Interview Questions for Proficiency in Basic Math Calculations

This problem involves basic arithmetic operations – addition and subtraction. Following the order of operations (PEMDAS/BODMAS), we perform addition and subtraction from left to right.

1. First, add 35 and 17: 35 + 17 = 52
2. Next, subtract 12 from the result: 52 – 12 = 40

Therefore, the result of 35 + 17 – 12 is 40. This type of calculation is fundamental in many areas, from balancing a checkbook to calculating project budgets.

To calculate a percentage of a number, we convert the percentage to a decimal and then multiply it by the number. 25% can be written as 0.25 (or 25/100).

Calculation: 0.25 * 120 = 30

Therefore, 25% of 120 is 30. This is a common calculation used in various applications, such as calculating discounts, sales tax, or tips.

For example, if a store offers a 25% discount on an item priced at $120, the discount amount would be $30.

To find the average (or mean) of a set of numbers, we sum all the numbers and then divide by the total count of numbers.

1. Sum of the numbers: 15 + 22 + 31 = 68
2. Total count of numbers: 3
3. Average: 68 / 3 = 22.666… (approximately 22.67)

Therefore, the average of 15, 22, and 31 is approximately 22.67. Averages are frequently used to represent central tendencies in data sets, for instance, calculating the average score on a test or the average monthly rainfall.

This is a simple algebraic equation. We need to isolate ‘x’ to solve for its value.

1. Subtract 5 from both sides of the equation: 2x + 5 – 5 = 11 – 5 This simplifies to 2x = 6
2. Divide both sides by 2: 2x / 2 = 6 / 2 This gives us x = 3

Therefore, the solution to the equation 2x + 5 = 11 is x = 3. Solving algebraic equations is essential in various fields, including physics, engineering, and finance, for modeling and problem-solving.

The area of a rectangle is calculated by multiplying its length and width.

Area = Length × Width

In this case, Length = 10 cm and Width = 5 cm.

Area = 10 cm × 5 cm = 50 cm²

Therefore, the area of the rectangle is 50 square centimeters. Calculating areas is crucial in various applications, such as determining the amount of carpet needed for a room or the size of a building lot.

The perimeter of a square is the total distance around its four sides. Since all sides of a square are equal, we can calculate the perimeter by multiplying the length of one side by 4.

Perimeter = 4 × side length

In this case, the side length is 7 cm.

Perimeter = 4 × 7 cm = 28 cm

Therefore, the perimeter of the square is 28 centimeters. Perimeter calculations have applications in various fields, such as fencing a yard or determining the frame size for a picture.

Division is the process of splitting a number into equal parts. In this case, we need to find out how many times 3 goes into 15.

15 / 3 = 5

Therefore, 15 divided by 3 is 5. Division is a fundamental operation used extensively in various calculations, from splitting costs equally among individuals to calculating unit prices.

Multiplication is a fundamental arithmetic operation that involves repeated addition. To calculate 12 multiplied by 6 (12 x 6), we can think of it as adding 12 six times: 12 + 12 + 12 + 12 + 12 + 12. Alternatively, we can use the standard multiplication method, which is faster for larger numbers.

Step-by-step calculation:

• Multiply 6 by the ones digit of 12 (6 x 2 = 12). Write down ‘2’ and carry-over ‘1’.
• Multiply 6 by the tens digit of 12 (6 x 1 = 6). Add the carry-over ‘1’ (6 + 1 = 7).
• The result is 72.

Therefore, 12 multiplied by 6 equals 72. This is a frequently used calculation in everyday life, from calculating the cost of multiple items to determining the area of a rectangle.

Converting a fraction to a decimal involves dividing the numerator (the top number) by the denominator (the bottom number). In the case of 3/4, we divide 3 by 4.

Step-by-step calculation:

• Perform the division: 3 ÷ 4 = 0.75

Therefore, the fraction 3/4 is equal to the decimal 0.75. This conversion is crucial in various fields such as finance (calculating percentages), engineering (dealing with measurements), and data analysis.

To convert a decimal to a fraction, we express the decimal as a fraction with a denominator that is a power of 10. The number of decimal places determines the power of 10.

Step-by-step calculation:

• 0.75 has two decimal places, so we write it as 75/100.
• Simplify the fraction by finding the greatest common divisor (GCD) of 75 and 100, which is 25. Divide both the numerator and denominator by 25: (75 ÷ 25) / (100 ÷ 25) = 3/4

Therefore, the decimal 0.75 is equivalent to the fraction 3/4. This skill is essential in various mathematical and scientific applications where fractions are preferred or necessary for calculations.

The square root of a number is a value that, when multiplied by itself, gives the original number. Finding the square root of 64 involves determining which number, when multiplied by itself, equals 64.

Solution:

8 x 8 = 64, therefore, the square root of 64 is 8.

Square roots are commonly used in geometry (calculating distances and areas), physics (analyzing motion and forces), and many other scientific and engineering disciplines.

The cube root of a number is a value that, when multiplied by itself three times, equals the original number. To find the cube root of 27, we need to find a number that, when cubed (multiplied by itself three times), results in 27.

Solution:

3 x 3 x 3 = 27, therefore, the cube root of 27 is 3.

Cube roots have applications in various areas like volume calculations (e.g., determining the side length of a cube given its volume) and solving cubic equations.

Adding fractions with a common denominator is straightforward. We simply add the numerators and keep the denominator the same.

Step-by-step calculation:

• The fractions 5/8 and 3/8 have a common denominator of 8.
• Add the numerators: 5 + 3 = 8
• Keep the denominator the same: 8
• The result is 8/8, which simplifies to 1.

Therefore, 5/8 + 3/8 = 1. This is a basic concept used in many real-world situations, such as combining parts of a whole.

Subtracting fractions requires a common denominator. If the fractions don’t have a common denominator, we need to find one before subtracting.

Step-by-step calculation:

• Find the least common multiple (LCM) of the denominators 3 and 6, which is 6.
• Convert 2/3 to an equivalent fraction with a denominator of 6: (2 x 2) / (3 x 2) = 4/6
• Subtract the numerators: 4 – 1 = 3
• Keep the denominator the same: 6
• The result is 3/6, which simplifies to 1/2.

Therefore, 2/3 – 1/6 = 1/2. This type of calculation is frequently used in various scenarios, from splitting resources to comparing quantities.

To express a percentage as a fraction, we write the percentage as a fraction with a denominator of 100 and then simplify. Think of a percentage as ‘per hundred’.

For 40%, we write it as 40/100. Both the numerator (40) and the denominator (100) are divisible by 20, so we simplify the fraction by dividing both by 20: 40/100 = 2/5.

Therefore, 40% expressed as a fraction is 2/5. Imagine you have a pizza cut into five slices; 40% represents two of those slices.

To express a decimal as a percentage, we multiply the decimal by 100 and add a percentage sign (%).

For 0.25, we multiply it by 100: 0.25 * 100 = 25. Adding the percentage sign gives us 25%.

This is equivalent to saying that 0.25 represents 25 parts out of 100. Think about having a dollar; 0.25 represents a quarter or 25 cents, which is 25% of a dollar.

This is a simple subtraction problem. If you start with 3 apples and eat 1, you’re left with 3 - 1 = 2 apples.

This is a fundamental concept of subtraction, representing the removal of a quantity from an initial amount. It applies to many real-world situations, from counting inventory to managing finances.

To calculate the distance traveled, we multiply the speed by the time. This is based on the formula: Distance = Speed x Time.

In this case, the speed is 60 miles per hour, and the time is 2 hours. Therefore, the distance traveled is 60 miles/hour * 2 hours = 120 miles.

Imagine planning a road trip; understanding this calculation is crucial for estimating travel time and fuel consumption.

This involves simple subtraction. If you begin with $50 and spend $15, the remaining amount is $50 - $15 = $35.

This is a basic application of subtraction in personal finance. Understanding this helps in tracking expenses and managing a budget effectively.

There are a couple of ways to solve this. The most straightforward is to simply add the numbers: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55.

Alternatively, you can use the formula for the sum of an arithmetic series: n(n+1)/2, where ‘n’ is the number of terms. In this case, n = 10, so the sum is 10(10+1)/2 = 55.

This concept is fundamental in various areas, including finance (calculating total interest earned), statistics, and computer science (looping and summing).

To find a percentage of a number, we convert the percentage to a decimal and multiply it by the number. First, convert 35% to a decimal by dividing by 100: 35% = 35/100 = 0.35.

Now multiply this decimal by 200: 0.35 * 200 = 70.

Therefore, 35% of 200 is 70. This is commonly used in scenarios like calculating discounts (e.g., a 35% discount on a $200 item), sales tax, or calculating tips.

Subtraction involves finding the difference between two numbers. Think of it like taking away a certain quantity from a larger quantity. To subtract 125 from 500, we simply perform the operation 500 – 125.

Step-by-step solution:

1. Start with the larger number: 500
2. Subtract the smaller number: 500 – 125
3. Borrowing (if necessary): In this case, we don’t need to borrow.
4. Perform the subtraction column by column: 500 – 125 = 375

Therefore, 500 – 125 = 375. Imagine you have 500 apples and you give away 125; you’ll have 375 left.

Addition is the process of combining two or more numbers to find their total. Think of it like putting together collections of items. To add 72 and 48, we align the numbers vertically and add them column by column, starting from the rightmost digit (the ones place).

Step-by-step solution:

1. Align the numbers vertically:
   72
+48
2. Add the ones column: 2 + 8 = 10. Write down ‘0’ and carry-over ‘1’ to the tens column.
3. Add the tens column, including the carry-over: 1 + 7 + 4 = 12

Therefore, 72 + 48 = 120. For example, if you have 72 oranges in one basket and 48 oranges in another, combining them gives you a total of 120 oranges.

Division is the process of splitting a number into equal parts. It’s like sharing something equally among a group of people. To divide 48 by 6, we find how many times 6 goes into 48.

Step-by-step solution:

We can think of this as: ‘How many times does 6 fit into 48?’ You can use long division or repeated subtraction to solve this. In this case, 6 goes into 48 exactly 8 times (6 x 8 = 48).

Therefore, 48 ÷ 6 = 8. For instance, if you have 48 cookies and want to share them equally among 6 friends, each friend gets 8 cookies.

Multiplication is repeated addition. It’s like adding the same number multiple times. To multiply 12 by 8, we are essentially adding 12 eight times (12 + 12 + 12 + 12 + 12 + 12 + 12 + 12).

Step-by-step solution:

You can use a multiplication table or perform the calculation directly: 12 x 8 = 96

Therefore, 12 x 8 = 96. Imagine you have 12 rows of chairs with 8 chairs in each row; you have a total of 96 chairs.

Simplifying a fraction means reducing it to its lowest terms. We do this by finding the greatest common divisor (GCD) of the numerator (top number) and the denominator (bottom number) and dividing both by it.

Step-by-step solution:

1. Find the GCD of 12 and 18. The factors of 12 are 1, 2, 3, 4, 6, 12. The factors of 18 are 1, 2, 3, 6, 9, 18. The greatest common factor is 6.
2. Divide both the numerator and denominator by the GCD: 12 ÷ 6 = 2 and 18 ÷ 6 = 3.

Therefore, the simplified fraction is 2/3. This means that 12/18 represents the same proportion as 2/3. For example, if you have 12 pieces of a pizza that’s been cut into 18 slices, you have 2/3 of the pizza.

To calculate a percentage of a number, we convert the percentage to a decimal and then multiply it by the number. To calculate 15% of 60, we convert 15% to its decimal equivalent (15/100 = 0.15) and multiply it by 60.

Step-by-step solution:

1. Convert 15% to a decimal: 15% = 0.15
2. Multiply the decimal by the number: 0.15 x 60 = 9

Therefore, 15% of 60 is 9. For instance, if a store offers a 15% discount on an item costing $60, the discount amount is $9.

The order of operations, often remembered by the acronyms PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) or BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction), dictates the sequence in which calculations should be performed in a mathematical expression.

Explanation:

• Parentheses/Brackets: Calculations within parentheses or brackets are performed first.
• Exponents/Orders: Exponents (powers) are calculated next.
• Multiplication and Division: These operations are performed from left to right.
• Addition and Subtraction: These operations are performed from left to right.

Example: Consider the expression: 2 + 3 × 4. Following PEMDAS/BODMAS, we first perform the multiplication: 3 × 4 = 12. Then, we perform the addition: 2 + 12 = 14. The incorrect order of operations would result in a different answer (e.g., 2 + 3 = 5, then 5 × 4 = 20).