Mastering the Art of Adding Mixed Numbers and Fractions

Adding mixed numbers and fractions can feel intimidating, can't it? But don’t fret! When you're gearing up for the Oilers/Plant Tenders (HHC) Civil Service Exam, mastering this skill can give you a notable edge. Let’s turn this complexity into clarity together, exploring how to add mixed numbers while keeping it engaging.

First up, let’s break down an example: the sum of 3 1/4, 4 1/8, 6 3/8, and 125/8. Easy enough, right? But to tackle this like a pro, we’ll convert each mixed number into improper fractions. Here’s how that goes:

Mixing it Up: Converting Mixed Numbers

Starting with 3 1/4, we convert it as follows:

• (3 \times 4 + 1 = 12 + 1 = 13). Voilà! This transforms into (\frac{13}{4}).

Now let’s do the same for 4 1/8:

• (4 \times 8 + 1 = 32 + 1 = 33), resulting in (\frac{33}{8}).

Next, we tackle 6 3/8:

• This converts to (6 \times 8 + 3 = 48 + 3 = 51), translating to (\frac{51}{8}).

And lucky for us, 125/8 is already ready to roll!

Finding Common Ground: The Common Denominator

Now that we have our improper fractions, it’s time to find a common denominator. The least common denominator between 4 and 8? Drumroll, please... it’s 8!

To make calculations neat and tidy, we’ll convert (\frac{13}{4}) to have a denominator of 8:

• Multiply the numerator and denominator by 2 to get (\frac{26}{8}).

Now that each fraction is dressed in the same attire, summing them becomes straightforward:

[ \frac{26}{8} + \frac{33}{8} + \frac{51}{8} + \frac{125}{8} = \frac{26 + 33 + 51 + 125}{8} = \frac{235}{8} ]

Dressing it Up: Converting Back

Hold the phone! We still need to convert (\frac{235}{8}) back to a mixed number. Performing the division of 235 by 8 gives us 29 with a remainder of 3—now that’s a result we can wrap our heads around!
So, (29 \frac{3}{8}), which simplifies our earlier answers to find the correct choice: it’s 26 3/8.

Recap and Wrap Up!

Adding fractions and mixed numbers doesn’t have to be a math course nightmare. Instead, it becomes a nifty skill to wield, especially in the context of civil service exams. With practice, you’ll have no problem summing up numbers, whether for exams or everyday life.

As you prepare for the Oilers/Plant Tenders exam, remember—you’ve got this! Embrace the challenge and keep refining your skills with the practice you need. Every fraction you conquer brings you one step closer to success!