Decimals

UK Secondary (7-11)

Order of operations with decimals (4ops and brackets)

Lesson

In the chapter, How to 'Operate' in Maths, we discussed the order in which problems with more than one operation should be solved. The same order applies whether we are looking at questions with whole numbers, decimals or a combination of both.

Just to remind you, the order goes:

Step 1: Do operations inside grouping symbols such as parentheses (...), brackets [...] and braces {...}.

Step 2: Do multiplication (including powers) and division (including roots) going from left to right.

Step 3: Do addition and subtraction going from left to right.

**Evaluate:** $\left(4.5\times2.2\right)^2$(4.5×2.2)2

**Think:** Remember the order of operations. We solve operations inside parentheses first. Then we solve multiplication.

**Do:**

$\left(4.5\times2.2\right)^2$(4.5×2.2)2 | $=$= | $9.9^2$9.92 |

$=$= | $98.01$98.01 |

**Evaluate:** $7.2\div0.9-\left(3.2+4\right)$7.2÷0.9−(3.2+4)

**Think:** Remember the order of operations. Operations inside the parentheses, then multiplication/division, then addition/ subtraction.

**Do:**

$7.2\div0.9-\left(3.2+4\right)$7.2÷0.9−(3.2+4) | $=$= | $7.2\div0.9-7.2$7.2÷0.9−7.2 |

$=$= | $8-7.2$8−7.2 | |

$=$= | $0.8$0.8 |

The same order applies for word problems.

**Evaluate:** Decrease the quotient of $525$525 and $2.1$2.1 by $3.42$3.42

**Think:** How do we write this as a number sentence? $525\div2.1-3.42$525÷2.1−3.42. Then consider the order of operations.

**Do:**

$525\div2.1-3.42$525÷2.1−3.42 | $=$= | $250-3.42$250−3.42 |

$=$= | $246.58$246.58 |

Find the value of $8\times\left(9.7+5.2\right)$8×(9.7+5.2), giving your answer as a decimal.

Decrease the product of $0.307$0.307 and $0.5$0.5 by $0.02$0.02.

Find the value of $5.22+19.11\div0.7+94.87$5.22+19.11÷0.7+94.87, giving your answer as a decimal.