4 1/6 Divided by 1 1/8 as a Fraction
In this article, we will explore how to divide two mixed numbers, 4 1/6 and 1 1/8, and express the result as a fraction.
Converting Mixed Numbers to Improper Fractions
Before we can divide these two mixed numbers, we need to convert them into improper fractions. An improper fraction is a fraction where the numerator is greater than the denominator.
Converting 4 1/6 to an Improper Fraction
To convert 4 1/6 to an improper fraction, we need to multiply the whole number part (4) by the denominator (6) and add the numerator (1).
4 × 6 = 24 24 + 1 = 25
So, 4 1/6 is equivalent to the improper fraction 25/6.
Converting 1 1/8 to an Improper Fraction
To convert 1 1/8 to an improper fraction, we need to multiply the whole number part (1) by the denominator (8) and add the numerator (1).
1 × 8 = 8 8 + 1 = 9
So, 1 1/8 is equivalent to the improper fraction 9/8.
Dividing the Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can divide them.
25/6 ÷ 9/8
To divide two fractions, we need to multiply the first fraction by the reciprocal of the second fraction.
25/6 × 8/9
We can simplify this expression by canceling out common factors.
25 × 8 = 200 6 × 9 = 54
So, the result of dividing 4 1/6 by 1 1/8 is 200/54.
Simplifying the Result
We can simplify the fraction 200/54 by dividing both the numerator and the denominator by their greatest common divisor (GCD).
The GCD of 200 and 54 is 2. Therefore, we can simplify the fraction as follows:
200 ÷ 2 = 100 54 ÷ 2 = 27
So, the final result of dividing 4 1/6 by 1 1/8 is 100/27.
