You know, sometimes numbers just look simpler when they're written as fractions. That little decimal point can feel a bit… slippery, can't it? And when you're faced with something like 1.375, you might find yourself wondering, 'What's the real story behind this number?' Well, let's peel back the layers and see.
Think of any number, really, as a fraction waiting to happen. The easiest way to start is by giving it a denominator of 1. So, 1.375 becomes 1.375/1. That's technically a fraction, but it's not quite what we're aiming for, is it? We want to get rid of that decimal part entirely, making the top number (the numerator) a nice, clean whole number.
To do that, we need to look at how many digits are hanging out after the decimal point. In 1.375, we've got three digits: 3, 7, and 5. Each digit represents a power of ten. One digit after the decimal means we're dealing with tenths (multiply by 10), two digits mean hundredths (multiply by 100), and three digits, like we have here, mean we're dealing with thousandths. So, we need to multiply both the numerator and the denominator by 1,000 to clear out that decimal.
Let's do the math: 1.375 multiplied by 1,000 gives us 1375. And 1 multiplied by 1,000 is, of course, 1000. So now we have the fraction 1375/1000.
Now, this is a perfectly valid fraction, but it's like a puzzle that's not quite finished. We can simplify it further. The goal is to find the largest number that divides evenly into both 1375 and 1000. This is often called the Greatest Common Factor (GCF) or Greatest Common Divisor (GCD).
After a bit of number crunching (or using a handy calculator if you prefer!), we find that 25 is the GCF for 1375 and 1000. So, we divide both the numerator and the denominator by 25.
1375 divided by 25 equals 55. 1000 divided by 25 equals 40.
This brings us to the fraction 55/40.
We're getting closer! But wait, can we simplify even more? Yes, we can! Both 55 and 40 are divisible by 5.
55 divided by 5 is 11. 40 divided by 5 is 8.
And there we have it: 11/8.
Now, 11/8 is an improper fraction (the numerator is larger than the denominator). Sometimes, it's helpful to express this as a mixed number. We ask ourselves, 'How many times does 8 go into 11?' It goes in once, with a remainder of 3. So, 11/8 is the same as 1 and 3/8.
So, that decimal 1.375? It's really just a friendly way of saying 1 and 3/8. Pretty neat, right? It’s a reminder that numbers have different faces, and sometimes, a little bit of digging reveals a simpler, more elegant form.
