Calculating 2 Divided By 5/12: Simple Steps Explained
Table of Contents :
To calculate ( 2 \div \frac{5}{12} ), we will break down the steps in a clear and straightforward manner. Dividing by a fraction can seem daunting at first, but with the right approach, it becomes much simpler. Let’s explore how to handle this division step-by-step.
Understanding Division by a Fraction
When you divide by a fraction, you can instead multiply by its reciprocal. The reciprocal of a fraction is simply the fraction inverted. For example, the reciprocal of ( \frac{5}{12} ) is ( \frac{12}{5} ).
Step 1: Identify the Problem
We are tasked with solving:
[ 2 \div \frac{5}{12} ]
This can be rewritten using multiplication by the reciprocal:
[ 2 \times \frac{12}{5} ]
Step 2: Converting Whole Numbers to Fractions
Before multiplying, it’s easier if we convert the whole number into a fraction. We can write ( 2 ) as ( \frac{2}{1} ). So now we have:
[ \frac{2}{1} \times \frac{12}{5} ]
Step 3: Multiply the Numerators and Denominators
Now, we will multiply the numerators together and the denominators together:
[ \text{Numerator: } 2 \times 12 = 24 ] [ \text{Denominator: } 1 \times 5 = 5 ]
This gives us:
[ \frac{24}{5} ]
Step 4: Simplify the Result (if necessary)
The fraction ( \frac{24}{5} ) is already in its simplest form, but we can convert it to a mixed number if desired.
Step 5: Converting to a Mixed Number
To convert ( \frac{24}{5} ) into a mixed number, we divide the numerator by the denominator:
- ( 24 \div 5 = 4 ) with a remainder of ( 4 ).
So, we have:
[ \frac{24}{5} = 4 \frac{4}{5} ]
Conclusion
Thus, the answer to ( 2 \div \frac{5}{12} ) is ( \frac{24}{5} ) or as a mixed number, ( 4 \frac{4}{5} ).
By following these steps, we have simplified what initially seemed like a complex problem into a series of straightforward calculations. Whether you stick with the improper fraction ( \frac{24}{5} ) or prefer the mixed number ( 4 \frac{4}{5} ), understanding how to divide by a fraction can significantly enhance your mathematical skills.
Now you can confidently tackle similar problems in the future! 🚀