Understanding Division of Mixed Numbers and Fractions

In this article, we will explore how to divide mixed numbers and fractions, as well as convert the results between improper fractions and mixed numbers. We’ll also look at practical examples to understand the concepts better.

Dividing 1 1/4 by 3/4

Let's start by understanding the problem: What is 1 1/4 divided by 3/4? This can be written as:

As a Mixed Number

Step 1: Convert the Mixed Number to an Improper Fraction

Convert 1 1/4 to an improper fraction:

1 1/4 4/4 1/4 5/4

Step 2: Perform the Division

Divide 5/4 by 3/4:

5/4 ÷ 3/4 5/4 × 4/3 5/3

Convert 5/3 back to a mixed number:

5/3 1 2/3 (Since 5

Additional Perspectives

String of Divisors: 5/4 ÷ 3/4 5/4 × 4/3 20/12 1 8/12 1 2/3

String of Inversions: 5/4 ÷ 4/3 5/4 × 3/4 15/16 1 3/16

Partial Expressions: 1 1/4 ÷ 3/4 (5/4 ÷ 3) × 4 5/12 × 4 20/12 1 8/12 1 2/3

Another Example: 3 ÷ 1 1/4

Now let's solve a different problem: What is 3 ÷ 1 1/4?

Step 1: Convert the Mixed Number to an Improper Fraction

1 1/4 5/4

Thus, 3 ÷ 5/4 3 × 4/5 12/5

Convert 12/5 to a mixed number:

12/5 2 2/5 or 2.4

A Further Example: What Fraction of 3 1/4 is 1 1/3?

We can re-phrase “What fraction of 3 1/4 is 1 1/3” to “1 1/3 is what part of 3 1/4”. Let's solve this problem step-by-step:

Step 1: Express the Mixed Numbers as Improper Fractions

3 1/4 13/4

1 1/3 4/3

Step 2: Perform the Division

Divide 4/3 by 13/4:

4/3 ÷ 13/4 4/3 × 4/13 16/39

Convert 16/39 to a decimal:

16/39 ≈ 0.410256 (repeating)

CHECK: To verify, we can multiply 16/39 by 39/16 to get back to 1:

Conclusion

By following these detailed steps, we can effectively solve problems involving the division of mixed numbers and fractions. Understanding these operations is crucial for any mathematical problem involving fractions and mixed numbers.