Yeah yeah, I know, but check THIS out…
UNBELIEVABLY AWESOME ON A LEVEL NOT YET SEEN.
Proportions might sound fancy, but they’re just equal fractions in disguise. The SAT loves to spice things up by putting a variable, like x, in both fractions, and then sneaking in a constant, like k, on the right side. Your mission? Solve for that constant. If test anxiety or SAT anxiety makes you nervous, don’t worry—cross-multiplication is your secret weapon, and this process is way easier than it seems.
Let’s break it all down step by step so you can tackle these problems like a pro.
What’s a Proportion?
Use Cross-Multiplication
When you see a proportion, cross-multiplication is the magic trick that simplifies it into a single equation. Here’s how it works:
- Multiply the numerator of the first fraction by the denominator of the second.
- Multiply the numerator of the second fraction by the denominator of the first.
- Set the two products equal to each other.
Solve for the Constant
Let’s continue with the example.
A Full Example Problem
Let’s work through a complete SAT-style problem.
Another Practice Problem
Step 6: Watch Out for Common Traps
When solving proportions with variables, keep an eye out for these common mistakes:
Test Anxiety Tip: Take It Step by Step
If SAT anxiety has you feeling frazzled, just break these problems into smaller pieces:
- Cross-multiply.
- Expand and simplify.
- Solve for the constant by dividing.
Keeping your work neat and organized can make a huge difference in staying calm and focused.
Final Thoughts
Proportion problems with variables are just puzzles waiting to be solved. Cross-multiplying is your best friend, and with practice, these questions will start to feel like second nature.
For more tips and tricks to make SAT math easier, check back on this blog. With a little practice and a clear plan, you’ve got everything you need to tackle these problems and ace your SAT. Good luck, and go show those fractions who’s boss!