Problem Solving & Data Analysis • 15% of test
Ratios & Proportions
Select your difficulty level to start practicing. We recommend mastering each level before moving to the next.
Beginner5 Sets
Beginner Practice
Start here to build your foundation. Clear problems and straightforward calculations.
Target Score
400-550
Intermediate5 Sets
Intermediate Practice
Level up with more complex equations and multi-step problems.
Target Score
550-700
Advanced3 Sets
Advanced Practice
Master the hardest concepts. Complex word problems and abstract applications.
Target Score
700-800
What is Ratios & Proportions?
Ratios compare quantities, rates include units, and proportions set ratios equal. These concepts appear in real-world contexts like recipes, maps, and speed problems.
Step-by-Step Strategy
⚠️ Common Traps to Avoid
Frequently Asked Questions
What's the difference between ratio and rate?
Ratios compare same units (3 apples to 2 oranges). Rates compare different units (60 miles per hour).
How do I convert part-to-part to part-to-whole?
If ratio is 3:2, the parts are 3 and 2. Whole is 3+2=5. Part-to-whole is 3/5 or 2/5.
When should I cross-multiply?
When you have a proportion (two equal ratios). Set up a/b = c/d, then ad = bc.
How do I handle inverse proportions?
When one quantity increases, the other decreases. Product stays constant: xy = k.
What's a unit rate?
A rate with denominator 1, like '60 miles per hour'. Find more rate problems in our <a href='/math'>Problem Solving data analysis section</a>.
How common are proportion questions?
Very common! Expect 2-3 questions involving ratios, rates, or proportional relationships.
How do I handle double-ratio problems like A:B and B:C?
Find a common multiplier for B so that the two ratios can be combined into a single A:B:C relationship.
What is a 'Scale Factor' in geometry?
It's the ratio of corresponding side lengths between two similar figures. Area scales by (factor)², and Volume by (factor)³.
How do I calculate density (mass/volume)?
Density is a rate. Use the formula Density = Total Mass / Total Volume. Keep units consistent (e.g., g/cm³) during calculation.
What is a 'Weighted Average'?
When components have different 'weights', multiply each by its weight, sum them up, and divide by the total weight. Common in grade calculations.
How do I solve 'Work Rate' problems?
Sum their individual rates. If A takes 2h and B takes 3h, their combined rate is 1/2 + 1/3 = 5/6 jobs per hour. Then take the reciprocal to find total time.
What if the units are squared, like square feet to square yards?
Remember to square the conversion factor. Since 3 ft = 1 yd, then (3 ft)² = (1 yd)², meaning 9 sq ft = 1 sq yd.
How do I handle currency conversion problems?
Set up a proportion: (Amount in A / Rate A) = (Amount in B / Rate B). Ensure the rates correspond to the same unit.
What is 'Direct Variation'?
A relationship where y = kx. The ratio y/x is constant. Master variation in our <a href='/math/ratios-proportions/intermediate'>Intermediate Ratios & Proportions sets</a>.
What is 'Inverse Variation'?
A relationship where y = k/x. The PRODUCT x·y is always constant, rather than the ratio.