a) 20 divided into 5 is 4 b) 5 divided into 20 is 4 c) 5 is a factor of 20 d) 20 is a divisor of 5 e) 5 divides into 20 f) 20 is a multiple of 5 g) 5 is divisible by 20 h) 20 divided by 5 is 4 i) 5 divided by 20 is 4 j) 20 is a factor of 5 k) 5 is a divisor of 20 1) 20 divides into 5 m) 5 is a multiple of 20 n) 20 is divisible by 5
The Correct Answer and Explanation is :
Correct Statements:
- (a) 20 divided into 5 is 4 → Incorrect
- (b) 5 divided into 20 is 4 → Correct
- (c) 5 is a factor of 20 → Correct
- (d) 20 is a divisor of 5 → Incorrect
- (e) 5 divides into 20 → Correct
- (f) 20 is a multiple of 5 → Correct
- (g) 5 is divisible by 20 → Incorrect
- (h) 20 divided by 5 is 4 → Correct
- (i) 5 divided by 20 is 4 → Incorrect
- (j) 20 is a factor of 5 → Incorrect
- (k) 5 is a divisor of 20 → Correct
- (l) 20 divides into 5 → Incorrect
- (m) 5 is a multiple of 20 → Incorrect
- (n) 20 is divisible by 5 → Correct
Explanation (300 Words):
The mathematical relationship between numbers, especially division, factors, multiples, and divisors, often causes confusion. Let’s analyze these terms and apply them to the given statements.
- Division:
- Division involves dividing one number by another. The result is the quotient. For example, ( 20 \div 5 = 4 ), so statement (h) is correct. The reverse, ( 5 \div 20 ), gives a fraction, not 4, making (i) incorrect.
- Factors and Multiples:
- A factor of a number is a whole number that divides it exactly. Since ( 5 \times 4 = 20 ), 5 is a factor of 20, making (c) correct. The reverse, “20 is a factor of 5,” is incorrect because 20 does not divide 5 exactly.
- A multiple of a number is the product of that number and an integer. Since ( 20 = 5 \times 4 ), 20 is a multiple of 5, making (f) correct.
- Divisors:
- A divisor divides another number without a remainder. Since ( 20 \div 5 = 4 ), 5 is a divisor of 20, making (k) correct. However, 20 is not a divisor of 5, so (d) is incorrect.
- Divisibility:
- A number is divisible by another if the division yields a whole number. Since ( 20 \div 5 = 4 ), 20 is divisible by 5, making (n) correct. Conversely, ( 5 \div 20 ) does not yield a whole number, so (g) is incorrect.
This careful analysis highlights correct and incorrect statements based on arithmetic rules.