2 divided by 5/12 in fraction form

2 divided by 5/12 in fraction form

The Correct Answer and Explanation is:

To solve the expression ( \frac{2}{\frac{5}{12}} ), we follow a process of dividing by a fraction, which is equivalent to multiplying by the reciprocal of that fraction.

Step 1: Understand the problem

The problem asks us to divide 2 by the fraction ( \frac{5}{12} ). To divide by a fraction, we multiply by its reciprocal (the fraction flipped upside down).

Step 2: Find the reciprocal

The reciprocal of ( \frac{5}{12} ) is ( \frac{12}{5} ). So, the division becomes:

[
\frac{2}{\frac{5}{12}} = 2 \times \frac{12}{5}
]

Step 3: Multiply the whole number by the fraction

To multiply a whole number by a fraction, we can write the whole number as a fraction with a denominator of 1. Thus, we rewrite 2 as ( \frac{2}{1} ) and then multiply:

[
\frac{2}{1} \times \frac{12}{5} = \frac{2 \times 12}{1 \times 5} = \frac{24}{5}
]

Step 4: Simplify if necessary

The fraction ( \frac{24}{5} ) is already in its simplest form because 24 and 5 have no common factors other than 1.

Step 5: Final Answer

Thus, ( \frac{2}{\frac{5}{12}} = \frac{24}{5} ).

Explanation:

When dividing by a fraction, the rule is to multiply by the reciprocal of the fraction. This is based on the principle that dividing by a number is the same as multiplying by its inverse. For example, when dividing ( \frac{2}{\frac{5}{12}} ), we are essentially finding how many times ( \frac{5}{12} ) fits into 2. By converting the division into a multiplication problem, we make the computation straightforward, ensuring the process is accurate and efficient. The final fraction ( \frac{24}{5} ) represents the result of this multiplication, which shows the equivalent value of the original division.