Match your result to the answer field
ETS distinguishes between one-field numerical answers, for an integer or decimal, and two-field fraction answers: numerator followed by denominator. If there is no rounding instruction, enter the exact value. These exercises specify the expected format; compare your answer with the worked solution, as there is no automated scoring.
To avoid a final-entry mistake, write your answer with its units in your notes, then remove the units only when entering it. If the prompt asks for cents and you calculate $2.40, enter 240. The calculator will not catch this mismatch because your calculations may be perfectly accurate.
Exercise 1: convert before calculating speed
Speed is distance divided by time. Putting the correct units in the denominator is safer than memorizing an automatic multiplication rule.
A cyclist travels 18 kilometers in 45 minutes at a constant speed. What is the cyclist’s speed in kilometers per hour? Enter a number.
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The solution, step by step
24.
The method in action
- Forty-five minutes is 45/60 = 3/4 of an hour. The speed is 18 ÷ (3/4) = 24 km/h.
- 0.4 is kilometers per minute, not the requested unit. 13.5 results from multiplying instead of dividing. Check: traveling 18 km in less than an hour requires a speed above 18 km/h.
Exercise 2: keep the exact value
Fractions help you avoid rounding a repeating decimal too early. Enter the numerator and denominator in the correct order; the word of often asks for a proportion of the whole, not the ratio between two subgroups.
A box contains 14 blue tokens and 10 green tokens. A token is selected at random, with each token equally likely to be selected. What fraction of the tokens are green? Enter your answer as a fraction.
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The solution, step by step
Numerator: 5; denominator: 12.
The method in action
- There are 24 tokens in total, 10 of which are green. The fraction is 10/24 = 5/12.
- 10/14 compares green tokens with blue tokens, rather than giving the fraction of the total. 12/5 reverses the proportion and is greater than 1. A rounded decimal such as 0.42 does not use the requested fraction format.
Exercises 3 and 4: keep full precision until the end
Rounding each step and reusing the rounded number can change the final result. Keep a fraction or enough digits during the calculation and round only once, as instructed.
A runner covers 5 kilometers in 27 minutes. What is the runner’s average speed in kilometers per hour? Round your answer to the nearest tenth.
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The solution, step by step
11.1.
The method in action
- The speed is 5 × 60 / 27 = 100/9 = 11.111… km/h. Rounded to the nearest tenth, it is 11.1; English decimal notation uses a period.
- 11 is rounded to the nearest whole number and 11.11 to the nearest hundredth. About 0.2 would express speed in kilometers per minute.
Each storage crate can hold at most 8 identical devices. What is the least number of crates needed to store 53 devices? Enter an integer.
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The solution, step by step
7.
The method in action
- 53/8 = 6.625, but the number of crates must be an integer. Six crates hold at most 48 devices; seven are enough for 53.
- This is not a standard rounding instruction: least and at most define a capacity. In a different situation, such as the number of complete batches you can make, the whole-number choice could go in the other direction.
The pitfall
The pitfall to avoid
Rounding because a decimal looks too long is a mistake. Precision comes from the question, not from how the result looks. Keep an exact fraction when the format requires it; for a count of objects, reason from the situation.
A three-step check
Before finishing, ask what your number measures. “24” alone says nothing; “24 kilometers per hour” can be compared directly with the prompt. Then check its scale: a probability is between zero and one, a duration is positive, and a capacity is sufficient.
Finally, reread the question and check the expected format. In your error log, separate modeling, calculation, and entry errors. If the model and calculation were correct, repeating ten identical operations is less useful than practicing this final check across five different quantities.
Key takeaways
- Write the result with its units first.
- Keep the exact value until the final calculation.
- Distinguish requested rounding from a decision that requires a whole number.