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The Number System Practice Questions

Common Core (US) · Common Core Math Grade 8 · 143 free MCQs with instant results and detailed explanations.

143
Total
43
Easy
73
Medium
27
Hard

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Sample Questions from The Number System

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Q1
Easy
What is the result of adding the rational numbers 3/4 and 2/5?
A. 23/20
B. 7/20
C. 19/20
D. 1/5
Show Answer & Explanation
Correct Answer: A
To add 3/4 and 2/5, we need a common denominator which is 20. Rewriting: 3/4 = 15/20 and 2/5 = 8/20. Adding these gives 15/20 + 8/20 = 23/20.
Q2
Easy
Which of the following is a decimal representation of the rational number 5/8?
A. 0.625
B. 0.75
C. 0.5
D. 0.9
Show Answer & Explanation
Correct Answer: A
Dividing 5 by 8 gives 0.625. Thus, the decimal representation of the rational number 5/8 is 0.625.
Q3
Easy
If a number is expressed as -2.5, what type of number is it?
A. Natural Number
B. Integer
C. Rational Number
D. Whole Number
Show Answer & Explanation
Correct Answer: C
The number -2.5 can be expressed as a fraction (-5/2), making it a rational number since rational numbers can be expressed as a fraction of two integers.
Q4
Medium
What is the value of -7 + 4?
A. -3
B. 3
C. 1
D. -1
Show Answer & Explanation
Correct Answer: A
When you add a positive number to a negative number, you subtract the positive from the absolute value of the negative. Here, |-7| is 7, and 7 - 4 = 3, so -7 + 4 = -3.
Q5
Medium
Which expression is equivalent to 3(-2x + 4)?
A. -6x + 12
B. 6x + 12
C. -6x - 12
D. 6x - 12
Show Answer & Explanation
Correct Answer: A
Distributing 3 to both terms inside the parentheses gives us 3 * -2x = -6x and 3 * 4 = 12, resulting in -6x + 12.
Q6
Medium
Which of the following represents the decimal equivalent of the fraction 3/8?
A. 0.375
B. 0.25
C. 0.5
D. 0.625
Show Answer & Explanation
Correct Answer: A
To convert 3/8 to a decimal, divide 3 by 8, which equals 0.375. Hence, option A is correct.
Q7
Medium
If -4 is a root of the equation x^2 + px + q = 0, what is the value of p if the other root is 2?
A. -2
B. 2
C. 6
D. -6
Show Answer & Explanation
Correct Answer: A
Using Vieta's formulas, the sum of the roots is -4 + 2 = -2, so p = -(-2), thus p = -2.
Q8
Hard
If the number of students in a school is 3/4 of the total capacity, and the total capacity is represented by 'C', what expression represents the number of students?
A. C/4
B. C - C/4
C. 3C/4
D. C + C/4
Show Answer & Explanation
Correct Answer: C
If the number of students is 3/4 of the total capacity, it can be directly represented as 3/4 times the capacity, which is 3C/4. This shows the proportional relationship between the students and the total capacity.
Q9
Hard
What is the value of x in the equation √(x + 7) = 5?
A. 18
B. 25
C. 32
D. 5
Show Answer & Explanation
Correct Answer: A
To find x, we square both sides of the equation: (√(x + 7))^2 = 5^2, which gives us x + 7 = 25. Thus, x = 25 - 7 = 18.
Q10
Hard
A number is divided by 12 and the result is 3. What is the original number?
A. 36
B. 24
C. 30
D. 18
Show Answer & Explanation
Correct Answer: A
To find the original number, we multiply the result (3) by the divisor (12). Thus, the original number is 3 * 12 = 36.

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The Number System — Common Core (US) Common Core Math Grade 8 Practice Questions Online

This page contains 143 practice MCQs for the chapter The Number System in Common Core (US) Common Core Math Grade 8. The questions are organized by difficulty — 43 easy, 73 medium, 27 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.