Understanding Fraction Division: A Comprehensive Guide to Dividing 7/8 by 3/16

Understanding how to divide fractions, particularly when dealing with specific examples like 7/8 divided by 3/16, is a crucial skill. This article will break down the process with detailed steps, ensuring that you master the concept and can apply it to similar problems.

Introduction to Fraction Division

Fraction division involves taking one fraction and dividing it by another, a concept that is essential in many mathematical applications. This can often be more intuitive once you understand the reciprocal multiplication method. Instead of directly dividing one fraction by another, you multiply the first fraction by the reciprocal of the second fraction.

Step-by-Step Guide

1. Write the Problem as a Multiplication

First, write the problem in a way that makes it easier to understand. Start with the division of fractions:

[ frac{7}{8} div frac{3}{16} ]

Now, rewrite the division as a multiplication by the reciprocal of the second fraction:

[ frac{7}{8} div frac{3}{16} frac{7}{8} times frac{16}{3} ]

2. Multiply the Numerators

Next, multiply the numerators of the two fractions. In this example, the numerators are 7 and 16:

[ 7 times 16 112 ]

3. Multiply the Denominators

Then, multiply the denominators of the two fractions. The denominators here are 8 and 3:

[ 8 times 3 24 ]

Combine the results to get:

[ frac{112}{24} ]

4. Simplify the Fraction

To simplify the fraction, find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 112 and 24 is 8. Divide both the numerator and the denominator by 8:

[ frac{112 div 8}{24 div 8} frac{14}{3} ]

The simplified fraction is

[ frac{14}{3} ], which is approximately 4.666.

5. Convert to a Mixed Number

You can also express the improper fraction as a mixed number. To do this, divide the numerator by the denominator:

[ 14 div 3 4 , text{with a remainder of} , 2 ]

Thus, the mixed number is:

[ 4 frac{2}{3} ]

6. Verify the Calculation

To double-check your result, you can perform the division directly:

[ frac{7/8}{3/16} 7/8 times 16/3 frac{7 times 16}{8 times 3} frac{112}{24} 4 frac{2}{3} ]

This confirms that your answer is correct.

Conclusion

By understanding the steps involved in dividing fractions, you can solve problems like dividing 7/8 by 3/16 effortlessly. Remember to always convert fractions to their simplest form and utilize the reciprocal multiplication method. This skill is invaluable in many areas of mathematics and can help in solving real-world problems involving proportions and ratios.

If you need further practice or have questions, feel free to explore more problems or consult additional resources.

Related Keywords: fraction division, dividing fractions, fraction multiplication