Algebra: factor, exponent, solve the x or y (from Mathisfun.com)

Solve 7 + y = 12

Start with: 7 + y = 12 Subtract 7 from both sides: 7 - 7 + y = 12 - 7 A little arithmetic (7 - 7 = 0 and 12 - 7 = 5) becomes: 0 + y = 5 Which is: y = 5 answer (5 is the missing number)

Solve 9 - x = 3½

Start with: 9 - x = 3½ Subtract 9 from both sides: 9 - 9 - x = 3½ - 9 Some arithmetic: 0 - x = -5½ Which is: -x = -5½ And so: x = 5½ answer (5 1/2 is the missing number)

Solve 10 - y = 6

Start with: 10 - y = 6 Subtract 10 from both sides: 10-10 - y = 6-10 Some arithmetic: 0 - y = -4 Which is: -y = -4 So: y = 4 answer (4 is the missing number)

Solve 3x = 12

Start with: 3x = 12 Divide both sides by 3: 3x/3 = 12/3 A little arithmetic (3/3 = 1 and 12/3 = 4) becomes: 1x = 4 Which is just: x = 4 answer ( 3 x _____= 12 ) (3 x 4 = 12), so 4 is the missing number

Example: Sam bought 3 boxes of chocolates online. Postage was $9 and the total cost was $45. How much was each box?

Example: Sam bought 3 boxes of chocolates online. Postage was $9 and the total cost was $45. How much was each box? Let's use x for the price of each box. 3 times x plus $9 is $45: 3x + 9 = 45 Let's solve! Start with: 3x + 9 = 45 Subtract 9 from both sides: 3x + 9 − 9 = 45 − 9 Simplify: 3x = 36 Divide by 3: 3x /3 = 36 /3 Simplify: x = 12 So each box was $12 answer ______________________________________________________ Advanced: we can also do the "divide by 3" first (but we must do it to all terms): Start with: 3x + 9 = 45 Divide by 3: 3x/3 + 9/3 = 45/3 Simplify: x + 3 = 15 Subtract 3 from both sides: x + 3 − 3 = 15 − 3 Simplify: x = 12

Exponents

Exponents 8 to the Power 2 The exponent (such as the 2 in x2) says how many times to use the value in a multiplication. Examples: 82 = 8 × 8 = 64 y3 = y × y × y y2z = y × y × z Exponents make it easier to write and use many multiplications Example: y4z2 is easier than y × y × y × y × z × z, or even yyyyzz

How do we solve this? x / 3 + 2 = 5

It might look hard, but not if we solve it in stages. First let us get rid of the "+2": Start with: x/3 + 2 = 5 To remove the plus 2 use minus 2 (because 2-2=0) x/3 + 2 -2 = 5 -2 A little arithmetic (2-2 = 0 and 5-2 = 3) becomes: x/3 + 0 = 3 Which is just: x/3 = 3 --------------------------------------- Now, get rid of the "/3": Start with: x/3 = 3 If we multiply by 3 we can cancel out the divide by 3: x/3 ×3 = 3 ×3 A little arithmetic (3/3 = 1 and 3×3 = 9) becomes: 1x = 9 Which is just: x = 9 Solved! (Quick Check: 9/3 + 2 = 3+2 = 5) _______________________________________________________ When you get more experienced: When you get more experienced, you can solve it like this: Start with: x/3 + 2 = 5 Subtract 2 from both sides: x/3 + 2 -2 = 5 -2 Simplify: x/3 = 3 Multiply by 3 on both sides: x/3 ×3 = 3 ×3 Simplify: x = 9 __________________________________________________________ Or even like this: Start with: x/3 + 2 = 5 Subtract 2: x/3 = 3 Multiply by 3: x = 9

Like Terms

Like Terms Like Terms are terms whose variables (and their exponents such as the 2 in x2) are the same. In other words, terms that are "like" each other. (Note: the coefficients can be different) Example: (1/3)xy2 / −2xy2 / 6xy2 Are all like terms because the variables are all xy2

Monomial, Binomial, Trinomial

Monomial, Binomial, Trinomial There are special names for polynomials with 1, 2 or 3 terms: monomial (1 term): 3xy2 (exponent 2) binomial (2 terms): 5x-1 trinomial(3 terms): 3x + 52 (exponent 2)-3

PEMDAS: Orders of Operations

Order of Operations PEMDAS Operations "Operations" means things like add, subtract, multiply, divide, squaring, etc. If it isn't a number it is probably an operation. But, when you see something like ... 7 + (6 × 52 + 3) ... what part should you calculate first? Start at the left and go to the right? Or go from right to left? Warning: Calculate them in the wrong order, and you will get a wrong answer ! So, long ago people agreed to follow rules when doing calculations, and they are: _________________________________________________ Order of Operations Do things in PARENTHESIS First yes 6 × (5 + 3) = 6 × 8 = 48 NOT 6 × (5 + 3) = 30 + 3 = 33 (wrong) __________________________________________________ EXPONENTS (Powers, Roots) before Multiply, Divide, Add or Subtract yes 5 × 22 = 5 × 4 = 20 NOT 5 × 22 = 102 = 100 (wrong) ____________________________________________________ MULTIPLY or DIVIDE before you ADD or SUBTRACT yes 2 + 5 × 3 = 2 + 15 = 17 NOT 2 + 5 × 3 = 7 × 3 = 21 (wrong) _____________________________________________ Otherwise just go left to right yes 30 ÷ 5 × 3 = 6 × 3 = 18 NOT 30 ÷ 5 × 3 = 30 ÷ 15 = 2 (wrong) ___________________________________________________ How Do I Remember It All ... ? PEMDAS ! P Parentheses first E Exponents (ie Powers and Square Roots, etc.) MD Multiplication and Division (left-to-right) AS Addition and Subtraction (left-to-right) __________________________________________________________ Divide and Multiply rank equally (and go left to right). Add and Subtract rank equally (and go left to right) ________________________________________________________- So do it this way: pemdas After you have done 1) "P" and 2) "E", just go from left to right doing any 3) "M" or "D" as you find them. Then go from left to right doing any 4) "A" or "S" as you find them. thought bubble You can remember by saying "Please Excuse My Dear Aunt Sally". Or ... Pudgy Elves May Demand A Snack Popcorn Every Monday Donuts Always Sunday Please Eat Mom's Delicious Apple Strudels People Everywhere Made Decisions About Sums Note: in the UK they say BODMAS (Brackets,Orders,Divide,Multiply,Add,Subtract), and in Canada they say BEDMAS (Brackets,Exponents,Divide,Multiply,Add,Subtract). It all means the same thing! It doesn't matter how you remember it, just so long as you get it right. ______________________________________________ Examples Example: How do you work out 3 + 6 × 2 ? Multiplication before Addition: First 6 × 2 = 12, then 3 + 12 = 15 ___________________________________________ Example: How do you work out (3 + 6) × 2 ? Parentheses first: First (3 + 6) = 9, then 9 × 2 = 18 _________________________________________ Example: How do you work out 12 / 6 × 3 / 2 ? Multiplication and Division rank equally, so just go left to right: First 12 / 6 = 2, then 2 × 3 = 6, then 6 / 2 = 3 _______________________________________ A practical example: ball throw Example: Sam threw a ball straight up at 20 meters per second, how far did it go in 2 seconds? The formula is: height = v × t − (1/2) × 9.8 × t2 Where v = velocity of throw (20 m/s) t = time (2 s) Putting in Sam's numbers: height = 20 × 2 − (1/2) × 9.8 × 22 Now calculate: 20 × 2 − (1/2) × 9.8 × 22 20 × 2 − 0.5 × 9.8 × 22 Start inside Parentheses 20 × 2 − 0.5 × 9.8 × 4 Then Exponents (22=4) 40 − 19.6 Then the Multiplies 20.4 Subtract and DONE ! The ball reaches 20.4 meters after 2 seconds ______________________________________ EXPONENTS OF EXPONENTS ... What about this example? 432 Exponents are special: they go top-down (do the exponent at the top first). So we calculate this way: Start with: 432 32 = 3×3: 49 49 = 4×4×4×4×4×4×4×4×4: 262144 And finally, what about the example from the beginning? 7 + (6 × 52 + 3) 7 + (6 × 25 + 3) Start inside Parentheses, and then use Exponents First 7 + (150 + 3) Then Multiply 7 + (153) Then Add 7 + 153 Parentheses completed, last operation is an Add 160 DONE !

Polynomial

Polynomial Example of a Polynomial: 3x2 + x - 2 A polynomial can have constants, variables and the exponents 0,1,2,3,... But it never has division by a variable. A Polynomial: exponents: 0, 1, 2, ... 5xy2(exponent 3) -3x + 5y3-3 (exponent 3) NOT Polynomials: 3xy-2 (exponent -2) fraction 2/x + 2

Parts of an Equation

Parts of an Equation So people can talk about equations, there are names for different parts (better than saying "that thingy there"!) Here we have an equation that says 4x − 7 equals 5, and all its parts: 4x-7=5: 4 is coefficient, x is variable, 7 and 5 constant, - is operator A Variable is a symbol for a number we don't know yet. It is usually a letter like x or y. A number on its own is called a Constant. A Coefficient is a number used to multiply a variable (4x means 4 times x, so 4 is a coefficient) Variables without a number have a coefficient of 1 (x is really 1x) Sometimes a letter stands in for the number: Example: ax2 + bx + c x is a variable a and b are coefficients c is a constant An Operator is a symbol (such as +, ×, etc) that shows an operation (ie we want to do something with the values). 4x-7=5: 4x-7 is expression, 4x, 7 and 5 are terms A Term is either a single number or a variable, or numbers and variables multiplied together. An Expression is a group of terms (the terms are separated by + or − signs) So, now we can say things like "that expression has only two terms", or "the second term is a constant", or even "are you sure the coefficient is really 4?"

Solve 5x = 30

Start with: 5x = 30 Divide both sides by 5: 5x/5 = 30/5 A little arithmetic (5/5 = 1 and 30/5 = 6) becomes: 1x = 6 Which is just: x = 6 answer (5 x ____= 30) (5 x 6 = 30), so 6 is the missing number

Solve x + 2 = 6

Start with: x + 2 = 6 Subtract 2 from both sides: x + 2 - 2 = 6 - 2 A little arithmetic (2 - 2 = 0 and 6 - 2 = 4) becomes: x + 0 = 4 Which is: x = 4 answer (4 is the missing number)

Solve x + 2½ = 10

Start with: x + 2½ = 10 Subtract 2½ from both sides: x + 2½ - 2½ = 10 - 2½ A little arithmetic (2½ - 2½ = 0 and 10 - 2½ = 7½) becomes: x + 0 = 7½ Which is just: x = 7½ answer (7 1/2 is the missing number)

Solve x + 5 = 11

Start with: x + 5 = 11 Subtract 5 from both sides: x + 5 - 5 = 11 - 5 A little arithmetic (5 - 5 = 0 and 11 - 5 = 6) becomes: x + 0 = 6 Which is just: x = 6 answer (6 is the missing number)

Solve x - 3 = 8

Start with: x - 3 = 8 Add 3 to both sides: x - 3 + 3 = 8 + 3 A little arithmetic (-3 + 3 = 0 and 8 + 3 = 11) becomes: x + 0 = 11 Which is just: x = 11 answer (11 is the missing number)

Solve x - 8 = 7

Start with: x - 8 = 7 Add 8 to both sides: x - 8 + 8 = 7 + 8 By arithmetic (-8 + 8 = 0 and 7 + 8 = 15) becomes: x + 0 = 15 Which is just: x = 15 answer (15 is the missing number)

Solve this one: x / 3 = 5

Start with: x/3 = 5 ( ____ divided by 3 = 5, so 15 is the missing number ) What we are aiming for is an answer like "x = ...", and the divide by 3 is in the way of that! If we multiply by 3 we can cancel out the divide by 3 (because 3/3=1) So, let us have a go at multiplying by 3 on both sides: x/3 ×3 = 5 ×3 A little arithmetic (3/3 = 1 and 5×3 = 15) becomes: 1x = 15 Which is just: x = 15 Solved! (Quick Check: 15/3 = 5) (15 divided by 3 = 5)

Solve y + 3 = 9

Start with: y + 3 = 9 Subtract 3 from both sides: y + 3 - 3 = 9 - 3 A little arithmetic (3 - 3 = 0 and 9 - 3 = 6) becomes: y + 0 = 6 Which is: y = 6 answer quick check: 9 - 3 = 6 _____ + 3 = 9 therefore, 6 + 3 = 9 (6 is the missing number)

Solve y - 5 = 9

Start with: y - 5 = 9 Add 5 to both sides: y - 5 + 5 = 9 + 5 A little arithmetic (-5 + 5 = 0 and 9 + 5 = 14) becomes: y + 0 = 14 Which is just: y = 14 answer (14 is the missing number)

What is an Equation

What is an Equation An equation says that two things are equal. It will have an equals sign "=" like this: x + 2 = 6 That equation says: what is on the left (x + 2) is equal to what is on the right (6) So an equation is like a statement "this equals that"

What is the value of (12 ÷ 3 + 4) - (42exponent - 6 × 2)?

answer = 4 Order of Operations are: * Parentheses (Brackets) first * Exponents (Orders, Powers, Square Roots, etc.) next * Multiplication and Division (left-to-right) next * Addition and Subtraction (left-to-right) last So we should work out what's inside the Parentheses first. There are two sets of Parentheses, so do one at a time. First Parentheses: 12 ÷ 3 + 4 Do Division first: 12 ÷ 3 + 4 = 4 + 4 Then do Addition: 4 + 4 = 8 Second Parentheses: 42 - 6 × 2 Do the Exponent first: 42 - 6 × 2 = 16 - 6 × 2 [Remember that 42 means 4 × 4 = 16, not 4 × 2 = 8] Next do Multiplication: 16 - 6 × 2 = 16 - 12 Next Subtraction: 16 - 12 = 4 Now we've simplified what's inside the two sets of Parentheses, we can complete the problem with the final Subtraction: (12 ÷ 3 + 4) - (42 - 6 × 2) = 8 - 4 = 4 IN SHORT: (12/3+4)-(42-6×2) = (4+4)-(42-6×2) = 8-(42-6×2) = 8-(16-6×2) = 8-(16-12) = 8-4 = 4

What is the value of (5 + 2)2 exponent - 9 × 3 + 23 exponent ?

answer: 30 Order of Operations are: * Parentheses (Brackets) first * Exponents (Orders, Powers, Square Roots, etc.) next * Multiplication and Division (left-to-right) next * Addition and Subtraction (left-to-right) last So we do the Parentheses first: 5 + 2 = 7 ⇒ (5 + 2)2 - 9 × 3 + 23 = 72 - 9 × 3 + 23 Next we do the Exponents (remember: 72=7×7, and 23=2×2×2) 72 = 49 and 23 = 8 ⇒ 72 - 9 × 3 + 23 = 49 - 9 × 3 + 8 Next we do the Multiplication: ⇒ 49 - 9 × 3 + 8 = 49 - 27 + 8 Next we do the Subtraction, and Addition as they occur left-to-right: ⇒ 49 - 27 + 8 = 22 + 8 = 30 ______________________________________ PEMDAS What is the value of (5 + 2)2 - 9 × 3 + 23 ?

What is the value of 4 × 4 - 3 × 3 - 16 ÷ 4 (You may use your calculator.)

answer: = 3 Order of Operations are: * Parentheses (Brackets) first * Exponents (Orders, Powers, Square Roots, etc.) next * Multiplication and Division (left-to-right) next * Addition and Subtraction (left-to-right) last So we do the Division and Multiplication (in order left to right) before the Addition and Subtraction (in order left to right): 4 × 4 - 3 × 3 - 16 ÷ 4 = 16 - 3 × 3 - 16 ÷ 4 = 16 - 9 - 16 ÷ 4 = 16 - 9 - 4 = 7 - 4 = 3_______________________________ PEMDAS What is the value of 4 × 4 - 3 × 3 - 16 ÷ 4 P-n/a E-n/a M 16 - 9 - 16 div 4 ( 4 x 4 = 16 - 3 x 3 = 9) D 16 - 9- 4 (16 div 4 = 4) A-n/a S 16 - 9= 7 - 4= 3 answer: = 3

Which number is a factor of 42? a. 24 b. 9 c. 21 d. 40

answer: c. 21 Explanation: Factors are numbers you can multiply together to get another number. The factors of 42 are 7,6,2,21,1,42,14 and 3 . From the choices given, 21 is the correct answer. Report a problem

Solve 3x - 2 = 7

answer: x = 3 Start with: 3x - 2 = 7 Add 2 to both sides: 3x - 2 + 2 = 7 + 2 A little arithmetic (-2 + 2 = 0 and 7 + 2 = 9) becomes: 3x + 0 = 9 Which is just: 3x = 9 Divide both sides by 3: 3x/3 = 9/3 A little arithmetic (3/3 = 1 and 9/3 = 3) becomes: 1x = 3 Which is: x = 3 answer _________________________________________ or the easiest way to solve is: Solve 3x -2 = 7 7 + 2 = 9 3 x ______= 9 therefore, 3 x 3 = 9 (so the missing number is 3) quick check: (9 - 2 = 7)

Solve 5x - 1 = 19

answer: x = 4 the quickest way to solve it: Solve 5x - 1 = 19 19 + 1 = 20 5 x ____= 20 therefore, 5 x 4 = 20 the missing number is 4; thus, x = 4 answer ________________________ or Start with: 5x - 1 = 19 Add 1 to both sides: 5x - 1 + 1 = 19 + 1 A little arithmetic (-1 + 1 = 0 and 19 + 1 = 20) becomes: 5x + 0 = 20 Which is just: 5x = 20 Divide both sides by 5: 5x/5 = 20/5 A little arithmetic (5/5 = 1 and 20/5 = 4) becomes: 1x = 4 Which is: x = 4

Solve this one: x + 5 = 12

answer: x = 7 (7 is the missing number) Start with: x + 5 = 12 What we are aiming for is an answer like "x = ...", and the plus 5 is in the way of that! We can cancel out the plus 5 by doing a subtract 5 (because 5−5=0) So, let us have a go at subtracting 5 from both sides: x+5 −5 = 12 −5 A little arithmetic (5−5 = 0 and 12−5 = 7) becomes: x+0 = 7 Which is just: x = 7 Solved! (Quick Check: 7+5=12)

Solve ½(y - 6) = 7

answer: y = 20 Start with: ½(y - 6) = 7 Multiply both sides by 2: ½(y - 6) × 2 = 7 × 2 A little arithmetic (½ × 2 = 1 and 7 × 2 = 14) becomes: y - 6 = 14 Add 6 to both sides: y - 6 + 6 = 14 + 6 A little arithmetic (-6 + 6 = 0 and 14 + 6 = 20) becomes: y + 0 = 20 Which is: y = 20

What is the value of (52exponent - 5) / (42exponent + 8 - 7 × 2) ?

answer= 2 Order of Operations are: * Parentheses (Brackets) first * Exponents (Orders, Powers, Square Roots, etc.) next * Multiplication and Division (left-to-right) next * Addition and Subtraction (left-to-right) last So we should work out what's inside the Parentheses first. There are two sets of Parentheses, so do one at a time. First Parentheses: 52 - 5 Do Exponents first (remember: 52 = 5×5, not 5×2): 52 - 5 = 25 - 5 Then do Subtraction: 25 - 5 = 20 Second Parentheses: 42 + 8 - 7 × 2 Do Exponents first (remember: 42 = 4×4, not 4×2): 42 + 8 - 7 × 2 = 16 + 8 - 7 × 2 Next do Multiplication: 16 + 8 - 7 × 2 = 16 + 8 - 14 Next do Addition and Subtraction as they occur, left-to-right: 16 + 8 - 14 = 24 - 14 = 10 Now we've simplified what's inside the two sets of Parentheses, we can complete the problem with the final Division: (52 - 5) / (42 + 8 - 7 × 2) = 20 / 10 = 2

What is the value of (33exponent - 9 / 3) + (4 × 3 - 32exponent) ?

answer= 27 Order of Operations are: * Parentheses first * Exponents (Powers, Square Roots, etc.) next * Multiplication and Division (left-to-right) next * Addition and Subtraction (left-to-right) last So we should work out what's inside the Parentheses first. There are two sets of Parentheses, so do one at a time. First Parentheses: 33 - 9 / 3 Do Exponents first (remember 33=3×3×3, not 3×3): 33 - 9 / 3 = 27 - 9 / 3 Then do Division: 27 - 9 / 3 = 27 - 3 and finally Subtraction: 27 - 3 = 24 Second Parentheses: 4 × 3 - 32 Do Exponents first (remember 32=3×3, not 3×2): 4 × 3 - 32 = 4 × 3 - 9 Next do Multiplication: 4 × 3 - 9 = 12 - 9 Next do Subtraction: 12 - 9 = 3 Now we've simplified what's inside the two sets of Parentheses, we can complete the problem with the final Addition: (33 - 9 / 3) + (4 × 3 - 32) = 24 + 3 = 27 IN SHORT: (33-9/3)+(4×3-32) = (27-9/3)+(4×3-32) = (27-3)+(4×3-32) = 24+(4×3-32) = 24+(4×3-9) = 24+(12-9) = 24+3 = 27

What is the value of (7 - √9) × (42exponent - 3 + 1) ?

answer= 56 Order of Operations are: * Parentheses first * Exponents (Powers, Square Roots, etc.) next * Multiplication and Division (left-to-right) next * Addition and Subtraction (left-to-right) last So we should work out what's inside the Parentheses first. There are two sets of Parentheses, so do one at a time. First Parentheses: 7 - √9 Do Exponents (square root) first: 7 - √9 = 7 - 3 Then do Subtraction: 7 - 3 = 4 Second Parentheses: 42 - 3 + 1 Do Exponents first: 42 - 3 + 1 = 16 - 3 + 1 Next do Subtraction: 16 - 3 + 1 = 13 + 1 Next do Addition: 13 + 1 = 14 Now we've simplified what's inside the two sets of Parentheses, we can complete the problem with the final Multiplication: (7 - √9) × (42 - 3 + 1) = 4 × 14 = 56 Here it is again, line by line: (7 - √9) × (42 - 3 + 1) = (7 - 3) × (42 - 3 + 1) = 4 × (42 - 3 + 1) = 4 × (16 - 3 + 1) = 4 × (13 + 1) = 4 × 14 = 56

{Solve} frac{x}{2}=3

start with: fraction X/2= 3 multiply both sides by 2: fraction x/2 x 2 = 3 x 2 a little arithmetic (fraction 1/2 x 2 = 1 and 3 x 2 = 6) becomes: 1x = 6 which is just: x = 6 answer **

evaluate a + bc if a = 3 b = 2 c = 9 a. 14 b. 21 c. 33 d. 45

answer: 21 3 + 2 (9) 3 + 18 3 + 18 = 21

Solve 2x + 5 = 13

x = 4 answer the quickest way to solve it: Solve 2x + 5 = 13 13 - 5 = 8 2 x _______= 8 therefore, 2 x 4 = 8 (so the missing number is 4) quick check: 8 + 5 = 13 ------------------------------- or Start with: 2x + 5 = 13 Subtract 5 from both sides: 2x + 5 - 5 = 13 - 5 A little arithmetic (5 - 5 = 0 and 13 - 5 = 8) becomes: 2x + 0 = 8 Which is just: 2x = 8 Divide both sides by 2: 2x/2 = 8/2 A little arithmetic (2/2 = 1 and 8/2 = 4) becomes: 1x = 4 Which is: x = 4

What is the value of this? \frac{2^4+(16-3\times4)} {(6+3^2)\div(7-4)}

answer = 4 Order of Operations are: * Parentheses (Brackets) first * Exponents (Orders, Powers, Square Roots, etc.) next * Multiplication and Division (left-to-right) next * Addition and Subtraction (left-to-right) last This problem involves a quotient. We must simplify the Numerator and Denominator separately first. 1. Numerator 24 + (16 - 3 × 4) First we must simplify what's inside the Parentheses: (16 - 3 × 4) And inside the Parentheses, we do the Multiplication first: 16 - 3 × 4 = 16 - 12 Then the Subtraction: 16 - 12 = 4 Next we do the Exponent: 24 = 2 × 2 × 2 × 2 = 16 So putting the two parts of the Numerator together, we get: 24 + (16 - 3 × 4) = 16 + 4 Now we do the Addition: 16 + 4 = 20 We've simplified the Numerator as much as possible, and got 20. 2. Denominator (6 + 32) ÷ (7 - 4) There are two sets of Parentheses, so we must simplify what's inside each set first: First Parentheses (6 + 32) Next do Exponents: (6 + 32)= 6 + 9 [Remember that 32 = 3 × 3 = 9, not 3 × 2 = 6] Then do the Addition: 6 + 9 = 15 Second Parentheses (7 - 4) = 3 Now we've worked out what's inside both sets of Parentheses, we can work out the Denominator: (6 + 32) ÷ (7 - 4) = 15 ÷ 3 = 5 We've simplified the Denominator as much as possible, and got 5 Finally we can work out the answer, by calculating the quotient of Numerator over Denominator: \frac{2^4+(16-3\times4)}{(6+3^2)\div(7-4)}=\frac{20}{5}=4

What is the value of 6 × 4 - 12 ÷ 3 - 8

answer: 12 Order of Operations are: * Parentheses (Brackets) first * Exponents (Orders, Powers, Square Roots, etc.) next * Multiplication and Division (left-to-right) next * Addition and Subtraction (left-to-right) last So we do the division and multiplication before the addition and subtraction, but division and multiplication rank equally. So we do 6 × 4 and 12 ÷ 3 first, then the subtractions: 6 × 4 - 12 ÷ 3 - 8 = 24 - 12 ÷ 3 - 8 = 24 - 4 - 8 = 20 - 8 = 12 _______________________ PEMDAS What is the value of 6 × 4 - 12 ÷ 3 - 8 P-n/a E- n/a M- 24 - 12 div 3 - 8 (6 x 4 = 24) D- 24 - 4 - 8 ( 12 divide 3 = 4 ) A-n/a S- 24- 4= 20 - 8 = 12 answer: = 12

What is the value of 20 - (3 × 23 - 5)?

answer: = 1 Order of Operations are: * Parentheses (Brackets) first * Exponents (Orders, Powers, Square Roots, etc.) next * Multiplication and Division (left-to-right) next * Addition and Subtraction (left-to-right) last So, we start inside the Parentheses, and then use "Exponents" first: 20 - (3 × 23 - 5) = 20 - (3 × 8 - 5) [Because 23 means 2 × 2 × 2 = 8, not 2 × 3 = 6] Next Multiply: 20 - (3 × 8 - 5) = 20 - (24 - 5) Next Subtract (still working inside the parentheses): 20 - (24 - 5) = 20 - 19 Now the Parentheses are completed, the last operation is Subtract: 20 - 19 = 1 Next QuestionNext Question ________________________ order of operation: PEMDAS What is the value of 20 - (3 × 23 - 5)? P E-n/a M D-n/a A-n/a S

What is the value of 6 ÷ 3 + 4 × 2 ?

answer: = 10 Order of Operations are: * Parentheses (Brackets) first * Exponents (Orders, Powers, Square Roots, etc.) next * Multiplication and Division (left-to-right) next * Addition and Subtraction (left-to-right) last So we do the division and multiplication before any addition or subtraction: 6 ÷ 3 + 4 × 2 = 2 + 4 × 2 = 2 + 8 = 10 ------------------------------------- PEMDAS what is the value of 6 div 3 + 4 x 2 P-parenthesis does not apply in this case E-Exponent does not apply in this case 6 div 3 + 8 (4 x 2 = 8 -Multiply) 2 + 8 (6 div 3 = 2 -Division) 2 + 8 = 10 (Addition) =10 answer S-subtraction does not apply in this case

Solve this one: x + 5 = 12

answer: X = 7 ( 7 is the missing number) Start with: x + 5 = 12 What we are aiming for is an answer like "x = ...", and the plus 5 is in the way of that! We can cancel out the plus 5 by doing a subtract 5 (because 5−5=0) So, let us have a go at subtracting 5 from both sides: x+5 −5 = 12 −5 A little arithmetic (5−5 = 0 and 12−5 = 7) becomes: x+0 = 7 Which is just: x = 7 Solved! (Quick Check: 7+5=12)

Solve fraction x/3 = 4

answer: x = 12 start with: fraction x/3 = 4 multiply both sides by 3: fraction x/3 x 3 = 4 x 3 a little arithmetic (fraction 1/3 x 3 = 1 and 4 x 3 = 12) becomes: 1x = 12 which is just: x = 12

Solve 2(x + 3) = 10

answer: x = 2 Start with: 2(x + 3) = 10 Divide both sides by 2: 2(x + 3)/2 = 10/2 A little arithmetic (2/2 = 1 and 10/2 = 5) becomes: x + 3 = 5 Subtract 3 from both sides: x + 3 - 3 = 5 - 3 A little arithmetic (3 - 3 = 0 and 5 - 3 = 2) becomes: x + 0 = 2 Which is: x = 2

Solve x/5 + 2 = 6

answer: x = 20 Start with: x/5 + 2 = 6 Subtract 2 from both sides: x/5 + 2 - 2 = 6 - 2 A little arithmetic (2 - 2 = 0 and 6 - 2 = 4) becomes: x/5 + 0 = 4 Which is just: x/5 = 4 Multiply both sides by 5: x/5 × 5 = 4 × 5 A little arithmetic (1/5 × 5 = 1 and 4 × 5 = 20) becomes: 1x = 20 Which is just: x = 20 answer

Solve x - 2 = 4

answer: x = 6 (6 is the missing number) explanation: x represents a blank box for missing number. In algebra we use the x or y for missing number called "unknown" or "variable", we do not use blank boxes. And it doesn't have to be x, it could be y or w ... or any letter or symbol we like. _____ - 2= 4 (6-2= 4, so 6 is the missing number) therefore, x=6 answer how to solve it: We want to remove the "-2" x - 2 = 4 To remove it, do the opposite, in this case add 2: x - 2 = 4 + 2 = ____________ 0 Do it both sides: x - 2 = 4 + 2 + 2 _______ _____ 0 6 Which is ..... x + 0 = 6 Solved! x = 6 Why did we add 2 to both sides? To "keep the balance"... balance x - 2 vs 4 In Balance Add 2 to Left Side unbalanced x - 2 + 2 vs 4 Out of Balance! Add 2 to Right Side Also balanced x - 2 + 2 vs 4 + 2 In Balance Again Just remember this: To keep the balance, what we do to one side of the "=" we should also do to the other side!