Division of Mixed Numbers: 1 7/6 divided by 1 3/5 as a Reduced Fraction
In this article, we will explore the process of dividing mixed numbers, specifically 1 7/6 divided by 1 3/5, and simplify the result as a reduced fraction.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. For example, 1 7/6 is a mixed number, where 1 is the whole number and 7/6 is the fraction.
Converting Mixed Numbers to Improper Fractions
To divide mixed numbers, we need to convert them to improper fractions first. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.
Converting 1 7/6 to an Improper Fraction
To convert 1 7/6 to an improper fraction, we multiply the whole number part (1) by the denominator (6) and then add the numerator (7):
1 × 6 = 6 6 + 7 = 13
So, 1 7/6 is equal to the improper fraction 13/6.
Converting 1 3/5 to an Improper Fraction
Similarly, we convert 1 3/5 to an improper fraction:
1 × 5 = 5 5 + 3 = 8
So, 1 3/5 is equal to the improper fraction 8/5.
Dividing Improper Fractions
Now that we have converted both mixed numbers to improper fractions, we can divide them:
13/6 ÷ 8/5
To divide fractions, we multiply by the reciprocal of the second fraction:
13/6 × 5/8
Simplifying the Result
To simplify the result, we multiply the numerators and denominators separately:
(13 × 5) / (6 × 8) 65 / 48
So, 1 7/6 divided by 1 3/5 is equal to 65/48 as a simplified fraction.
Conclusion
In this article, we learned how to divide mixed numbers by converting them to improper fractions and then dividing them. The result of 1 7/6 divided by 1 3/5 is 65/48 as a simplified fraction.
