Odd and Even Numbers

1Summary 重點摘要

Odd: 1,3,5,7,9. Even: 2,4,6,8,10. Look at the last digit.

2Vocabulary cards Vocabulary

3Step by step Steps

1. Step 1: Pair them upTo tell odd from even, split things into pairs of two; this is the most basic and reliable method. Why does it work? Because an even number is exactly one whose things can all be paired. Example: 6 sweets split in twos make exactly 3 pairs with none left, so 6 is even. Take care that every pair must hold exactly two things; never group them in threes, for grouping in threes has nothing to do with odd and even.
2. Step 2: One left over means oddAfter splitting into twos, if one thing is left without a partner, the number is odd. Why is one left over? Because the things in an odd number can never all find partners, so one is always left alone. Example: 7 sweets in twos make 3 pairs and 1 sweet extra; that sweet has no partner, so 7 is odd. The easiest mistake is forgetting the leftover one and thinking the split worked out; whether anything is left over is the biggest difference between odd and even.
3. Step 3: Look at the ones digitFor big numbers you need not really split anything; just look at the ones digit on the far right. Why only the ones digit? Whole tens and hundreds always split into pairs exactly, so the ones digit alone decides. Example: 47 has tens digit 4 and ones digit 7; 7 belongs to the odd family, so 47 is odd. The common error is dragging the tens digit into the decision, seeing the 4 there and calling 47 even, which is always wrong.
4. Step 4: The odd familyNumbers whose ones digit is 1, 3, 5, 7 or 9 are odd; these five digits form the odd family. Once you know the members, telling odd from even becomes a simple lookup. Example: 21 ends in 1, 33 ends in 3 and 45 ends in 5, so they are all odd. Watch numbers like 5, 15 and 25: they end in 5 and are odd, so never treat them as even because they sound close to the tens; a clear look at the ones digit keeps you safe.
5. Step 5: The even familyNumbers whose ones digit is 0, 2, 4, 6 or 8 are even; these five digits form the even family. The odd family and the even family together cover every whole number, and each whole number belongs to one of them. Example: 20 ends in 0, 34 ends in 4 and 58 ends in 8, so they are all even. The usual mistake is thinking 0 belongs to neither family; in fact 0 means the split came out exact with nothing left, so 0 belongs to the even family, and this is worth memorising.
6. Step 6: Big numbers use the same trickHowever big the number, the method is the same: find the far-right digit first, then check which family it belongs to. Example: 86 ends in 6, which is in the even family, so 86 is even; 99 ends in 9, which is in the odd family, so 99 is odd. Take care that the longer the number, the calmer you must stay: look only at the ones digit, let the long string of digits in front not frighten you, and never start pairing from the very beginning, which is slow and easy to get wrong.

4Diagrams Diagrams

5Worked example Example

6Common mistakes Mistakes

7Quick check Quick check

8Recap Recap

• Use the ones digit to tell odd or even.
• Odd: 1, 3, 5, 7, 9.
• Even: 0, 2, 4, 6, 8.
• All paired with none left = even.
• The rule works for any size number.