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Mathematics Activity :
Even Numbers and Odd Numbers
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1. 450
There are 900 three-digit numbers starting with 100 and ending with 999. Half of these are odd numbers and half of these are even numbers.
3. 45
There are 90 two-digit numbers starting with 10 and ending with 99. Half of these are even numbers and half of these are even numbers.
5. 567
The even numbers are 322 and 456. The odd numbers are 567 and 989. So, the smallest odd number is 567.
7. 2640
2640 > 2604 > 2406 > 2046.
9. 3
The 3 ways to express 48 as the product of two even numbers are 2 × 24, 4 × 12, 6 × 8. The fourth way is 3 × 16, but 3 is an odd number.
11. 219
The next odd number after 192 is 193. The 13th odd number after 193 will be 193 + (13 × 2) = 219.
13. 97
When a number is multiplied by 5, it gives a number with a 0 or 5 in the units place. Only an odd number when multiplied by 5 gives an odd number with a 5 in the units place.
15. 0
The sum of two odd numbers will always be an even number. If an even number is divided by 2, the remainder is 0.
17. 7
The fourth odd number serially after 198 is 205. Note that 198 + 7 = 205.
19. 175
The odd numbers between 30 and 40 are 31, 33, 35, 37, 39. Their sum is (30 × 5) + (1 + 3 + 5 + 7 + 9) = 150 + 25 = 175. Note that 175 is simply 5 times the middle number (i.e., 5 × 35 = 175).
21. 252
The sixth, seventh and eighth even numbers after 70 are 82, 84, 86. Their sum is (80 × 3) + (2 + 4 + 6) = 240 + 12 = 252.
23. 6
The difference between consecutive odd numbers is 2. Therefore the difference between the 23rd and the 26th odd numbers will be 2 × (26 − 23) = 6.
25. 5
The even numbers are 22, 24, 26, 28, 30. The odd numbers are 21, 23, 25, 27, 29. Thus, the answer is
(22 + 24 + 26 + 28 + 30) − (21 + 23 + 25 + 27 + 29)
= (22 − 21) + (24 − 23) + (26 − 25) + (28 − 27) + (30 − 29)
= 1 + 1 + 1 + 1 + 1 = 5.
27. 8997
The greatest four-digit even number is 9998. The smallest four-digit odd number is 1001. Their difference is 8997.
29. 2
The 2 three-digit odd numbers that can be formed are 507 and 705.
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