Carry The Two

Please Excuse My Dear Aunt Sally: Parentheses Exponents Multiplication Division  Addition  Subtraction When you have a problem with parentheses, multiplication, addition, etc. It is often difficult to decide what part to calculate first. PEMDAS stands for  Please Excuse My Dear Aunt Sally (as seen above).  It is an acronym used to remind us of the order of operations.   Parentheses first, for example: 5 + (7 + 8) = 5 + (15)  = 20 Hint: Absolute value bars are treated like parentheses considering they are evaluated first. Exponents, including powers and roots, first. Then multiply, divide, add or subtract: 10 x 8 ²  =10 x 64 = 640 Multiplication/division is completed before addition or subtraction: 7 x 4 - 5 = 28 - 5 = 23 Hint: Multiplication and division rank equally so you would just go from left to right if you had a problem with both: Problem 1 49 / 7 x 2 / 2 Step 1  Right to left: 49 / 7 = 7 Step 2 7 x 2 / 2 Right to left: 7 x 2 = 14 Step 3 14...

Linear Function A linear function’s equation does not have exponents Exponent A quantity representing the power to which a given number is to be raised.  Expressed as a raised symbol beside the number or equation (e.g. 3 in 2 3 ) Question #1 Is y = 6x 2  + 7 a linear equation? Step 1 Ask yourself: Are there any exponents? Yes, y = 6x 2  + 7 has an exponent: The 2 in x 2  is an exponent Answer: y = 6x 2  + 7 is not a linear equation Question #2 Is y = 3x + 2 a linear equation? Step 1 Ask yourself: Are there any exponents? No, y = 3x + 2 does not have an exponent Answer: y = 3x + 2 is a linear equation The form for a Linear Equation Ax + By = C Another method, to determine if an equation is linear is to determine whether the equation can be rewritten in linear equation form. Question #3 Is y = x - 1 a linear equation? Step 1 Ask yourself: Can y = x – 1 be rewritten in linear equation form? ...

Radical A radical is the term under a square root symbol.   In the picture above, x would be the radical. Cube Root The expression for cube root is a small 3 above the radical/to the left.   This number is called the index.   To calculate the cube root of a number, we must find the number multiplied by itself, and then multiplied by itself again, is equaled to the original number. Problem #1 What is the cube root of 8? Step 1 We ask ourselves: What number multiplied by itself twice, equals 8? Step 2 Guess and check: Try 2 2 x 2 x 2 = 8 Therefore the cube root of 8 = 2 Answer: 2 Further Explanation Taking the cube root of a number is the inverse of cubing, therefore the answer is 2 because 2 3 = 8. If Problem #1’s explanation does not make sense, lets think about what we do when we cube a number. To cube a number, we multiply it 3 times. For example, when we cube the number 5: 5 x 5 x 5 = 125 A cube root goes in the...

Problem #1 Convert .58 into a fraction in simplest form. Step One Write .58 as a fraction using 100 as the denominator: 58/100 Step Two Reduce the fraction to its simplest form.  Divide both the numerator (58) and the denominator (100) by 2: 58/2 = 29 100/2 = 50 ANSWER = 29/50 Problem #2 Write -1/5 as a decimal. Step One Find an equivalent fraction to -1/5 with 10 as the denominator. Step Two In order to get the denominator (the 5) to equal 10, we must multiply the fraction by 2: -1 x 2 = -2 5 x 2 = 10 = -2/10 Step Three Convert the new fraction to a decimal: -2/10 = -.2 Problem #3 Convert .35 into a fraction in simplest form. Step One Write .35 as a fraction using 100 as the denominator: 35/100 Step Two Reduce the fraction to its simplest form.  Divide both the numerator (35) and the denominator (100) by 5: 35/5 = 7 100/5 = 20 ANSWER = 7/20 Problem #4 Convert .6 into a fraction in simplest form. Step One Write 6 as a fract...

PROBLEM #1 (4x - 4)(x + 4) FOIL First Outside Inside Last Step One First: • The first term in the first binomial is 4x • The first term in the second binomial is x • So we multiply them: (4x)(x) = 4x2 Step Two Outside: • The outside term in the first binomial is 4x • The outside term in the second binomial is 4 • So we multiply them: (4x)(4) = 16x Step Three Inside: • The inside term in the first binomial is - 4 • The inside term in the second binomial is x • So we multiply them: (- 4)(x) = - 4x Step Four Last: • The last term in the first binomial is - 4 • The last term in the second binomial is 4 • So we multiply them: (- 4)(4) = - 16 Step Five • Write out your calculations as one equation: • 4x2 + 16x – 4x – 16 Step Six • Combine like terms • The 16x and - 4x are the only set of terms that are like • 16x – 4x = 12x • Therefore your answer is: ANSWER 4x2 + 12x – 16 PROBLEM #2 (4x - 4)(3x + 2) FOIL First Outside ...

PROBLEM #1 Solve for x. -24 - 3x = 9x Step One Add 3x to each side: (You are attempting to get your variables (x's) on one side) -24 = 12x Step Two Divide both sides by 12 (You divide by 12 in order to get the x by itself) -2 = x Step Three Check your answer by plugging in the -2 for the x's in the original equation: -24 - 3(-2) = 9(-2) -24 + 6 = -18 -18 = -18 -18 does equal -18 therefore we know our answer (x = -2) is correct. PROBLEM #2 Solve for x. 4x = -8 + 5x Step One Subtract 5x from each side: (You are attempting to get your variables (x's) on one side) -x = -8 Step Two Use logical reasoning to determining what x is equaled to, considering you know what negative x equals: If -x = -8, then x = 8 Step Three Check your answer by plugging in the 8 for the x's in the original equation: 4(8) = -8 + 5(8) 32 = -8 + 40 32 = 32 32 does equal 32 therefore we know our answer (x = 8) is correct.