TEAS Math: Ratios, Rates, and Proportions Explained
Ratios, rates, and proportions are useful mathematical concepts that appear in many everyday situations. They help you compare quantities, calculate costs, and solve problems involving different units. The key to solving these questions is identifying what is being compared and keeping the units consistent.
1. Understand ratios
A ratio compares two quantities. It can be written using a colon, as a fraction, or in words. Suppose a study group has 8 nursing students and 12 students from other programs. The ratio of nursing students to other students is: \[ 8:12=2:3 \] Both numbers can be divided by 4 to simplify the ratio. Pay attention to the order. The ratio of nursing students to other students is not the same as the ratio of other students to nursing students.
2. Calculate unit rates
A rate compares quantities measured in different units. A unit rate expresses the comparison per one unit. For example, if a student completes 45 practice questions in 90 minutes, the rate is: \[ \frac{45\text{ questions}}{90\text{ minutes}} =0.5\text{ questions/minute} \] That is equivalent to 30 questions per hour. Unit rates are useful for comparing speed, prices, production, and other quantities. Always include the appropriate units so you know what the result means.
3. Solve proportions
Read the problem carefully and identify the quantities that have a consistent relationship. Suppose four notebooks cost $12 at the same price per notebook. How much would ten notebooks cost? First, calculate the price of one notebook: \[ \$12\div4=\$3 \] Then multiply by ten: \[ 10\times\$3=\$30 \] This method is often easier than setting up a proportion immediately. Both approaches work when the relationship is proportional.
5. Avoid common errors
Common mistakes include reversing a ratio, mixing units, and assuming that every relationship is proportional. For example, a discount or a delivery fee may change the relationship between the number of items and the total price. Read the conditions before applying a formula. After calculating an answer, ask whether its size makes sense. If ten notebooks cost less than four notebooks at the same unit price, recheck your work.
6. Build accuracy through practice
Practise several questions involving simplified ratios, unit rates, and proportions. Show each step rather than relying on mental calculations alone. If you get an answer wrong, determine whether the error came from setting up the relationship, performing the calculation, or interpreting the units.
Final thoughts
Ratios, rates, and proportions become easier when you identify the quantities being compared and keep the units consistent. Practise with different problem formats and use estimation to check whether your answers are reasonable.
