Simplifying Expressions: A Guide to TEAS ATI Mathematics

When it comes to the Test of Essential Academic Skills (TEAS) ATI Mathematics Practice Test, understanding how to simplify expressions can be a game-changer. You might ask, why does simplifying matter? Well, in mathematics, simplifying expressions not only saves time but also leads to clearer problem-solving. Ready to dig into a classic example? Let’s simplify the expression (4 \left( \frac{2}{3} \right) / 1 \left( \frac{1}{6} \right)).

First off, let’s tackle that mixed number. It can be tricky at times, but don’t fret! To convert (1 \left( \frac{1}{6}\right)) into an improper fraction, multiply the whole number by the denominator, then add the numerator. So here we have (1 \times 6 + 1 = 7). This means (1 \left( \frac{1}{6}\right)) becomes (\frac{7}{6}). Simple enough, right?

Now, let’s rewrite (4 \left( \frac{2}{3}\right)). Do you feel a little confused about multiplying whole numbers and fractions? No worries! Just remember that multiplication means multiplying the numerators and denominators separately. Here, (4 \times \frac{2}{3} = \frac{8}{3}).

Now we’ve transformed our problem into multiplying fractions: [ \frac{8}{3} \div \frac{7}{6} ]. If you’re wondering how to manage division of fractions, here’s a nifty little trick: change it to multiplication by the reciprocal! So instead of dividing, you’ll now multiply: [ \frac{8}{3} \times \frac{6}{7}. ]

Time to multiply it out! Multiply the numerators together (8 \times 6 = 48) and the denominators (3 \times 7 = 21), giving us (\frac{48}{21}). Can you simplify that? You bet! Both numbers can be divided by their greatest common factor, which here is 3. That leads us to: [ \frac{16}{7} \quad \text{or as a mixed number} \quad 2 \frac{2}{7}. ]

Now, for the sake of context, let's circle back to that answer option. The correct answer would indeed be (4), if we mistook it along the way. Initially, you might have felt daunted by mixed numbers or misunderstood how to transform division into multiplication, but now, look at how clear it all looks!

As you gear up for the TEAS, us math lovers remember that every little step in simplifying shapes how we attack larger problems. So, practice these techniques! Who knew that simplifying could be both a strategy for the test and a confidence builder for your math skills?

Oh, and speaking of practice — don’t forget to explore various questions and examples. It’s all about sharpening those skills. You'll face plenty more mixed numbers and fraction work in the TEAS, so the more you simplify, the better you get! So, the next time you walk into that testing room, you’ll be pumped and ready to simplify with the best of them!