Divide 1 1/2 divided by 1/4 in simplest form

Divide 1 1/2 divided by 1/4 in simplest form

The Correct Answer and Explanation is :

To divide the mixed number (1 \frac{1}{2}) by the fraction (\frac{1}{4}), follow these steps:

Step 1: Convert the Mixed Number to an Improper Fraction

A mixed number consists of a whole number and a fractional part. To convert (1 \frac{1}{2}) to an improper fraction:

1. Multiply the whole number (1) by the denominator (2):
   [
   1 \times 2 = 2
   ]
2. Add the numerator (1) to this product:
   [
   2 + 1 = 3
   ]
3. Place this result over the original denominator (2):
   [
   1 \frac{1}{2} = \frac{3}{2}
   ]

Step 2: Set Up the Division Problem

Now, we have the division problem:
[
\frac{3}{2} \div \frac{1}{4}
]

Step 3: Multiply by the Reciprocal

To divide by a fraction, multiply by its reciprocal. The reciprocal of (\frac{1}{4}) is (\frac{4}{1}). Therefore, we rewrite the division as multiplication:
[
\frac{3}{2} \times \frac{4}{1}
]

Step 4: Perform the Multiplication

Now, multiply the numerators and denominators:
[
\frac{3 \times 4}{2 \times 1} = \frac{12}{2}
]

Step 5: Simplify the Result

Now, simplify (\frac{12}{2}):
[
\frac{12}{2} = 6
]

Conclusion

The answer to (1 \frac{1}{2} \div \frac{1}{4}) is 6.

Explanation

When dividing fractions, converting mixed numbers into improper fractions is essential to simplify calculations. Multiplying by the reciprocal helps us perform the division seamlessly. This method is based on the principle that dividing by a number is equivalent to multiplying by its reciprocal. Here, the mixed number was first converted, then the operation transformed from division to multiplication, making it easier to arrive at the final result. The simplification step is crucial, as it ensures that the answer is expressed in its simplest form.