What is the quotient of 4 divided by 9/2 ?
The Correct Answer and Explanation is:
To find the quotient of (4) divided by (\frac{9}{2}), we’ll start by understanding the division of a whole number by a fraction.
Step 1: Rewrite the Division as Multiplication
When you divide by a fraction, it’s the same as multiplying by the reciprocal of that fraction. The reciprocal of a fraction is created by swapping its numerator and denominator. Here, the reciprocal of (\frac{9}{2}) is (\frac{2}{9}).
So:
[
4 \div \frac{9}{2} = 4 \times \frac{2}{9}
]
Step 2: Perform the Multiplication
Now that we’ve changed the division to multiplication, we can multiply:
[
4 \times \frac{2}{9} = \frac{4 \times 2}{9} = \frac{8}{9}
]
So, the answer is:
[
\frac{8}{9}
]
Detailed Explanation
- Dividing by a Fraction: Dividing by a fraction essentially means finding how many times the fraction fits into the number you are dividing. For example, dividing by (\frac{9}{2}) is like asking, “How many times does (\frac{9}{2}) go into (4)?” This can be tricky to visualize directly, which is why we convert division by a fraction into multiplication by the reciprocal.
- Multiplying by the Reciprocal: This method makes it easier to perform the operation. Instead of dividing by a fraction, which can be complex, we simply multiply by the flipped version of that fraction. This approach is a standard rule in math for dividing by fractions and simplifies calculations.
- Simplifying the Calculation: By rewriting (4 \div \frac{9}{2}) as (4 \times \frac{2}{9}), we avoid dealing with complex division and instead perform simple multiplication. Multiplying (4) by (\frac{2}{9}) gives us (\frac{8}{9}), which is already in its simplest form since (8) and (9) have no common factors other than (1).
Final Answer
The quotient of (4) divided by (\frac{9}{2}) is (\frac{8}{9}).