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Understanding BODMAS: The Essential Order of Operations in Mathematics

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williamssharon
19 diapositives · 642 Views · Jan 04, 2020

BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction) is a fundamental rule in mathematics that dictates the order in which operations should be performed to ensure accurate results. When faced with expressions like 7 + (6 × 52 + 3), following BODMAS helps avoid errors. This guide explains each component of BODMAS, provides examples, and highlights common pitfalls when ignoring this order. Learning BODMAS is crucial for problem-solving in mathematics and aids in mastering more complex equations.

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  1. BODMAS

  2. Why do we need BODMAS ? 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? Calculate them in the wrong order, and you will get a wrong answer ! So, long ago people agreed to always follow certain rules when doing calculations. One of them is “BODMAS”

  3. What is BODMAS ? • Bracket = ( ) • Orders or power Of = Powers and Square Roots, etc. • Multiplication = × • Division = ÷ • Addition = + • Subtraction = - • Other names for BODMAS = "Exponents" is used in Canada, and so you might prefer "BEDMAS". There is also "Indices" so that makes it "BIDMAS". In the US they say "Parenthesis" instead of Brackets, so they say "PEMDAS“.

  4. How do I Remember ? BODMAS! • B Brackets first • O Orders (i.e. Powers and Square Roots, etc.) • DM Division and Multiplication (left-to-right) • AS Addition and Subtraction (left-to-right)

  5. Brackets • Brackets are Parenthesis ( ). • Brackets are used to group things. • This is the first thing you do in a question. • Do things in Brackets First.  6 × (5 + 3) = 6 × 8 = 48  6 × (5 + 3) = 30 + 3 = 33 (wrong)

  6. Order or Exponents • (Powers, Roots) before Multiply, Divide, Add or Subtract. Example • Exponents are used to shorten the equation. • If you see an exponent, you multiply the main number by itself that many times. •  Solve the Exponents first  5 × 22 = 5 × 4 = 20 5 × 22 = 102 = 100 (wrong)

  7. Multiplication/ Division • In the Order of Operations, you would complete the equation left to right, doing which ever one appears first, Multiplication or Division. • The symbol for multiplication is ‘x’. • Remember to go from left to right. • Multiply or Divide before you Add or Subtract.  2 + 5 × 3 = 2 + 15 = 17 2 + 5 × 3 = 7 × 3 = 21 (wrong)

  8. Division is an equation that puts numbers in to groups. • The Division symbol is ÷ • Remember to go from left to right  30 ÷ 5 × 3 = 6 × 3 = 18    30 ÷ 5 × 3 = 30 ÷ 15 = 2(wrong)

  9. Addition / Subtraction • In the Order of Operations, you would complete the equation left to right, doing which ever one appears first, Addition or Subtraction. • Addition is adding numbers together. • The symbol for addition is +. Example: 6 + 9 = 15

  10. Subtraction is taking away a specific number. • The symbol for subtraction is -. Example: 17 – 8 = 9

  11. Summary BODMAS is a word which helps us to remember the order we do in a maths sum. It stands for first, then . Next do or (it does not matter which way round you do these). Finally do or (again, it does not matter which way you do these.) Some people use the word Bidmas. In this case is replaced by , which means the same thing. operations brackets powers of multiplication division addition subtraction powers of indices Copy and fill in the gaps using the words below operations multiplication brackets subtraction division powers of addition

  12. Sample Equation 4 × 3 + 6 - (12 ÷ 22 + 5) = 4 × 3 + 6 - (12 ÷ 4+ 5) = 4 × 3 + 6 - (3+ 5) = 4 × 3 + 6 - (8) = 12 + 6 – 8 = 10

  13. BODMAS Practice 7 + 9 x 8 79 9 x 3 + 6 33 9 + 4 x 2 17 6 x 9 - 34 20 7 + 2 - 6 3 9 x 3 + 9 x 2 45 8 x 4 - 3 x 4 20 24 ÷ 4 - 5 1 BODMAS Questions BODMAS Answer

  14. Solve the following without a calculator? • A) 2 + 3 x 4 B) 4 x 3 ² - ( 7 +2 )

  15. Solve the equations then complete the puzzle. W= 6 + 3 x 5 R = 3 x 8 + 2 G= 3 ÷ 8 x 2 I= 4 + 7 x 3 O= 4 x 7 ÷ 3 N=6 + 5 x 9 P=6 x 5 + 9 T=14 – 3 x 2 S= 16 – 2 x 7 Q=7 + 8 x 2 U= 5 x 7 – 8 C=22 – 3 x 4 M= 22 – 3 – 4 L= 28 – 6 x 2 D= 7 x 2 + 4 E= 8 + 7 x 4 A= 32 – 6 x 3 H=9 x 3 + 2

  16. 29 14 8 29 14 39 39 36 51 36 18 8 31 • 29 36 39 16 14 51 8 25 51 8 29 36 • 14 8 29 2 10 16 14 2 2 ? • 8 19 26 36 21 2 23 27 14 26 36 • 26 31 31 8 2

  17. Solution

  18. Additional exercise to complete • http://www.commoncoresheets.com/Operations.php