ISEE Upper Level Quantitative Reasoning Flashcards: Estimation And Reasonableness

What this deck covers

This deck focuses on Estimation And Reasonableness, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Upper Level Quantitative Reasoning.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: What is the closest estimate of $\frac{51}{98}$ using a benchmark fraction?

Answer: $\frac{51}{98} \approx \frac{1}{2}$. 51/98 simplifies close to 1/2, a benchmark fraction useful for estimating proportions or divisions.

Flashcard 2: Identify the reasonable estimate for $\frac{5000}{0.5}$: $2500$, $10{,}000$, or $100{,}000$?

Answer: $10{,}000$. Dividing by 0.5 is equivalent to multiplying by 2, so 5000 × 2 = 10,000 is the reasonable estimate.

Flashcard 3: Identify the reasonable estimate for $0.02 \times 300$: $0.6$, $6$, or $60$?

Answer: $6$. The product 0.02 × 300 equals 6 exactly, making it the reasonable choice among the given estimates.

Flashcard 4: What is the closest estimate of $\frac{398}{8}$ using compatible numbers?

Answer: $\frac{400}{8} = 50$. Adjusting 398 to the compatible number 400, which is easily divisible by 8, gives a close approximation of the quotient.

Flashcard 5: What is the closest estimate of $\frac{7}{8}$ as a decimal to assess reasonableness?

Answer: $\frac{7}{8} = 0.875 \approx 0.88$. Approximating 0.875 to 0.88 simplifies decimal operations while maintaining reasonable accuracy for assessments.

Flashcard 6: What is the closest estimate of $\frac{0.48}{0.12}$ using compatible numbers?

Answer: $\frac{0.48}{0.12} = 4$. 0.48 and 0.12 are compatible as they divide evenly to 4, matching the exact quotient for estimation.

Flashcard 7: What is the closest estimate of $12\%$ of $79$ using rounding?

Answer: $10\%$ of $80$ is $8$ (so about $9$ to $10$). Rounding to 10% of 80 gives 8, then adjusting for the slight increase in percentage and decrease in base estimates 9 to 10.

Flashcard 8: What is the closest estimate of $\frac{602}{29}$ using compatible numbers?

Answer: $\frac{580}{29} = 20$. Adjusting 602 to 580, a multiple of 29 (29 × 20 = 580), simplifies to an underestimate of the quotient.

Flashcard 9: What is the closest estimate of $\frac{5}{6}$ as a decimal to assess reasonableness?

Answer: $\frac{5}{6} \approx 0.83$. Converting the fraction to approximately 0.83 allows for easy comparison in calculations involving decimals.

Flashcard 10: What is the closest estimate of $0.49 \times 198$ using easy rounding?

Answer: $0.5 \times 200 = 100$. Rounding 0.49 up to 0.5 and 198 up to 200 uses easy numbers to approximate the product for quick verification.

Flashcard 11: What is the closest estimate of $\sqrt{50}$ using nearby perfect squares?

Answer: $\sqrt{49} = 7$. Since 50 is close to the perfect square 49, its square root approximates to 7, aiding in reasonableness checks.

Flashcard 12: What is the closest estimate of $\frac{19}{21}$ using a benchmark fraction?

Answer: $\frac{19}{21} \approx 1$. The fraction 19/21 is close to 1, a benchmark that overestimates slightly for quick reasonableness assessments.

Flashcard 13: What is the closest estimate of $\sqrt{130}$ using nearby perfect squares?

Answer: $\sqrt{121} = 11$. 130 is nearer to 121 than to 144 among perfect squares, so its square root estimates closer to 11.

Flashcard 14: What is the closest estimate of $99 + 101 + 203$ by rounding to the nearest ten?

Answer: $100 + 100 + 200 = 400$. Rounding each number to the nearest ten—99 to 100, 101 to 100, 203 to 200—yields a close sum approximation.

Flashcard 15: Identify the reasonable estimate for $198 \times 51$: $1000$, $10{,}000$, or $100{,}000$?

Answer: $10{,}000$. Estimating 200 × 50 = 10,000 provides a reasonable order of magnitude among the options for the product.

Flashcard 16: What is the closest estimate of $15\%$ of $60$ using $10\%$ and $5\%$?

Answer: $6 + 3 = 9$. Breaking 15% into 10% and 5% of 60 simplifies to 6 + 3, providing an exact estimate for reasonableness.

Flashcard 17: What is the closest estimate of $35\%$ of $200$ using benchmark percents?

Answer: $0.35 \times 200 = 70$. Treating 35% as 0.35 and multiplying by 200 uses a benchmark approach for an exact yet estimative calculation.

Flashcard 18: What is the closest estimate of $\frac{2}{9}$ using a benchmark fraction?

Answer: $\frac{2}{9} \approx \frac{1}{4}$. Among benchmark fractions like 0, 1/4, 1/2, 2/9 is nearest to 1/4 for approximate comparisons.

Flashcard 19: What is the closest estimate of $49^2$ by rounding $49$ to a nearby number?

Answer: $50^2 = 2500$. Rounding 49 up to 50 simplifies squaring, offering an overestimate that assesses the reasonableness of the actual 2401.

Flashcard 20: What is the closest estimate of $\frac{3}{11}$ as a decimal to assess reasonableness?

Answer: $\frac{3}{11} \approx 0.27$. Rounding the repeating decimal 0.2727... to 0.27 provides a useful estimate for evaluating calculation reasonableness.

Flashcard 21: What is the closest estimate of $4.98 \times 0.19$ using easy rounding?

Answer: $5 \times 0.2 = 1$. Rounding 4.98 to 5 and 0.19 to 0.2 uses simple values to overestimate the product for reasonableness.

Flashcard 22: What is the closest estimate of $498 + 503$ by rounding to the nearest ten?

Answer: $500 + 500 = 1000$. Rounding 498 to 500 and 503 to 500, as the units digits dictate rounding up and down respectively, provides a quick sum estimate.

Flashcard 23: What is the closest estimate of $\frac{71}{9}$ by using a nearby multiple of $9$?

Answer: $\frac{72}{9} = 8$. Using 72 as a nearby multiple of 9 simplifies the division, providing an estimate near the actual value of about 7.89.

Flashcard 24: What is the closest estimate of $\frac{3.9}{0.2}$ by rounding to friendly numbers?

Answer: $\frac{4}{0.2} = 20$. Rounding 3.9 to 4 while keeping 0.2 creates friendly numbers for an overestimate of the quotient.

Flashcard 25: What is the closest estimate of $19.8 \times 5.1$ by rounding to whole numbers?

Answer: $20 \times 5 = 100$. Rounding 19.8 up to 20 and 5.1 down to 5, based on decimal places, yields an approximate product for reasonableness.