Solve: 6÷0.75 - 2×3 | Order of Operations with Decimals

To solve the expression $\frac{6}{0.75} - 2 \times 3$, we need to carefully follow the order of operations. The order of operations is often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, there are no parentheses or exponents, so we focus on multiplication, division, subtraction in the given order.

• Step 1: Division
  First, perform the division: $\frac{6}{0.75}$. To divide by a decimal, convert it to a fraction or adjust the dividend and divisor by a power of 10 to make the divisor a whole number. Here, $\frac{6}{0.75}$ becomes $\frac{6 \times 100}{0.75 \times 100} = \frac{600}{75}$.
  Next, simplify $\frac{600}{75}$. Both numbers are divisible by 15:
  $600 \div 15 = 40$ and $75 \div 15 = 5$, so $\frac{600}{75} = 40 \div 5 = 8$.
• Step 2: Multiplication
  Next, perform the multiplication: $2 \times 3$ which equals $6$.
• Step 3: Subtraction
  Finally, subtract the results of the previous operations: $8 - 6$. This gives $2$.

By carefully following the order of operations, the final answer to the expression $\frac{6}{0.75} - 2 \times 3$ is $2$, which matches the correct answer provided.