what is 7/8 divided by 3/4

2 min read 05-02-2025

Dividing fractions can seem tricky, but it's actually a straightforward process once you understand the steps. This article will walk you through how to solve 7/8 divided by 3/4, explaining the method clearly and concisely. We'll also explore the underlying concept of fraction division.

Understanding Fraction Division

Before diving into the calculation, let's quickly review the concept of dividing fractions. When you divide by a fraction, you're essentially asking "how many times does this fraction fit into that fraction?" To solve this, we use a technique called "keep, change, flip."

Keep, Change, Flip: The Easy Way to Divide Fractions

The "keep, change, flip" method simplifies fraction division. Here's how it works:

Keep: Keep the first fraction exactly as it is (7/8).
Change: Change the division sign (÷) to a multiplication sign (×).
Flip: Flip the second fraction (reciprocal). The reciprocal of 3/4 is 4/3.

Calculating 7/8 Divided by 3/4

Now, let's apply the "keep, change, flip" method to our problem: 7/8 ÷ 3/4

Keep: 7/8
Change: ×
Flip: 4/3

This transforms the problem into a multiplication problem: 7/8 × 4/3

To multiply fractions:

Multiply the numerators (top numbers): 7 × 4 = 28
Multiply the denominators (bottom numbers): 8 × 3 = 24

This gives us the improper fraction 28/24.

Simplifying the Result

The fraction 28/24 can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator. The GCD of 28 and 24 is 4. Divide both the numerator and denominator by 4:

28 ÷ 4 = 7 24 ÷ 4 = 6

Therefore, the simplified answer is 7/6.

Converting to a Mixed Number (Optional)

While 7/6 is a perfectly acceptable answer, you might want to express it as a mixed number. To do this, divide the numerator (7) by the denominator (6):

7 ÷ 6 = 1 with a remainder of 1

This means 7/6 is equal to 1 1/6.

Conclusion: 7/8 Divided by 3/4 = 7/6 or 1 1/6

We've successfully solved the problem! Remember the "keep, change, flip" method for dividing fractions – it makes the process much simpler. Understanding fraction division is a fundamental skill in mathematics, and mastering this technique will pave the way for more complex calculations.