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Chapter Overview

Learning Goals

**Learning Goals**

- Know the order of operations known as BODMAS

Maths

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BODMAS is used in multi-step calculations and when questions have a few different operations. BODMAS is an acronym for the order of operations, with the priority order of each operation.

**BODMAS = **__ B__racket,

Priority | BODMAS | Symbol |

1 | Brackets | $()$ |

2 | Other | $\sqrt{x},\, x^n$ |

3 | Division | $\div$ |

Multiplication | $\times$ | |

4 | Addition | $+$ |

Subtraction | $-$ |

*Note:** When there is both multiplication and division, or addition and subtraction in the question, you work from left to right.*

1. | Calculate the value inside the brackets. |

2. | Calculate the value of any terms raised to a certain power. |

3. | Calculate the value of any terms being multiplied and/or divided. |

4. | Calculate the value of any additions and/or subtractions. |

*Calculate the positive solution to $(26 - 18) \times \sqrt9$*

*First calculate what is inside the brackets: *

*$(26 - 18) = 8$*

*Secondly calculate the other operation, such as square root of $9$:*

*$\sqrt 9 = 3$*

*Lastly multiply the results together: *

*$8 \times 3 = 24$*

*Therefore, the answer is $(26 - 18 ) \times \sqrt9 = \underline{24}$*

* Note: The reason the question specifies 'positive solution' is because, strictly speaking, *$\sqrt{9}=\pm3$. $-3$

*Evaluate the positive solution to $\dfrac{\sqrt{(8-4)}\times15}{2^3+7}$*

*First calculate what is inside the brackets:*

*$8-4 = 4$*

*Calculate the other operations such as square root then the indices:*

*$\sqrt4 = 2\\ 2^3= 8$*

**

*Now the fraction becomes:*

*$\dfrac{2 \times 15}{8 +7}$*

*Now you may want to carry out this fraction first as it is division but in this case treat each the numerator and denominator like they have separate brackets:*

*$\dfrac{(2 \times 15)}{(8+7)} = \dfrac{30}{ 15}$*

*Calculate the final division: *

*$\dfrac{30}{15}= 2$*

*Therefore the positive solution to $\dfrac{\sqrt{(8-4)}\times15}{2^3+7} = \underline{2}$ *

BODMAS is used in multi-step calculations and when questions have a few different operations. BODMAS is an acronym for the order of operations, with the priority order of each operation.

**BODMAS = **__ B__racket,

Priority | BODMAS | Symbol |

1 | Brackets | $()$ |

2 | Other | $\sqrt{x},\, x^n$ |

3 | Division | $\div$ |

Multiplication | $\times$ | |

4 | Addition | $+$ |

Subtraction | $-$ |

*Note:** When there is both multiplication and division, or addition and subtraction in the question, you work from left to right.*

1. | Calculate the value inside the brackets. |

2. | Calculate the value of any terms raised to a certain power. |

3. | Calculate the value of any terms being multiplied and/or divided. |

4. | Calculate the value of any additions and/or subtractions. |

*Calculate the positive solution to $(26 - 18) \times \sqrt9$*

*First calculate what is inside the brackets: *

*$(26 - 18) = 8$*

*Secondly calculate the other operation, such as square root of $9$:*

*$\sqrt 9 = 3$*

*Lastly multiply the results together: *

*$8 \times 3 = 24$*

*Therefore, the answer is $(26 - 18 ) \times \sqrt9 = \underline{24}$*

* Note: The reason the question specifies 'positive solution' is because, strictly speaking, *$\sqrt{9}=\pm3$. $-3$

*Evaluate the positive solution to $\dfrac{\sqrt{(8-4)}\times15}{2^3+7}$*

*First calculate what is inside the brackets:*

*$8-4 = 4$*

*Calculate the other operations such as square root then the indices:*

*$\sqrt4 = 2\\ 2^3= 8$*

**

*Now the fraction becomes:*

*$\dfrac{2 \times 15}{8 +7}$*

*Now you may want to carry out this fraction first as it is division but in this case treat each the numerator and denominator like they have separate brackets:*

*$\dfrac{(2 \times 15)}{(8+7)} = \dfrac{30}{ 15}$*

*Calculate the final division: *

*$\dfrac{30}{15}= 2$*

*Therefore the positive solution to $\dfrac{\sqrt{(8-4)}\times15}{2^3+7} = \underline{2}$ *