Simplify: 12 + 6 2 3 - 4

17. By BODMAS, do division and multiplication first, left to right: 6 2 = 3, then 3 3 = 9. The expression becomes 12 + 9 - 4 = 17.

48. Work left to right: 89 of 72 is 64, and 34 of 64 is 48.

0.08. 0.0064 = 64 10^-4, so 0.0064 = 8 10^-2 = 0.08 (check: 0.08 0.08 = 0.0064).

Simplify: (0.5 0.5 + 0.5 0.3) 0.5

0.8. Factor the numerator: 0.5(0.5 + 0.3) = 0.5 0.8 = 0.4. Dividing by 0.5 gives 0.8.

If x = 12, find the value of x2 + 2x - x^2.

4. With x = 12: x2 = 14, 2x = 4 and x^2 = 14. So the value is 14 + 4 - 14 = 4.

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Quantitative Aptitude · Numbers & Simplification

Simplification — Questions & Answers

Simplification questions test whether you apply the BODMAS order correctly and handle fractions, decimals and powers without slips. Work strictly left to right within each precedence level.

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Key formulas

BODMAS order: Brackets, Orders (powers/roots), Division and Multiplication (left to right), Addition and Subtraction (left to right)
'of' behaves like multiplication but is applied before division: $\tfrac{1}{2}\text{ of }8 \div 2 = 4 \div 2 = 2$
$a \div \dfrac{b}{c} = a \times \dfrac{c}{b}$

5 solved Simplification questions

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01
Simplify: $12 + 6 \div 2 \times 3 - 4$
5 steps · reveal one at a time
1. Step 1: Apply BODMAS Rule
  Remember the order of operations, often called BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction). We perform operations from left to right within each priority level.
2. Step 2: Perform Division
  Following BODMAS, we first tackle division and multiplication from left to right. The first operation is $6 \div 2$ . This gives us $3$ . The expression now becomes $12 + 3 \times 3 - 4$ .
3. Step 3: Perform Multiplication
  Next, we perform the multiplication: $3 \times 3$ . This equals $9$ . Our expression is now simplified to $12 + 9 - 4$ . We've completed all division and multiplication.
4. Step 4: Perform Addition and Subtraction
  Finally, we perform addition and subtraction from left to right. First, $12 + 9 = 21$ . Then, $21 - 4 = 17$ . This is our final simplified value.
5. Step 5: The answer
  So the answer is (B) 17, because applying the BODMAS rule leads to $12 + 9 - 4 = 17$ after performing division and multiplication.
02
Find $\dfrac{3}{4}$ of $\dfrac{8}{9}$ of 72.
5 steps · reveal one at a time
1. Step 1: Understand the question
  The question asks us to find a fraction of a fraction of a number. The word "of" in mathematics usually means to multiply. We will solve this by working from left to right.
2. Step 2: Calculate the first part
  First, let's find " $\dfrac{8}{9}$ of 72". This means we need to multiply $\dfrac{8}{9}$ by 72. So, $\dfrac{8}{9} \times 72 = 8 \times \dfrac{72}{9} = 8 \times 8 = 64$ .
3. Step 3: Calculate the second part
  Now we need to find " $\dfrac{3}{4}$ of" the result from the previous step, which was 64. So, we need to calculate $\dfrac{3}{4}$ of 64. This is $\dfrac{3}{4} \times 64$ .
4. Step 4: Perform the final multiplication
  To find $\dfrac{3}{4} \times 64$ , we can write this as $3 \times \dfrac{64}{4}$ . Since $64 \div 4 = 16$ , the calculation becomes $3 \times 16 = 48$ .
5. Step 5: The answer
  So the answer is (A) 48, because $\dfrac{8}{9}$ of 72 is 64, and $\dfrac{3}{4}$ of 64 is 48.
03
Evaluate $\sqrt{0.0064}$ .
4 steps · reveal one at a time
1. Step 1: Convert to fraction
  To evaluate $\sqrt{0.0064}$ , it's helpful to express the decimal as a fraction. The number $0.0064$ can be written as $\frac{64}{10000}$ because there are four decimal places.
2. Step 2: Find individual square roots
  Now, we need to find the square root of the numerator and the denominator separately. We know that $\sqrt{64} = 8$ and $\sqrt{10000} = 100$ . Remember that $100 \times 100 = 10000$ .
3. Step 3: Combine and simplify
  Putting these together, we have $\sqrt{\frac{64}{10000}} = \frac{\sqrt{64}}{\sqrt{10000}} = \frac{8}{100}$ . To convert this fraction back to a decimal, divide $8$ by $100$ .
4. Step 4: The answer
  So the answer is (C) 0.08. Dividing $8$ by $100$ gives $0.08$ , which is the square root of $0.0064$ (check: $0.08 \times 0.08 = 0.0064$ ).
04
Simplify: $(0.5 \times 0.5 + 0.5 \times 0.3) \div 0.5$
5 steps · reveal one at a time
1. Step 1: Analyze the expression
  Let's look at the expression: $(0.5 \times 0.5 + 0.5 \times 0.3) \div 0.5$ . Notice that $0.5$ is a common factor in the terms inside the first set of parentheses. This is a good place to start simplifying.
2. Step 2: Factor the numerator
  We can factor out the common term $0.5$ from the numerator. This changes $(0.5 \times 0.5 + 0.5 \times 0.3)$ to $0.5 \times (0.5 + 0.3)$ . This makes the calculation much simpler.
3. Step 3: Simplify inside parentheses
  Next, perform the addition inside the parentheses: $0.5 + 0.3 = 0.8$ . So, the numerator becomes $0.5 \times 0.8$ . Multiplying these gives $0.4$ .
4. Step 4: Perform the final division
  Now that the numerator is simplified to $0.4$ , we can complete the division. The expression becomes $0.4 \div 0.5$ . Performing this division gives us $0.8$ .
5. Step 5: The answer
  So the answer is (C) 0.8. This is the simplified value of the original expression after factoring and performing the operations.
05
If $x = \dfrac{1}{2}$ , find the value of $\dfrac{x}{2} + \dfrac{2}{x} - x^2$ .
4 steps · reveal one at a time
1. Step 1: Substitute x value
  The question asks us to find the value of the expression $\dfrac{x}{2} + \dfrac{2}{x} - x^2$ when $x = \dfrac{1}{2}$ . We will substitute $x = \dfrac{1}{2}$ into each part of the expression.
2. Step 2: Calculate each term
  Now, let's evaluate each term individually. For the first term, $\dfrac{x}{2} = \dfrac{1/2}{2} = \dfrac{1}{4}$ . For the second term, $\dfrac{2}{x} = \dfrac{2}{1/2} = 2 \times 2 = 4$ . For the third term, $x^2 = (\dfrac{1}{2})^2 = \dfrac{1}{4}$ .
3. Step 3: Combine the terms
  Now we substitute these calculated values back into the original expression: $\dfrac{x}{2} + \dfrac{2}{x} - x^2 = \dfrac{1}{4} + 4 - \dfrac{1}{4}$ . Notice that the $\dfrac{1}{4}$ and $-\dfrac{1}{4}$ terms cancel each other out.
4. Step 4: The answer
  So the answer is (B) 4, because after combining the terms, we are left with $4$ . The expression simplifies to $4$ .

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