Discovering the Simplest Fraction for 150 out of 1600

Cracking the Code of Fractions: Understanding 150 Out of 1600

If you’ve ever felt a bit lost in the world of fractions, don’t worry—you’re definitely not alone! Fractions are often one of the trickiest aspects of math. But understanding them is crucial, especially for certain professions, like firefighting. You see, as a firefighter, math isn’t just a school subject—it’s a tool you’ll use in planning and executing life-saving measures. Let’s dig into a specific fraction problem to unravel just how straightforward fractions can actually be.

What’s the Bottom Line?

Let’s imagine a scenario: you’ve got 150 out of a total of 1600, and you need to find out the smallest fraction that represents this. You might see this written as ( \frac{150}{1600} ). Now, if we break it down step by step, it becomes clearer than last night's pasta dinner.

• Understanding Fractions: So, what are we really looking at? A fraction is essentially a way to express a part of a whole. In this case, we are expressing how much of something (150) exists out of a total (1600). But, can we simplify this further? That’s the question!

Let’s Find the GCD

Now, it’s time to roll up our sleeves and find the greatest common divisor (GCD) of 150 and 1600. The GCD is the largest number that can evenly divide both numbers. To find it, we can use prime factorization. Sounds fancy, but it’s actually pretty simple!

• Step 1: Factor the Numbers

For 150, if we break it down, we’ll find ( 2 \times 3 \times 5^2 ).

For 1600, we factor it into ( 2^6 \times 5^2 ).

• Step 2: Identify Common Factors

Look closely now! The common factors appear to be ( 2 ) and ( 5^2 ). We multiply those together:

( 2 \times 5^2 = 2 \times 25 = 50 ).

Ta-da! That’s our GCD.

Time to Simplify

With our GCD in hand, simplifying the fraction becomes a piece of cake—or should I say a slice of pizza?

• Dividing Both Numbers by 50:

• For 150: ( 150 \div 50 = 3 )

• For 1600: ( 1600 \div 50 = 32 )

This gives us the simplified fraction of ( \frac{3}{32} ). Easy peasy!

Now, you might be wondering, “What does this have to do with the options given?” Let’s talk about that.

Time to Compare

The question provides several choices:

A. ( \frac{3}{40} )

B. ( \frac{1}{10} )

C. ( \frac{5}{80} )

D. ( \frac{1}{20} )

Here’s the crux: we need to find out which of these fractions is equivalent to our simplified fraction, ( \frac{3}{32} ).

Evaluating the Options

1. Option A: ( \frac{3}{40} )

This fraction doesn’t match because 40 is larger than 32, meaning 3 out of 40 simply isn’t the same as 3 out of 32.

2. Option B: ( \frac{1}{10} )

This one is interesting! Converting ( \frac{1}{10} ) gives us ( \frac{10}{100} ), and that’s not close at all to 32.

3. Option C: ( \frac{5}{80} )

This fraction can be simplified as well. Dividing by 5 gives us ( \frac{1}{16} ). Still too small compared to our fraction.

4. Option D: ( \frac{1}{20} )

Simplifying this by multiplying gives us ( 1 \times 16 = 16 ). So, nope!

After doing all that evaluating, you’ll find that the smallest fraction describing 150 out of 1600 is actually Option B: 1/10. Go ahead; give yourself a pat on the back for a job well done!

The Takeaway: Math Can Be Friendly

In the end, fractions might seem daunting at first glance, but they really aren’t the enemy—they just need some unpacking. Take it step by step, connect the dots, and before you know it, you’ll find yourself comfortable navigating through math like a pro.

You know what? The best part about understanding fractions is that it sharpens your analytical skills, which can come in handy not just in statistics or firefighting, but in life. So, the next time you find yourself staring down a fraction, remember, it’s just about decoding it one element at a time. You’ve got this!

Happy calculating!