Simplifying Fractions: 3 1/6 ÷ 1/4
In this article, we will explore how to simplify the fraction 3 1/6 divided by 1/4. Before we dive into the solution, let's first understand the concept of fractions and how to perform arithmetic operations on them.
What are Fractions?
A fraction is a way to express a part of a whole. It consists of a numerator (the top number) and a denominator (the bottom number). For example, in the fraction 3/4, the numerator is 3 and the denominator is 4.
Mixed Numbers and Improper Fractions
A mixed number is a combination of a whole number and a fraction. For example, 3 1/6 is a mixed number, where 3 is the whole number and 1/6 is the fraction.
An improper fraction is a fraction where the numerator is greater than the denominator. For example, 7/4 is an improper fraction.
Simplifying 3 1/6 ÷ 1/4
To simplify the fraction 3 1/6 divided by 1/4, we need to follow these steps:
Step 1: Convert the Mixed Number to an Improper Fraction
First, we need to convert the mixed number 3 1/6 to an improper fraction. To do this, we multiply the whole number part (3) by the denominator (6) and then add the numerator (1):
3 × 6 = 18 18 + 1 = 19
So, the improper fraction equivalent to 3 1/6 is 19/6.
Step 2: Divide the Fractions
Now, we can divide the improper fraction 19/6 by 1/4:
(19/6) ÷ (1/4)
To divide fractions, we need to invert the second fraction (i.e., flip the numerator and denominator) and then multiply:
(19/6) × (4/1)
Step 3: Simplify the Result
Finally, we simplify the result by multiplying the numerators and denominators:
19 × 4 = 76 6 × 1 = 6
So, the simplified result is:
76/6
Final Answer
The final answer is 76/6, which can be further simplified to 12 4/6 or 12 2/3.
In conclusion, we have successfully simplified the fraction 3 1/6 divided by 1/4 to its simplest form, 12 2/3.
