Podcast
Questions and Answers
What is the nature of the number calculated by the expression $5 × 11 × 13 + 7$?
What is the nature of the number calculated by the expression $5 × 11 × 13 + 7$?
Which expression always yields a number that ends with the digit 6?
Which expression always yields a number that ends with the digit 6?
For two positive rational numbers, $a$ and $b$ (where $a ≠ b$), what type of number is $(√a + √b)(√a - √b)$?
For two positive rational numbers, $a$ and $b$ (where $a ≠ b$), what type of number is $(√a + √b)(√a - √b)$?
If $p$ is a positive rational number which is not a perfect square, then what type of number is $-3p$?
If $p$ is a positive rational number which is not a perfect square, then what type of number is $-3p$?
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Which of the following is true in the Euclidean Division Lemma when $a = bq + r$?
Which of the following is true in the Euclidean Division Lemma when $a = bq + r$?
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What is always true about the Highest Common Factor (HCF) in relation to the Least Common Multiple (LCM)?
What is always true about the Highest Common Factor (HCF) in relation to the Least Common Multiple (LCM)?
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The product of two consecutive natural numbers is always which of the following?
The product of two consecutive natural numbers is always which of the following?
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For the expression $pn = (a × 5)^n$ to end with the digit zero, what should $a$ be for natural number $n$?
For the expression $pn = (a × 5)^n$ to end with the digit zero, what should $a$ be for natural number $n$?
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Which of the following is a property of the Highest Common Factor (HCF)?
Which of the following is a property of the Highest Common Factor (HCF)?
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What can be said about the product of two consecutive natural numbers?
What can be said about the product of two consecutive natural numbers?
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For which of the following expressions would the output always be an irrational number?
For which of the following expressions would the output always be an irrational number?
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If $p$ is a positive rational number that is not a perfect square, what can we conclude about $-3p$?
If $p$ is a positive rational number that is not a perfect square, what can we conclude about $-3p$?
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Which condition must hold true in Euclid's Division Lemma for $a = bq + r$?
Which condition must hold true in Euclid's Division Lemma for $a = bq + r$?
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What type of number is always represented by $√a - √b$ when $a$ and $b$ are two positive rational numbers and $a ≠ b$?
What type of number is always represented by $√a - √b$ when $a$ and $b$ are two positive rational numbers and $a ≠ b$?
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Determine the nature of the decimal representation of $3.131131113...$.
Determine the nature of the decimal representation of $3.131131113...$.
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Which expression is guaranteed to yield a number that is always positive?
Which expression is guaranteed to yield a number that is always positive?
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Study Notes
Multiple Choice Questions - Study Notes
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Terminating Decimal Expansion: Certain fractions have decimal expansions that end. Numbers like 37/45, 21/25 , and 17/49 do not have terminating decimal expansions. 22/32 and 89/49 are examples of non-terminating decimal expansions.
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HCF and LCM: The highest common factor (HCF) and lowest common multiple (LCM) of numbers are calculated to find relationships between them. For example: the HCF x LCM for 50 and 20 is 1000.
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Euclid's Division Lemma: This principle states that given two positive integers 'a' and 'b', there exist unique integers 'q' and 'r' so that a=bq+r where 0 ≤ r less than b. The remainder must be 0 or a positive number smaller than 'b'.
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Rational Number Decimal Expansion: Rational numbers have decimal expansions which either terminate (e.g., 22.5) like numbers in Q5, or repeat in a pattern. Fractions with denominators having only 2 and/or 5 as prime factors will terminate in their decimal representation, like 22.5 /32 or 11/22 .
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Co-prime Numbers: Two numbers are co-prime (or relatively prime) if their greatest common divisor (GCD) or highest common factor (HCF) is 1. If p and q are co-prime, then HCF(p, q)=1.
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Prime Numbers and LCM: If p and q are prime numbers, then the LCM(p, q) is pq.
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HCF and LCM relationship: HCF(a, b) × LCM(a, b)=a ×b, for any two positive integers a, and b. For example, HCF(2520, 6600) = 40 and LCM(2520, 6600) = 252k. If one knows these values and the relationship for a and b , one can find k by multiplying the given values in this way.
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Non-Terminating, Repeating Decimals: Not all rational numbers have terminating decimal expansions. If a fraction's denominator includes prime factors other than 2 and/or 5, its decimal expansion will repeat. For example, 35/14 which is 2.5 has a terminating decimal expansion. On the other hand, 7/12 has a non-terminating and repeating decimal.
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Prime Factorization: Finding the prime factors of a number is important in calculating their HCF and LCM. For example, 5005 = 5 x 7 x 11 x 13 has 4 prime factors.
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Odd/Even Integers: Integers can be expressed in specific forms using parameters, for example, every even integer is 2m. And an odd integer can be expressed as 2q+1.
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Coprime Numbers and Squares: If two positive integers a and b are coprime, then a² and b² are also coprime (i.e., HCF(a², b²)=1).
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Least Prime Factor: The least prime factor of a number is the smallest prime number that divides that number evenly.
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Irrational Numbers: Irrational numbers have decimals that do not repeat and do not terminate. For example, √2, π and √5 are irrational numbers.
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Description
Test your knowledge on decimal expansions, HCF, LCM, and Euclid's Division Lemma in this math quiz. Understand the characteristics of rational numbers and how to calculate their decimal representations. Perfect for students looking to strengthen their foundation in mathematics.
