Mastering Arithmetic Reasoning for the AFCT: Distance Calculation Made Easy

Are you gearing up to tackle the Arithmetic Reasoning section of the Armed Forces Classification Test (AFCT)? You're in the right place! Let's dissect a common question type that pops up: calculating distances based on map scales. Not only will we walk through this example, but you'll also get a chance to flex your math muscle along the way!

So, here’s the setup: You’ve got a map where 1 inch equals 80 miles. You need to find out how far apart two cities are when they’re 3 1/5 inches apart. The options are as follows:

• A. 240 miles
• B. 256 miles
• C. 300 miles
• D. 320 miles

Sounds straightforward, right? But let’s break it down step by step to ensure you grasp the concepts without feeling overwhelmed.

Converting Mixed Numbers Like a Pro

First things first, let’s convert that 3 1/5 inches into an improper fraction. Hang in there, because this part is key. Mixed numbers can sometimes throw you for a loop! Here’s how it works:

[ 3 \frac{1}{5} = 3 + \frac{1}{5} = \frac{(3 \times 5 + 1)}{5} = \frac{(15 + 1)}{5} = \frac{16}{5} ]

Who knew fractions could be this fun? Trust me; they get easier with practice.

The Distance Calculation

Now that we’ve got an improper fraction, it's time to transform that map measurement into actual miles. Using the scale of 1 inch = 80 miles, we can calculate the distance as follows:

[ \text{Distance in miles} = \text{Distance on map (in inches)} \times 80 \text{ miles/inch} ]

Plugging in what we've got:

[ \text{Distance in miles} = \left(\frac{16}{5} \text{ inches}\right) \times 80 \text{ miles/inch} ]

Now, here’s where things get interesting. Let’s multiply through:

[ \text{Distance in miles} = \frac{(16 \times 80)}{5} ]

That’s right! We just levelled up our math game. Now, doing the multiplication:

[ \text{Distance in miles} = \frac{1280}{5} \text{ miles} ]

And hey, we’re only one calculation away from victory. What does that reduce to?

[ \text{Distance in miles} = 256 \text{ miles} ]

Bringing It All Together

So, what’s the verdict? The distance between those two cities is 256 miles, making option B the correct answer.

Taking the time to understand how to decode map scales and work with fractions can make all the difference in your preparation for the AFCT. Remember, practice makes perfect.

If you feel a bit flustered when faced with fractions or map questions, don’t sweat it! Break things down. Use real-world examples, like calculating distances for a road trip—because who doesn't love planning an adventure? Just imagine cruising along, knowing you can measure distance like a pro.

So, keep practicing, stay curious, and best of luck with your AFCT prep! You’ve got this!