It’s a question that might pop up in a math class, or perhaps during a moment of quiet contemplation about fractions: what exactly is 5/12 divided by 1/3?
At first glance, division of fractions can seem a bit like a puzzle. We're used to adding, subtracting, and multiplying them, but division often brings a slight pause. The fundamental rule when dividing fractions is to "keep, change, flip." This means we keep the first fraction (5/12) as it is, change the division sign to a multiplication sign, and flip the second fraction (1/3) to its reciprocal, which is 3/1.
So, our problem transforms from 5/12 ÷ 1/3 into 5/12 × 3/1. Now, multiplication of fractions is straightforward. We multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together.
Multiplying the numerators: 5 × 3 = 15. Multiplying the denominators: 12 × 1 = 12.
This gives us a new fraction: 15/12.
But we’re not quite done yet. Most of the time, we want to simplify our fractions to their lowest terms. Both 15 and 12 are divisible by 3. Dividing 15 by 3 gives us 5, and dividing 12 by 3 gives us 4.
Therefore, 15/12 simplifies to 5/4.
And there you have it! 5/12 divided by 1/3 equals 5/4. It’s a neat little process, turning a division problem into a multiplication one, and then simplifying to find the answer. It’s a reminder that sometimes, a simple change in approach can unlock the solution to what seems like a complex problem.
