You know, sometimes a simple math problem can feel like a bit of a puzzle, especially when you're dealing with fractions. Take the question, '6 1/2 divided by 3/4.' It sounds straightforward enough, but the way fractions work can throw you for a loop if you're not careful.
Let's break it down, shall we? First off, that mixed number, 6 1/2, needs to be converted into an improper fraction. Think of it this way: you have 6 whole things, and each whole thing is made up of 2 halves. So, 6 wholes give you 6 * 2 = 12 halves. Add the extra half, and you've got 12 + 1 = 13 halves. So, 6 1/2 becomes 13/2.
Now, the division part. When you divide by a fraction, it's the same as multiplying by its reciprocal. The reciprocal is just the fraction flipped upside down. So, the reciprocal of 3/4 is 4/3.
Putting it all together, our problem now looks like this: 13/2 multiplied by 4/3.
Multiplying fractions is usually the easiest part. You just multiply the numerators (the top numbers) together and the denominators (the bottom numbers) together.
So, 13 * 4 = 52 (that's our new numerator). And 2 * 3 = 6 (that's our new denominator).
This gives us the fraction 52/6.
Now, we can simplify this fraction. Both 52 and 6 are even numbers, so they can be divided by 2.
52 divided by 2 is 26. 6 divided by 2 is 3.
So, our simplified fraction is 26/3.
Often, it's helpful to convert this back into a mixed number. How many times does 3 go into 26? Well, 3 * 8 is 24. That leaves us with a remainder of 2 (26 - 24 = 2). So, 26/3 is the same as 8 with a remainder of 2, which we write as 8 and 2/3.
And there you have it! 6 1/2 divided by 3/4 equals 8 2/3. It's a neat little process, isn't it? Just remember to convert mixed numbers and flip those fractions when you're dividing. It makes all the difference.
