Math topic中文

Clever calculation and speed arithmetic

Simplify arithmetic by rounding to friendly numbers, regrouping with the laws of operations, and using benchmark numbers.

Practice questions

  1. 1Find the value of the expression 100−98+96−94+92−90+⋯+8−6+4−2100 - 98 + 96 - 94 + 92 - 90 + \cdots + 8 - 6 + 4 - 2. A. 20 B. 40 C. 50 D. 80 E. 100
  2. 2What is the value of the product (1⋅32⋅2)(2⋅43⋅3)(3⋅54⋅4)⋯(97⋅9998⋅98)(98⋅10099⋅99)(\frac{1 \cdot 3}{2 \cdot 2})(\frac{2 \cdot 4}{3 \cdot 3})(\frac{3 \cdot 5}{4 \cdot 4}) \cdots (\frac{97 \cdot 99}{98 \cdot 98})(\frac{98 \cdot 100}{99 \cdot 99})…
  3. 3What is the ones digit of the value of the below expression? 222222−22222−2222−222−22−2222222 - 22222 - 2222 - 222 - 22 - 2 A. 0 B. 2 C. 4 D. 6…
  4. 4For positive integer nn, the factorial notation n!n! represents the product of the integers from nn to 1. (For example…
  5. 5What is the value of the following expression ? 1−2+3−4+5+6−7+8−9+10+11−121 - 2 + 3 - 4 + 5 + 6 - 7 + 8 - 9 + 10 + 11 - 12 A. 7 B. 10 C. 13 D. 1…
  6. 6What is the value of 1+3+5+⋯+2017+2019−2−4−6−⋯−2016−20181 + 3 + 5 + \dots + 2017 + 2019 - 2 - 4 - 6 - \dots - 2016 - 2018? A. -1010 B. -1009 C. 1008 D. 1…
  7. 7What is the value of 13⋅24⋅35⋯1820⋅1921⋅2022\frac{1}{3} \cdot \frac{2}{4} \cdot \frac{3}{5} \cdots \frac{18}{20} \cdot \frac{19}{21} \cdot \frac{20}{22}…
  8. 8Which of the following is the correct order of the fractions 1511\frac{15}{11}, 1915\frac{19}{15}, and 1713\frac{17}{13}, from…
  9. 9What is the sum of the 24 numbers in the below grid ? A. 60 B. 62 C. 64 D. 66 E. 68
  10. 10When 0.000315 is multiplied by 7928564 the product is closest to which of the following? A. 210 B. 240 C. 2100 D. 2400 E…
  11. 11Ningli looks at the 6 pairs of numbers directly across from each other on a clock. She takes the average of each pair of…
  12. 12计算 (1)312+(−12)−(−13)+223(2)−82+3×(−2)2+(−6)÷(−13)2(3)412×[−9×(−13)2−0.8]÷(−514)(1)3 \dfrac {1}{2}+(- \dfrac {1}{2})-(- \dfrac {1}{3})+2 \dfrac {2}{3}(2)-8^{2}+3×(-2)^{2}+(-6)÷(- \dfrac {1}{3})^{2}(3)4 \dfrac {1}{2}×[-9×(- \dfrac {1}{3})^{2}-0.8]÷(-5 \dfrac {1}{4})…
  13. 13What is the value of the below expression in decimal form? 4411+11044+441100\frac{44}{11} + \frac{110}{44} + \frac{44}{1100} A. 6.4 B.…
  14. 14What is the value of the expression 1⋅2⋅3⋅4⋅5⋅6⋅7⋅81+2+3+4+5+6+7+8\frac{1 \cdot 2 \cdot 3 \cdot 4 \cdot 5 \cdot 6 \cdot 7 \cdot 8}{1 + 2 + 3 + 4 + 5 + 6 + 7 + 8}…
  15. 15How many perfect cubes lie between 28+12^8 + 1 and 218+12^{18} + 1, inclusive? A. 4 B. 9 C. 10 D. 57 E. 58