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...