Question 20 of 25beginner🔧 ApplyShort Answer2 marks

Can you say, without actually calculating, which of these numbers are divisible by 9: 999, 909, 900, 90, 990?

Correct Answer

Rule: A number is divisible by 9 if the sum of its digits is divisible by 9.

Observation: All given numbers (999, 909, 900, 90, 990) are made up of only digits 0 and 9.

Why this works: Each digit contributes either 0 or 9 to the digit sum, and both are multiples of 9.

Verification: 999: sum = 27 (divisible by 9) 909: sum = 18 (divisible by 9) 900: sum = 9 (divisible by 9) 90: sum = 9 (divisible by 9) 990: sum = 18 (divisible by 9)

Answer: All of these numbers (999, 909, 900, 90, 990) are divisible by 9.

Exercise: A Shortcut for Divisibility by 9 | Q: 1 | (Page Page 12)
For More Understanding

Explanation

The chapter explains that any number made up of only digits 0 and 9 is divisible by 9 because each digit contributes either 0 or 9 to the digit sum, and both are multiples of 9. For 999: sum = 27 (divisible by 9). For 909: sum = 18 (divisible by 9). For 900: sum = 9 (divisible by 9). For 90: sum = 9 (divisible by 9). For 990: sum = 18 (divisible by 9). Since the sum of digits is divisible by 9 in each case, all numbers are divisible by 9.

Solution Steps

  1. Identify that all numbers are made up of only digits 0 and 9.

  2. Apply the divisibility rule: a number is divisible by 9 if the sum of its digits is divisible by 9.

  3. Recognize that digits 0 and 9 both contribute multiples of 9 to the digit sum.

  4. Conclude that all given numbers are divisible by 9.

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