a number and nine 4. The QUOTIENT of a number and nine 9 n 5. One nin. TH OF a number 6. Nine times THE QUANTITY OF a number increased by ten. 9(n + 10) or 7. A number SQUARED n 2 9. 8. A number CUBED n 3 A number LESS THAN nine n– 9 * When you see the phrase less than, reverse the terms.

Translating Variable Expressions Translate each mathematical expression into a verbal phrase without using the words: “plus”, “add”, “minus”, “subtracted”, “”take–away”, multiplied”, “times”, “over”, “power”, or “divided” 16. 13 a . the product of thirteen and a number 17. the quotient of fourteen and a number 18. y – 11 the difference of a number and eleven, OR eleven less than a number OR a number decreased by eleven 19. 3 y + 8 eight more than the product of three and a number, OR the product of three and a number increased by eight 20. 6 ÷ n 2 the quotient of six and a number squared 21. 7(x + 1) 3 22. b – 4 seven, times the quantity of one more than a number, OR seven, times the quantity of a number increased by one the difference of a number cubed and four, OR a number cubed decreased by four, OR four less than a number cubed

Simplifying Using Order of Operations 1. 2 (1 + 3) • 4 6 – 2 ÷ (– 1) 2 ( 4 ) • 4 16 • 4 64 6 – 2 ÷ (– 1) 6 – (– 2) 6 + 2 8 64 = 8 8 Evaluate the numerator and denominator separately 2. – 4 +[8 – (5 + 9)] • 2 – 4 +[8 – ( 14 )] • 2 – 4 +[ – 6 – 4 + ] • 2 – 16 Evaluate inside the brackets first. . . then treat the brackets like parenthesis

Evaluating Variable Expressions with Negative Variables 1) –x –(– 3) +3 3 2) 1. Substitute – 3 for x only. 2. Leave the negative (–) in front of the x alone. 3. Now, simplify the signs (kill the sleeping man) –y –(– 2) +2 2 3) Evaluate each expression using: x = – 3 y = – 2 z=6 1. Substitute – 2 for y only. 2. Leave the negative (–) in front of the y alone. 3. Now, simplify the signs. –z – 6 1. Substitute 6 for z only. 2. Leave the negative (–) in front of the z alone. 3. Now, simplify the signs.

Evaluating Variable Expressions with Negative Variables 4) – 3 – (– 2) – 3 + 2 – 1 5) 1. 2. 3. 4. Substitute – 3 for x , and – 2 for y only. Leave the subtraction sign (–) in front of the y alone. Now, simplify the signs. (keep->change) Add the integers. x–z – 3 – 6 – 9 6) Evaluate each expression using: x = – 3 y = – 2 z=6 x–y 1. Substitute – 3 for x , and 6 for z only. 2. Leave the subtraction sign (–) in front of the z alone. 3. Subtract the integers. z–x 6 – (– 3) 6 +3 9 1. 2. 3. 4. Substitute 6 for z , and – 3 for x only. Leave the subtraction sign (–) in front of the x alone. Now, simplify the signs. Add the integers.

Evaluating Variable Expressions with Negative Variables 7) xy – 3 • (– 2) 6 8) Evaluate each expression using: 1. 2. x = – 3 y = – 2 Substitute – 3 for x , and – 2 for y. Multiply –– * Why? Two variables right next to each other. yz – 2 • 6 – 12 9) 1. 2. Substitute – 2 for y , and 6 for z. Multiply –– * Why? Two variables right next to each other. –xz –(– 3) • 6 +3 • 6 18 10) 1. 2. 3. 4. Substitute – 3 for x , and 6 for z. Leave the negative sign in front of the x alone. Simplify the signs. Multiply 1. 2. 3. 4. Substitute – 3 for x , and 6 for z. Leave the negative sign in front of the parenthesis, ( ), alone. Multiply inside the parenthesis first. Simplify the signs. –(xz) –((– 3) • 6) –(– 18) 18 z=6

Evaluating Variable Expressions with Negative Variables 11) 2 x 2 2 • (– 3)2 2 • 9 18 12) x = – 3 36 z=6 Substitute – 3 for x. First, evaluate the exponent. Then, multiply. –– Why? When a number is right next to a variable, multiply. 1. 2. 3. Substitute – 3 for x. First, evaluate the exponent. Then, multiply. 1. 2. 3. Substitute – 3 for x. First, evaluate inside parenthesis, ( ). Then, evaluate the exponent. (– 2 x)2 (– 2 • (– 3))2 ( 6 )2 y = – 2 1. 2. 3. – 2 x 2 – 2 • (– 3)2 – 2 • 9 – 18 13) Evaluate each expression using:

Evaluating Variable Expressions with Negative Variables Evaluate each expression using: 14) 1. 2. 3. – 2 x 3 – 2 • (– 3)3 – 2 • (– 27) 54 16) y = – 2 z=6 2 x 3 2 • (– 3)3 2 • (– 27) – 54 15) x = – 3 Substitute – 3 for x. First, evaluate the exponent. * Remember, (– 3)3 is (– 3) • (– 3) = – 27 Then, multiply. –– Why? When a number is right next to a variable, multiply. 1. 2. 3. Substitute – 3 for x. First, evaluate the exponent. Then, multiply. 1. 2. 3. Substitute – 3 for x. First, evaluate inside parenthesis, ( ). Then, evaluate the exponent. (– 2 x)3 (– 2 • (– 3))3 ( 6 )3 216

Evaluating Variable Expressions 1. 2. 4 7 3. – 22 4. 5. 0 11 6. 21 7. 40 59

Simplifying Variable Expressions by Adding or Subtracting You can only add or subtract LIKE TERMS. – 7 a – 9 + 11 a – 3 terms with the same variable. or numbers without variables (constants) (like – 7 a and +11 a) 4 a – 12 (like – 9 and – 3) Circle the variable terms, . . . and box up the constants Add the like terms. 17 a +1 a 18 a 4. Remember, a = 1 a so, put a “ 1” in front of the a 14 x + 7 b – 9 x + 19 – 11 b – 21 2. – 10 – 7 y + 6 y – 3 – 1 y 5. 13 + 2(8 – g) 13 + 16 + 2 g – 4 b + 5 x – 2 29 + 2 g 3. 12 b + 5 – 12 b . . . or, get rid of the “ 1” Use Distributive Property to get rid of the parenthesis. outer times first, then outer times second 0 – 10 6. . or, get rid of the “ 0” 13 +(– 19) – 6(n + 1) – 10 n 13 +(– 19) – 6 n – 6 – 10 n – 12 – 16 n

Simplifying Variable Expressions by Multiplication 8. 7( – 3 x ) When you see constants (7 and – 3) and variables (x), it’s easiest to simplify them separately. First, multiply 7 and – 3… …then just bring down the x (Why? It’s the only x ) – 21 x 9. 10. – 19 a • 10 bc When you see constants (– 19 and 10) and multiple variables (a, b, and c), take it one at a time. – 190 abc First, multiply – 19 and 10… 10 …then bring down the a, b, and c (Why? There’s only 1 of each. ) ( – 1 )2 y (– 1)2 y – 2 y 11. – 5 a( – 5 c ) – 5 a(– 5 c) 25 ac 12. ( x • 8 )6 y (x • 8 )6 y 48 xy

Simplifying Variable Expressions Using the Distributive Property 13. When a number or variable term sits right next to terms inside parenthesis, use the Distributive Property to simplify. – 2(n +1) – 2 • n – 2 • +1 – 2 14. (9 – 6 x)3 27 – 18 x How? First, multiply the outer term, – 2 by the 1 st term in parenthesis, n. Then, multiply the outer term, – 2, by the 2 nd term in parenthesis, 1. 15. – 4(8 a + 7) – 32 a – 28 How to remember the Distributive Property? 16. (– 3 p + 1)(– 5) 15 p – 5 17. 10(–c – 6) – 10 c – 60 “Outer times 1 st, then outer times 2 nd”

Simplifying Variable Expressions by 18. Simplify x 4 • x 7 Multiplying Exponents Are the bases, x, the same? Are we multiplying or dividing the exponent terms? Multiplying Exponents Rule: When multiplying exponent terms with like bases, keep the base, then add the exponents. 4 + 7 = 11 So, we’re going to keep the base. . . …then add the exponents x 11 x 19. 6 9 a • a a 15 Rewrite. 1 20. b • b 5 b 6 Careful: What’s the invisible exponent over b ? 21. y • y 4 y 9

Simplifying Variable Expressions by GUIDED PRACTICE Multiplying Exponents Simplify 22. 7 x 2 • 7 x 4 7 x 2 • 7 x 4 When you see both constants, 7, and variables, x, it’s easiest to simplify them separately. Let’s multiply the 7’s first. . . 6 49 x 23. 10 y 7 • 4 y 7 10 y • 4 y 40 y 8 … then, multiply x 2 • x 4. 24. 3 a 5 b • 3 a 6 b 8 Don’t panic: Just multiply each part separately. 3 a 5 b • 3 a 6 b 8 9 a 11 b 9 25. 2 x 5 yz 3 • yz 2 x 5 y 2 z 4

Simplifying Variable Expressions by Dividing Exponents Simplify Are the bases, x, the same? 26. Are we multiplying or dividing the exponent terms? Dividing Exponents Rule: When dividing exponent terms with like bases, keep the base, then subtract the exponents. 12 – 7 = 5 x So, we’re going to keep the base. . . …then subtract the exponents Rewrite. 28. 27. 6 y 4 a ÷a 3 a 29. 30. b – 6 n (huh? ) or

Simplifying Variable Expressions by Dividing Exponents 31. Simplify When you see both constants, 12 and 6, and variables, y, it’s easiest to simplify them separately. Let’s simplify the fraction … then, divide y 9 and y 3. 2 y 6 32. 33. 34. Hint: The rest of the answers are fractions. 5 a first. . . 35. 36.