Divide 50 by half and add 20. What is the answer
The Correct Answer and Explanation is :
To solve the expression “divide 50 by half and add 20,” we need to follow the order of operations carefully.
Step 1: Understand “divide by half”
When we say “divide 50 by half,” we need to understand what it means mathematically. Dividing by half is equivalent to multiplying by 2. This is because if you divide a number by a fraction, you multiply by the reciprocal of that fraction. The half (or ( \frac{1}{2} )) has a reciprocal of 2. Therefore, the operation can be expressed as:
[
50 \div \frac{1}{2} = 50 \times 2
]
Step 2: Calculate ( 50 \div \frac{1}{2} )
Now, performing the multiplication:
[
50 \times 2 = 100
]
Step 3: Add 20
Next, we add 20 to the result we obtained from the division:
[
100 + 20 = 120
]
Final Answer
So, the final answer to “divide 50 by half and add 20” is:
[
\boxed{120}
]
Explanation
This problem illustrates a common misunderstanding when dealing with fractions. Many people might initially think that dividing by a smaller number will yield a smaller result, but dividing by a fraction (like half) actually increases the value. In this case, dividing 50 by ( \frac{1}{2} ) doubles it.
This concept is foundational in arithmetic and helps us understand how operations interact with fractions and whole numbers. It highlights the importance of being precise in mathematical language; the phrasing “divide by half” can lead to confusion if not properly interpreted. The subsequent step, adding 20, is straightforward addition that builds on the understanding from the first operation.
Thus, following these mathematical principles and carefully interpreting the operations lead us to the correct answer of 120.