Order of operations with decimals (with negatives)

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.

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

Examples

Question 1

Evaluate $4.7\times10-2.4$4.7×10−2.4, 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$29−0.2×6

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 $\left(6-1.1\right)\times\left(18+0.28\right)$(6−1.1)×(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+203.81$20.91+203.81

Now we need to show that (just) the investment doubles:

$20.91+203.81\times2$20.91+203.81×2

Then the investment loses $\$72.06$$72.06:

$20.91+203.81\times2-72.06$20.91+203.81×2−72.06

Now let's evaluate this expression:

$20.91+203.81\times2-72.06=\$356.47$20.91+203.81×2−72.06=$356.47

More Worked Examples

QUESTION 5

QUESTION 6

QUESTION 7

QUESTION 8