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Order of Operations

Order of Operations. There are 4 operations in mathematics. Addition 6+4=10 Subtraction 36-10=26 Multiplication 5X6=30 Division 60÷10=6. Addition Terms. Addends – the two numbers being added together 6 + 10 =

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Order of Operations

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  1. Order of Operations

  2. There are 4 operations in mathematics • Addition 6+4=10 • Subtraction 36-10=26 • Multiplication 5X6=30 • Division 60÷10=6

  3. Addition Terms • Addends – the two numbers being added together 6+10= • Sum- the total that results when the addends are combined, the answer 6+10=16 • Sign +

  4. Subtraction Terms • Difference – the answer to a subtraction number sentence. 10-3=7 • Sign -

  5. Multiplication Terms • Factor- the numbers being multiplied together 5X6= • Product- the result of multiplying the factors, the answer 5X6=30 • Sign X

  6. Division Terms • Dividend – the total number being divided into equal groups 48÷6= • Divisor- the number of equal groups being created when dividing up the dividend 48÷6= • Quotient- the answer to a division number sentence 48÷6=8 • Sign ÷ =

  7. Order of Operations • 3+4x4 • Begin by laying down 3 tiles. Next create a 4x4 array. • How many tiles are in your model?

  8. Order of Operations • 3+4x4 • Show 3+4 using two colors of tiles for each addend. Next, build an array for this amount times 4. • How many tiles are shown in this model? • What do you notice when you compare the two models? Write an expression to represent each model. Why is order important rather than solving from left to right?

  9. Order of Operations • Jay brought some juice boxes to soccer practice to share with his teammates. He had 3 single boxes and 4 multi-packs. There are 6 single boxes in each multi-pack. To determine how many boxes of juice Jay brought to practice, evaluate 3 + 4 × 6.

  10. Parenthesis • When solving a problem you should always begin with the expression found within the Parenthesis • 3X(4+9)-7=

  11. Order of Operations • When solving an expression you should begin solving the part of the problem in the ______________ first. • If you do not begin with the ____________ your answer will not be _______________.

  12. Order of Operations • Take two dice. • Roll the dice and create an expression using either multiplication X or division ÷. • Roll the dice again and expand on your expression using addition + and subtraction -. • Choose a place in your expression to add parenthesis. • Solve • Allow your neighbor to try and solve your problem. Are your answers the same? If not discuss. • Now move the parenthesis. Does your answer change? Why or why not?

  13. PEMDASPlease Excuse My Dear Aunt Sally • P= Parenthesis • E= Exponent • M= Multiplication • D= Division • A= Addition • S= Subtraction

  14. Brackets • Brackets- [ ] are like parenthesis. Anything inside them should be done before you solve exponents, multiplication, division, addition, or subtraction. They often contain an expression that uses parenthesis. 3+[4X9+(9+7-3)]=

  15. Braces • Braces- { } are used when an expression contains both parenthesis ( ) and brackets [ ]. 8x{6+[4x(15÷5)-1]x1} • When solving a problem that has Parenthesis, Brackets, and Braces start from the inside and work your way out.

  16. Exponents • Exponent- shorthand for showing repeated multiplication of the same number by itself. 53 = 5 × 5 × 5 = 125 24 = 2 × 2 × 2 × 2 = 16

  17. Practice • Parenthesis- 3+(56-38)x2 • Parenthesis and Brackets- 4x[32+(5x2)-21] • Parenthesis, Brackets, and Braces- 15+{17+[85-(21x2)+4]-12} • Parenthesis, Brackets, Braces, and Exponents 23+ {3X(4-1)-3+[33-2]-2}

  18. Using Words to Write Expressions • You can write an expression in word form example- the sum of three and two This expression can then be written using numbers it would be written in number form as 3+2= • Write the number form The product of fifteen and three added to one and subtracted by four

  19. Using Words to Write Expressions • The product of fifteen and three added to one and subtracted by four • You should have written 1+15X3-4 • It is important to remember when you need to add parenthesis!!! • Write the number form for The sum of three and seven multiplied by two and subtracted from twenty three

  20. Using Words to Write Expressions • The sum of three and seven multiplied by two and subtracted from twenty three • 23-2X(3+7)

  21. What is a Function? A function is a rule, sometimes using variables (letters to represent numbers), that changes a number (input), using multiplication, division, addition, and/or subtraction creating a new number (output)

  22. Functions In the incomplete equation + 5 = ___ , Is the input _____ is the output + 5 is the rule

  23. Practice using a Function In the incomplete equation + 5 = ___ , INPUT 2 into Apply the rule + 5 7 2 + 5= ____ OUTPUT

  24. Practice using a Function Solving the Rule If you are given the input and the output, you must determine how the number changed using addition, subtraction, multiplication, or division. + 3 + 3 6 ______ = 9 7 ________ = 10 The rule must be + 3 because 6 + 3=9 and 7 + 3 = 10

  25. Function Tables Let’s imagine this equation + 5 = ___ The output is the result of applying the rule ( + 5) The input is a number going in. + 5 is the rule

  26. Function Tables 15 21 3 10

  27. The rule is x 3

  28. Function Tables 23 34 22 6

  29. The rule is + 13

  30. Function Tables 6 8 15

  31. RULE (___+____)÷3

  32. Multiplication AlgorithmSteps The first step is to make sure the place values are lined up. They don’t have to be but it helps stay oraganized 26 x 12 Tens Ones

  33. Multiplication AlgorithmSteps 1 Think, 2 x 6 equals 12. Begin with multiplying the bottom factor’s one’s place with the top factors one’s place. 26 x 12 Because there is still the tens place to multiply, you must regroup the 1. 2

  34. Multiplication AlgorithmSteps Think, 2x2=4+1=5 1 Next, multiply the 2 and the other 2. Then, remember to add the 1 ten from the first step. 26 x 12 5 2

  35. Multiplication AlgorithmSteps Next, because we are multiplying tens, we need to use a 0 for a place holder. Place the 0 under the 2 in the products line. Cross out your regrouped ten from before. 1 26 x 12 5 2 0

  36. Multiplication AlgorithmSteps Next, begin to multiply the 1 in the tens place with ones in the top factor. Think 1x6=6. 26 x 12 5 2 6 0

  37. Multiplication AlgorithmSteps Next, begin to multiply the 1 in the tens place with tens in the top factor. Think 1x2=2. 26 x 12 5 2 2 6 0

  38. Multiplication AlgorithmSteps Add the ones place. Regroup if necessary. Finally, add the two products to find the final product. 26 Add the tens place. Regroup if necessary.. x 12 5 2 Add the hundreds place. Regroup if necessary. 1 + 2 6 0 3 1 2

  39. The product is 312

  40. Division AlgorithmWith 2 Digit Divisor

  41. Division AlgorithmWith 2 Digit Divisor 1. Divide 2. Multiply 3. Subtract 4. Bring down 5. Repeat or Remainder

  42. 2 Digit Division • Before you begin dividing write the first 9 multiples for the divisor. 21 168 42 189 63 84 105 126 147 2 1) 9 4 8

  43. Step 1 in 2 Digit Long Division 0 4 1. Write your multiples then Divide • Divide 21 into first number in the dividend. 2 1) 9 4 8 • 21 will not go into 9 so place a 0 over the 9 then • you look at 94. • Which multiple of 21 is closest to 94 without being greater? • The 4th multiple 84 is the closest write this multiple above the 4.

  44. Step 2 in 2 Digit Division 4 2. Multiply • Multiply the divisor times the first number in your quotient. 2 1) 9 4 8 8 4 • Write your answer directly under the 94 or the number you just divided into. 21 x4 84

  45. Step 3 in 2 Digit Long Division 4 3. Subtract • Draw a line under the 84. 2 1) 9 4 8 8 4 • Write a subtraction sign next to the 84. 1 0 • Subtract 84 from 94. • Write your answer directly below the 84.

  46. Step 4 in 2 Digit Long Division 4 4. Bring down • Go to the next number in the dividend to the right of the 4. 2 1) 9 4 8 8 4 1 0 8 • Write an arrow under that number. • Bring the 8 down next to the 10.

  47. Step 5 in 2 Digit Long Division 4 5. Repeat or Remainder • This is where you decide whether you repeat the 5 steps of division. 2 1) 9 4 8 8 4 1 0 8 • If your divisor can divide into your new number, 108, or if you have numbers in the dividend that have not been brought down, you repeat the 5 steps of division.

  48. Step 1 in 2 Digit Long Division 4 5 1. Divide • Divide 21 into your • new number, 108. 2 1) 9 4 8 8 4 • Which multiple of 21 is closest to 108 without being greater? 1 0 8 • Place your answer directly • above the 8 in your quotient.

  49. Step 2 in 2 Digit Long Division 4 5 2. Multiply • Multiply your divisor, 21, with your new number in the quotient, 5. 2 1) 9 4 8 8 4 1 0 8 • Place your product directly under the 108. 1 5 0

  50. Step 3 in 2 Digit Long Division 4 5 3. Subtract • Draw a line under the bottom number, 105. 2 1) 9 4 8 8 4 • Draw a subtraction sign. 1 0 8 • Subtract 0 1 5 3

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