4.2.6 PEMDAS Performed By Hand

Now let’s practice performing operations by hand in the correct order.

Activity symbol Activity: PEMDAS

In your math notebook, simplify each expression by following the correct order of operations.

(a) three plus four multiplication two

Hint symbol

Comment

For each problem, first go through and work on the parentheses. Next, look for exponents. Multiplication and division should be carried out from left to right. Finally, perform addition and subtraction from left to right.

Solution symbol

Answer

(a) three plus four multiplication two

P: There are no parentheses.

E: There are no exponents.

M/D: three plus eight(4 x 2 = 8)

A/S: 11

So, three plus four multiplication two equals 11.

(b) open eight minus three close squared plus 12 division four

Solution symbol

Answer

(b) open eight minus three close squared plus 12 division four

P: left parenthesis eight minus three equals five right parenthesis so now we have open five close squared plus 12 division four

E: (52 = 25) so now we have 25 plus 12 division four

M/D: (12 ÷ 4 = 3) so now we have 25 plus three

A/S: 28

So, open eight minus three close squared plus 12 division four equals 28.

(c) two multiplication open three close cubed plus six minus two multiplication open five minus two close plus one

Answer

Solution symbol

(c) two multiplication open three close cubed plus six minus two multiplication open five minus two close plus one

P: two multiplication open three close cubed plus six minus two multiplication three plus one

E: two multiplication 27 plus six minus two multiplication three plus one

M/D (from left to right): 54 plus six minus six plus one

A/S (from left to right): multiline equation line 1 60 minus six plus one equals 54 plus one equals 55

Thus, two multiplication open three close cubed plus six minus two multiplication open five minus two close plus one equals 55.

(d) 48 division six division two multiplication three squared

Solution symbol

Answer

(d) 48 division six division two multiplication three squared

P: There are none.

E: 48 division six division two multiplication nine

M/D (from left to right):

multiline equation line 1 eight division two multiplication nine equals four multiplication nine equals 36

Thus, 48 division six division two multiplication three squared equals 36.

4.2.5 PEMDAS Brainstretcher

4.3 Using Math in the Real World