Understanding the Solution to 1/2 ÷ 3/4 ÷ 1/3

Many math enthusiasts and students find themselves grappling with complex fractions and division operations. This article aims to break down the solution step by step, providing a clear explanation of how to tackle the problem 1/2 ÷ 3/4 ÷ 1/3, and presenting the answer in both improper fraction and mixed number formats.

Introduction to the Problem

The given problem is:

Solution to the Problem

Let's start by understanding the problem: we need to divide 1/2 by 3/4 and then divide the result by 1/3.

Step 1: Divide 1/2 by 3/4

When dividing by a fraction, we multiply by its reciprocal. So, 1/2 ÷ 3/4 can be rewritten as 1/2 × 4/3.

Mathematically:

y 1/2 × 4/3

Now, multiply the numerators together and the denominators together:

y (1 × 4) / (2 × 3) 4/6

Reduce the fraction by dividing the numerator and the denominator by their greatest common divisor (GCD), which is 2:

y 2/3

Step 2: Divide the Result by 1/3

Now, we need to divide 2/3 by 1/3. Again, we use the same rule: multiply by the reciprocal.

y 2/3 × 3/1

Multiply the numerators together and the denominators together:

y (2 × 3) / (3 × 1) 6/3

Reduce the fraction by dividing the numerator and the denominator by their GCD, which is 3:

y 2

In improper fraction form, 2 is simply 2/1.

Alternative: Mixed Number Form

2 can also be expressed in mixed number form as 2 and 0/1, but since there is no fractional part, it simplifies to just 2.

The decimal equivalent of 2 is 2.0, which can be rounded to 2 if needed.

Conclusion

To solve the problem 1/2 ÷ 3/4 ÷ 1/3, we perform the operations step by step. The final result is 2, which can also be expressed as an improper fraction 2/1 or a mixed number 2 and 0/1. The decimal form of the answer is 2.0.

Understanding these steps and practicing such problems can enhance your skills in manipulating fractions and solving complex arithmetic operations.

Keywords

math problem solving, improper fraction, mixed number