Solving Mathematical Expressions with Order of Operations

To find the value of the given expression, we need to follow the order of operations, often remembered by acronyms like BODMAS or PEMDAS.

• BODMAS: Brackets, Orders (powers, square roots), Division and Multiplication (from left to right), Addition and Subtraction (from left to right).
• PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

The given expression is:

\(3.8 - (4.2 \div 0.7 \times 3) + 5 \times 2 \div 0.5\)

Step-by-Step Calculation

Let's break down the expression following the BODMAS/PEMDAS rules:

Step 1: Solve the expression inside the Parentheses (Brackets).

Inside the parentheses, we have \(4.2 \div 0.7 \times 3\). Within this, we perform Division and Multiplication from left to right.

• First, perform the division: \(4.2 \div 0.7\)
• To divide decimals, we can convert them to fractions or remove the decimal by multiplying both numbers by a power of 10. Here, we can multiply both by 10 to get \(42 \div 7\).
• \(42 \div 7 = 6\).
• So, \(4.2 \div 0.7 = 6\).
• Now, perform the multiplication: \(6 \times 3\).
• \(6 \times 3 = 18\).

So, the value inside the parentheses is 18. The expression now becomes:

\(3.8 - 18 + 5 \times 2 \div 0.5\)

Step 2: Perform Multiplication and Division from left to right.

We have \(5 \times 2 \div 0.5\). Perform these operations from left to right.

• First, perform the multiplication: \(5 \times 2\).
• \(5 \times 2 = 10\).
• The expression part is now \(10 \div 0.5\).
• Perform the division: \(10 \div 0.5\).
• Dividing by 0.5 is the same as multiplying by 2. \(10 \div 0.5 = 10 \times 2 = 20\).

So, the value of \(5 \times 2 \div 0.5\) is 20. The expression now becomes:

\(3.8 - 18 + 20\)

Step 3: Perform Addition and Subtraction from left to right.

We have \(3.8 - 18 + 20\). Perform these operations from left to right.

• First, perform the subtraction: \(3.8 - 18\).
• \(3.8 - 18 = -14.2\).
• The expression is now \(-14.2 + 20\).
• Perform the addition: \(-14.2 + 20\).
• \(-14.2 + 20 = 20 - 14.2 = 5.8\).

The final value of the expression is 5.8.

Comparing with Options

Let's compare the calculated value with the given options:

The calculated value, 5.8, matches Option 4.

Revision Table: Order of Operations (BODMAS/PEMDAS)

Additional Information: Decimal Arithmetic

Working with decimals requires careful attention to place values, especially during division and multiplication.

• Decimal Division: To divide by a decimal, multiply both the divisor and the dividend by a power of 10 to make the divisor a whole number. For example, \(4.2 \div 0.7\) becomes \(42 \div 7\) by multiplying both by 10. \(10 \div 0.5\) becomes \(100 \div 5\) by multiplying both by 10, or simply recognize \(0.5 = 1/2\), so dividing by 0.5 is multiplying by 2.
• Decimal Multiplication: Multiply the numbers as if they were whole numbers. Then, count the total number of decimal places in the original numbers and place the decimal point in the product such that it has the same number of decimal places.
• Decimal Addition/Subtraction: Align the decimal points vertically and add or subtract as with whole numbers.