Question

\(50 / 40-5+4 \times 54\) is equal to : (a) 720 (b) 72 (c) 144 (d) none of these

Short answer

Question: Evaluate the expression \(50 / 40 - 5 + 4 \times 54\) and choose the correct answer from the given options. (a) 720 (b) 72 (c) 144 (d) none of these Answer: (d) none of these

Step-by-step solution

Apply Order of Operations

In the expression \(50 / 40 - 5 + 4 \times 54\), there are no parentheses or exponents, so we can start with division and multiplication. Perform the division first, then the multiplication as they appear from left to right: \(50 / 40 - 5 + 4 \times 54 = 1.25 - 5 + 4 \times 54\) Now perform the multiplication: \(1.25 - 5 + 216 = 1.25 - 5 + 216\)

Perform Addition and Subtraction from Left to Right

Now, we'll perform addition and subtraction from left to right: \(1.25 - 5 + 216 = -3.75 + 216\) \(-3.75 + 216 = 212.25\)

Compare with the Given Options

Now that we have our result, let's compare it with the options provided: (a) 720 (b) 72 (c) 144 (d) none of these Since the result we obtained (\(212.25\)) does not match any of the first three options, the correct answer is option (d) none of these.

Key concepts

PEMDAS/BODMAS Rule

Understanding the correct order of operations in mathematics is vital to solving expressions accurately. The PEMDAS/BODMAS rule is a mnemonic that helps us remember the sequence in which to perform operations. PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction. Similarly, BODMAS stands for Brackets, Orders (another word for exponents), Division, Multiplication, Addition, and Subtraction. The slight difference in terminology does not affect the sequence, as both imply that operations inside parentheses or brackets and exponents should be performed before other operations.

To clarify, multiplication and division are to be performed from left to right, as they occur in the equation, and hold the same level of priority. The same goes for addition and subtraction; they are performed from left to right after attending to multiplication and division. The major takeaway is that the rule helps prevent mistakes that can drastically change the outcome of a math problem.

Here's a simple breakdown using bullet points:

• Begin with operations inside parentheses or brackets.
• Proceed to exponents or orders.
• Move on to multiplication and division, from left to right.
• Wrap up with addition and subtraction, also from left to right.

By following this sequence, we ensure that we're working out the calculations in the correct order.

Mathematical Division

Mathematical division is one of the four basic arithmetic operations and serves as the inverse of multiplication. When we divide, we are essentially determining how many times one number is contained within another or splitting a number into equal parts. The number being divided is called the dividend, while the number you're dividing by is the known as the divisor, and the result of the division is the quotient.

Division can be simple with whole numbers, but when we encounter decimals or fractions, it can introduce complexity to the operation:

• Dividing by whole numbers is straightforward; for example, dividing 10 by 5 yields a quotient of 2.
• When the dividend is smaller than the divisor, as in our original exercise, the result is a fraction or decimal.
• It's also important to remember that division by zero is undefined, as you cannot divide a number into zero equal parts.

After division, it's crucial to carry out the next operations in the correct sequence, respecting the order dictated by PEMDAS/BODMAS rule.

Mathematical Multiplication

Mathematical multiplication is another essential arithmetic operation that represents repeated addition. For example, multiplying 4 by 3 means you're adding 4 to itself 3 times (4 + 4 + 4), which results in 12. When facing an expression involving multiplication, there are a few important points to bear in mind:

Firstly, multiplication has equal precedence with division; they should be performed as they appear from left to right before moving on to addition and subtraction.

• If you're dealing with whole numbers, simply multiply the numbers together as you've learned.
• Involving variables, apply the distributive property as needed.
• For numbers with decimals, multiply as if they were whole numbers first and then adjust the decimal point in the result accordingly.

In our example, after calculating the division part, we moved on to multiplication and only after these operations were complete did we perform the addition and subtraction. This ensures that we are consistent with the rules of operation order, leading us to the correct answer.