# 5 Hard math questions

Here are some hard math questions. They are not really that difficult when you know how to solve them, just like everything else.
A small hint; Use PEMDAS. If you do not know what PEMDAS (or BODMAS) is, it is explained in the answer in Question 1.

Question 1)

48 ÷ 2(9+3) = ?

To get the correct answer it is easiest to use PEMDAS (PE | MD | AS)
PEMDAS stands for: parentheses, Exponents, Multiplication, Division, Addition and Subtraction.
First, the parentheses and exponents are calculated, then multiplication and division, to finally calculate addition and subtraction.

The rule states that division and multiplication, such as addition and subtraction, are equal, but we begin the calculation from the left to right.
The calculation will then be as follows:

48 ÷ 2 (9 + 3)
Calculate parentheses first
48 ÷ 2 (12)

2 (12) is the same as 2 * 12 so we write it this way for ease.
48 ÷ 2 * 12
PEMDAS says that multiplication and division are equal and should be calculated from the left to right.
24 * 12

16 – 4 ÷ ¼ + 1 = ?

Using PEMDAS (PE | MD | AS), see extended explanation in first question.

The calculation will be as follows:

16 – 4 ÷ ¼ + 1

Using PEMDAS.
16 – 16 + 1

8 ÷ 2(2 + 2) = ?

Using PEMDAS (PE | MD | AS), see extended explanation in first question.

8 ÷ 2 (2 + 2) =?

Calculate parentheses first
8 ÷ 2 (2 + 2)

Calculate parentheses first and get
8 ÷ 2 (4)

2 (4) is the same as 2 × 4 so we write it this way for ease.
8 ÷ 2 x 4

Uses PEMDAS which says that multiplication and division are equal and should be calculated from left to right.
4 x 4

20 ÷ (4÷8) x (-9) + 25 = ?

Using PEMDAS (PE | MD | AS), see extended explanation in first question.

20 ÷ (4 ÷ 8) x (-9) + 25 =?

Uses PEMDAS and calculates parentheses first and gets:
20 ÷ (½) x (-9) + 25

Uses PEMDAS which says that multiplication and division should be calculated before addition and subtraction and that multiplication and division are equal and should be calculated from the left.
Here is both multiplication and division and must then be calculated from the left. We take the calculation of the first one first (for ease) and get:
40 x (-9) + 25

-360 + 25

-335

-10 ÷ (20 ÷ 2² × 5 ÷ 5) × 8 – 2 = ?

Using PEMDAS (PE | MD | AS), see extended explanation in first question.

-10 ÷ (20 ÷ 2² × 5 ÷ 5) × 8 – 2

Uses PEMDAS and calculates parentheses first step by step:
-10 ÷ (20 ÷ 4 × 5 ÷ 5) × 8 – 2

Uses PEMDAS and calculates parentheses first step by step:
-10 ÷ (5 x 5 ÷ 5) x 8 – 2

Uses PEMDAS and calculates parentheses first step by step:
-10 ÷ (25 ÷ 5) x 8 – 2

Uses PEMDAS and calculates parentheses first and gets:
-10 ÷ 5 x 8 – 2

Uses PEMDAS which says that multiplication and division should be calculated before addition and subtraction and that multiplication and division are equal and should be calculated from left to right.
– 2 * 8 -2

Uses PEMDAS which says that multiplication and division should be calculated before addition and subtraction and that multiplication and division are equal and should be calculated from left to right.

-16 – 2