BODMAS & Simplification: Order of Operations: 17 MCQs with answers

B · Brackets, Orders, Division/Multiplication, Addition/Subtraction

BODMAS stands for Brackets, Orders, Division/Multiplication, Addition/Subtraction, in that order.

C · 90

The smallest two-digit number is 10 and the largest is 99. Count = $99 - 10 + 1 = 90$.

B · 20

Inside the overline: $50 - 3 \times 10 = 50 - 30 = 20$.

D · It is a grouping symbol like parentheses.

The overline groups terms together, so you simplify the expression under it first.

B · $99 - 10 + 1$

The formula is last − first + 1, so $99 - 10 + 1 = 90$.

A · True

The number of two-digit natural numbers is 90, calculated as $99 - 10 + 1$.

A · 105

First simplify the overline: $50 - 30 = 20$. Then $100 - 20 = 80$. Then $400 \div 80 = 5$. Then $10 \times 10 = 100$. Finally $100 + 5 = 105$.

D · Multiply $2 \times 5 \times 11$

According to BODMAS, simplify inside the brackets first. Inside, do multiplication before addition: $2 \times 5 \times 11 = 110$.

B · They forgot to add 1 to include both endpoints.

The correct formula is last − first + 1. So $99 - 10 + 1 = 90$. Subtracting only gives 89, which is off by one.

B · 80

First simplify the overline: $50 - 3 \times 10 = 50 - 30 = 20$. Then $100 - 20 = 80$.

D · Multiplication

According to BODMAS, multiplication is done before addition. So compute $24 \times 2$ and $15 \times 5$ first.

C · 5

Simplify the overline: $50 - 30 = 20$. Then $100 - 20 = 80$. Then $400 \div 80 = 5$.

A · $\frac{119}{13}$

Simplify inside brackets: $2 \times 5 \times 11 = 110$, then $7 + 110 + 2 = 119$. Then multiply by $\frac{1}{13}$: $\frac{119}{13}$, which is not an integer.

B · They forgot to add the result of $400 \div 80$ to $100$.

The correct simplification gives $100 + 5 = 105$. Getting 100 means they omitted the final addition of 5.

B · Monday

The pattern repeats every 7 days. The 1st is Monday, so the 8th is Monday, and the 15th is also Monday.

B · 150

First do multiplications: $24 \times 2 = 48$, $15 \times 5 = 75$. Then add: $25 + 2 + 48 + 75 = 150$.

A · Adding all components from left to right without considering brackets.

The correct method requires following BODMAS/PEMDAS, which means simplifying brackets first. If a student adds all components from left to right without respecting the brackets, they will arrive at an incorrect answer.