117 total questions (5 free)
What is the value of 2/5 multiplied by ¾ divide by 8/5
Correct Answer: C
Rationale: To solve (2/5) * (3/4)÷ (8/5), first multiply the fractions: (2/5) * (3/4) = (2*3)/(5*4) = 6/20 = 3/10. Then, divide by 8/5, which is equivalent to multiplying by 5/8: (3/10) * (5/8) = (3*5)/(10*8) = 15/80 = 3/16. Thus, the correct answer is 3/16.
On a number line, what is the distance, in units, between 16 and -25
Correct Answer: 41 units
Rationale: The distance between two points on a number line is the absolute difference between them. Calculate |16 - (-25)| = |16 + 25| = 41. Thus, the distance is 41 units.
Simplify 6^2 - 3^2
Rationale: Calculate 6^2 = 36 and 3^2 = 9. Then, subtract: 36 - 9 = 27. Thus, the correct answer is 27.
2^3 * 27^(1/3) * 1^3
Correct Answer: B
Rationale: First, compute each term: 2^3 = 8, 27^(1/3) is the cube root of 27, which is 3 (since 3^3 = 27), and 1^3 = 1. Then, multiply: 8 * 3 * 1 = 24. Thus, the correct answer is 24.
((5^3 * 2^4)^2)(5^(-2) * 2^5)
Rationale: First, simplify inside the parentheses: (5^3 * 2^4)^2 = (5^3)^2 * (2^4)^2 = 5^6 * 2^8. Then, multiply by 5^(-2) * 2^5: (5^6 * 2^8) * (5^(-2) * 2^5) = 5^(6-2) * 2^(8+5) = 5^4 * 2^13. The negative in option D is incorrect as all bases are positive. Thus, the correct answer is 5^4 * 2^13.
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