Order of Operations BGCSE Core 1 3 Order

Order of Operations BGCSE Core

1. 3 – Order of Operations (BIDMAS) This section will show you how to: Ø Work out the answers to a problem with a number of different mathematical operations. How quickly can you complete these? 5+7 15 – 8 7 x 5 9+6 12 7 35 15 8 x 5 40 20 – 5 15 6 + 8 14 15 ÷ 3 5 36 – 9 25 3 x 7 27 ÷ 9 24 – 8 30 ÷ 5 42 ÷ 7 6 8 + 9 17 21 3 16 6 5+8 6 x 5 28 ÷ 4 8+7 15 24 ÷ 3 8 36 ÷ 6 6 7 + 9 16 4 x 6 24 9 x 8 72 54 - 8 46 13 30 7 Keywords: Brackets Operation Order

Order of Operations (BIDMAS) 4+5 x 2= ?

Order of Operations (BIDMAS) Suppose you have to work out the answer to 4 + 5 x 2. You may say the answer is 18, but the correct answer is 14. There is an order of operations which you must follow when working out calculations like this. The x is always done before the +. In 4 + 5 x 2 this gives 4 + 10 = 14.

Order of Operations (BIDMAS) Now suppose you have to work out the answer to (3 + 2) x (9 – 5). The correct answer is 20. You have probably realised that the parts in the brackets have to be done first, giving 5 x 4 = 20. So, how do you work out a problem such as 9 ÷ 3 + 4 x 2?

Order of Operations (BIDMAS) To answer questions like this, you must follow the BIDMAS (or BODMAS) rule. This tells you the order in which you must do the operations. B rackets I ndices D ivision M ultiplication A ddition S ubtraction B rackets O p. Owers D ivision M ultiplication A ddition S ubtraction

Order of Operations (BIDMAS) For example, work out 9 ÷ 3 + 4 x 2: First divide: 9÷ 3=3 giving 3 + 4 x 2 Then multiply: 4 x 2=8 giving 3 + 8 Then add: 3 + 8 = 11

Order of Operations (BIDMAS) For example, work out 60 – 5 x 3² + (4 x 2): First work out the brackets: (4 x 2) = 8 giving 60 – 5 x 3² + 8 Then the index (power): 9+8 3² = 9 Then multiply: 5 x 9 = 45 giving 60 – 45 + 8 Then add: 60 + 8 = 68 giving 68 – 45 Finally, subtract: 68 – 45 = 23 giving 60 – 5 x

Exercise 1 C: Work out each of these: 2 x 3+5 4 x 6÷ 2 3 x 4– 1 12 ÷ 6 + 2 11 12 11 4 6÷ 3+4 2 x 8– 5 3 x 4÷ 1 3+5 x 2 6 11 12 13 5+7– 2 3 x 4+1 12 ÷ 2 + 6 12 – 3 x 3 10 13 12 3 G

Exercise 1 C: Work out each of these (Remember to use BIDMAS): 2 x (3 + 5) 5 + (7 – 2) 2 x (8 – 5) 3 x (4 ÷ 1) 16 10 6 12 6 ÷ (2 + 1) 3 x (4 ÷ 2) 3 x (4 + 1) 12 ÷ (2 + 2) 2 6 15 3 (5 + 7) – 2 3 x (4 + 2) 3 x (4 – 1) (12 ÷ 2) + 2 10 18 9 8 G

Exercise 1 C: Copy each of these and put a ring around the part that you work out first. Then work out the answer. The first one has been done for you: 3 x 3 -2 9– 4÷ 2 10 ÷ 5 – 2 7+4 x 6 7 7 0 31 3+2 x 4 5 x 2+3 10 – 4 ÷ 2 6÷ 3+7 11 13 8 9 9÷ 3– 2 5+2 x 3 4 x 6– 7 7+6÷ 2 1 11 17 10 G

Exercise 1 C: Copy each of these and then put in brackets where necessary to make each answer correct. 3 x 4 + 1 = 15 6÷ 2+1=4 6÷ 2+1=2 4+4÷ 4=5 4+4÷ 4=2 16 – 4 ÷ 3 = 4 3 x 4 + 1 = 13 16 – 6 ÷ 3 = 14 20 – 10 ÷ 2 = 5 20 – 10 ÷ 2 = 3 x 5 + 5 = 30 6 x 4 + 2 = 36 15 15 – 5 x 2 = 20 4 x 7 – 2 = 20 12 ÷ 3 + 3 = 2 12 ÷ 3 + 3 = 7 24 ÷ 8 – 2 = 1 24 ÷ 8 – 2 = 4 G

Exercise 1 C: Copy each of these and then put in brackets where necessary to make each answer correct. 3 x (4 + 1) = 15 4 + (4 ÷ 4) = 5 (3 x 4) + 1 = 13 (6 ÷ 2) + 1 = 4 6 ÷ (2 + 1) = 2 (4 + 4) ÷ 4 = 2 (16 – 4) ÷ 3 = 4 16 – (6 ÷ 3) = (20 – 10) ÷ 2 = 14 5 3 x (5 + 5) = 30 6 x (4 + 2) = 36 20 – (10 ÷ 2) = 15 (15 – 5) x 2 = 20 4 x (7 – 2) = 20 12 ÷ (3 + 3) = 2 (12 ÷ 3) + 3 = 7 (24 ÷ 8) – 2 = 1 24 ÷ (8 – 2) = 4 G

Exercise 1 C: Three dice are thrown. They give scores of three, one and four. A class makes the following questions with the numbers. Work them out: 3+4+1 4 x 3 x 1 4 x (3 + 1) 8 13 12 16 3+4– 1 4 x 3– 1 (3 – 1) x 4 1 x (4 – 3) Jack says that 5 + 6 x 7 is equal to 77. Is he correct? 6 11 8 1 4+3– 1 (4 – 1) x 3 (4 + 1) x 3 4+1 x 3 Jack is incorrect. 6 9 15 7 G

Exercise 1 C: This is Micha’s homework. Copy the questions where she has made mistakes and work out the correct answers. 2+3 x 4 7– 1 x 5 20 30 8– 4÷ 4 2 x 7+2 7 16 6+3 x 2 9– 3 x 3 12 18 Three different dice give scores of 2, 3 and 5. Add ÷, x, +, - signs and brackets to make each calculation work. 2 3 5 = 11 2 =4 2 3 5 = 16 2 = 13 2 3 5 = 17 2 = 30 F

Exercise 1 C: Which is smaller: 4 + 5 x 3 or (4 + 5) x 3? Show your working. Here is a list of numbers, some signs and one pair of brackets. 2 5 6 18 - x = ( Use all of them to make a correct calculation. ) Here is a list of numbers, some signs and one pair of brackets. 3 4 5 8 - ÷ = ( Use all of them to make a correct calculation. ) F

A question to end on… Jeremy has a piece of pipe that is 10 m long. He wants to use his calculator to work out how much pipe will be left when he cuts off three pieces, each of length 1. 5 m Which calculations would give him the correct answer? 10 – 3 x 1. 5 10 – 1. 5 + 1. 5 10 – 1. 5