 Order of operations with decimals (with negatives)

Lesson

We've already learnt how to add, subtract, multiply and divide decimals. But what happens if we have more than one operation in a question? Well we follow the old order of operations.

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.

Now let's look at some examples to see the order of operations in action!

Careful!

You need to follow all the rules in the order of operations. Otherwise you might end up with a wrong answer.

Examples

Question 1

Evaluate $4.7\times10-2.4$4.7×102.4, writing your answer in its simplest form.

Think: Multiplication comes first, then subtraction.

Do:

 $4.7\times10-2.4$4.7×10−2.4 $=$= $47-2.4$47−2.4 $=$= $44.6$44.6

Question 2

Evaluate $29-0.2\times6$290.2×6

Think: Just like in question 1, multiplication comes first, then subtraction (even though the subtraction is written first in this question).

Do:

 $29-0.2\times6$29−0.2×6 $=$= $29-1.2$29−1.2 $=$= $27.8$27.8

Question 3

Evaluate $\left(6-1.1\right)\times\left(18+0.28\right)$(61.1)×(18+0.28)

Think: We solve what's inside the brackets, then do the multiplication.

Do:

 $\left(6-1.1\right)\times\left(18+0.28\right)$(6−1.1)×(18+0.28) $=$= $4.9\times18.28$4.9×18.28 $=$= $89.572$89.572

Question 4

Glen has $\$20.91$$20.91 in his wallet and \203.81$$203.81 that he invested in stock. In one day, his investment was doubled. The next day his investment lost $\$72.06$$72.06 Calculate how much in cash and investments Glen now has altogether. Think: We need to write each part of this story mathematically so we can create an equation and solve it. Do: Let's write an expression for how much money Glen has initially: 20.91+203.8120.91+203.81 Now we need to show that (just) the investment doubles: 20.91+203.81\times220.91+203.81×2 Then the investment loses \72.06$$72.06:

$20.91+203.81\times2-72.06$20.91+203.81×272.06

Now let's evaluate this expression:

$20.91+203.81\times2-72.06=\$356.47$20.91+203.81×272.06=$356.47

More Worked Examples

QUESTION 5

Evaluate $2.5\times7-1.8$2.5×71.8, writing your answer in its simplest form.

QUESTION 6

Evaluate $51-3.9\times7$513.9×7

QUESTION 7

Evaluate $\left(4-1.5\right)\times\left(14+0.41\right)$(41.5)×(14+0.41)

QUESTION 8

Glen has $£20.91$£20.91 in his wallet and $£203.81$£203.81 that he invested in stock. In one day, his investment was doubled. The next day his investment lost $£72.06$£72.06 .

Calculate how much in cash and investments Glen now has altogether.