Okay so today I was just doing some random math stuff – you know how it is, just noodling around with numbers – and this question pops into my head: what’s 2/7 times -10? Seems straightforward, right? But then I stopped and thought, wait, fractions and negatives together? Could get messy. Always trips people up. So I grabbed my notebook to figure it out properly, the kind where I scribble all my workings. Let me walk you through what I actually did, step-by-step, like I always do. Real talk, no shortcuts yet.
First thing, I wrote it down plain and simple: (2/7) (-10). Gotta see the whole picture. Now, I know multiplying fractions is usually top times top, bottom times bottom. But this negative sign is just hanging out there on the 10. So, I figured, that negative needs to go somewhere. Honestly, I could stick it right on the numerator. Makes sense to me. So I rewrote the whole thing as (2/7) (-10/1). Yeah, because any whole number is over one. Now it looks like two fractions to multiply. Less scary.
Alright, multiplying time. Numerators first: 2 times -10. Two times ten is twenty, but the negative sign tags along. So that’s -20. No brainer. Denominators next: 7 times 1. That’s just 7. So now I got (-20)/7. That’s the answer right there: negative twenty sevenths. Simple as that. So -20/7.
But you know me, I never just take the first answer. Gotta check if I can make it look cleaner. Is -20/7 simplified? Well, do 20 and 7 share any common factors? 20 splits into 2x2x5. 7 is just…7. Prime number. Nothing cancels out. So nope, it’s already as simple as it gets. I thought about turning it into a mixed number, like -2 and 6/7? But honestly, for multiplying, the improper fraction (-20/7) usually works better if you’re gonna do more math later. And the decimal? Oh lord, 20 divided by 7 is roughly -2.857 something something…nah, messy. Fraction is cleaner.
Here’s the core bits I figured out, the easy takeaways:
- Shove that negative sign onto the numerator right away. Makes the multiplication rules super clear.
- Multiply the tops (numerators): 2 -10 = -20
- Multiply the bottoms (denominators): 7 1 = 7
- Bang, you got -20/7. Check for simplifying, but it was fine.
- Fraction is king here. Decimal just gives you an ugly repeating number. Why bother?
Was tempted to reach for the calculator, but glad I stuck with the pencil and paper. Makes you really see it. -20/7, done. Nice and tidy. Now it’s straight into the notebook where all the messy scribbles live. Feels good to nail the basics down properly!
