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Number system and operations — SHSAT practice questions

Number system and operations on the SHSAT covers comparing fractions with decimals, integer arithmetic on a number line, and rounding before a total. A student has to rewrite mixed forms to rank them, treat a left move as subtraction and a right move as addition, and round each share of a bill then add. Comparison items list several cutoffs in mixed form and ask which is largest, with choices that match the given expressions, so ranking by numerators or ignoring place value is a common miss. Estimation items tempt students to add first and round once, while number-line items hide signed arithmetic in left and right wording.

  • Section: Mathematics 57 questions on the paper
  • 354 practice questions in the app

Sample questions

Question 1

In a quiz tournament, the score cutoffs are 274\dfrac{27}{4}, 6.8, 6910\dfrac{69}{10}, and 275\dfrac{27}{5}. Which cutoff is the greatest?

  1. A275\dfrac{27}{5}
  2. B274\dfrac{27}{4}
  3. C6.8
  4. D6910\dfrac{69}{10}
Show answer

Answer: D — 6910\dfrac{69}{10}

Convert the fractions to decimals: 275=5.4\dfrac{27}{5}=5.4, 274=6.75\dfrac{27}{4}=6.75, and 6910=6.9\dfrac{69}{10}=6.9. Since 6.9>6.8>6.75>5.46.9>6.8>6.75>5.4, the greatest cutoff is 6910\dfrac{69}{10}.

Question 2

In a math-club number-line game, a token starts at 4, moves left 11 units, then right 6 units. At what value does it end?

  1. A-13
  2. B-1
  3. C1
  4. D21
Show answer

Answer: B — -1

4−11+6=−14-11+6=-1.

Question 3

Three friends’ shares of a restaurant bill before tip are 14.62, 18.37, and 21.89. Round each share to the nearest dollar and add. What is the estimated total?

  1. A53
  2. B54
  3. C55
  4. D56
Show answer

Answer: C — 55

Rounding gives 15, 18, and 22. The estimated total is 15+18+22=5515 + 18 + 22 = 55 dollars.

Practice 354 Number system and operations questions in the app

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