Number bonds to 100
The pairs of numbers that make 100, the rule that finds any of them in seconds, and the slip to watch for.
The answer
Two numbers are a bond to 100 when they add up to 100. The tens bonds are 0 + 100, 10 + 90, 20 + 80, 30 + 70, 40 + 60 and 50 + 50. For any other number, the ones make 10 and the tens make 90: 37 + 63 = 100.
Every number bond to 100
| Tens bond | From the bond to 10 |
|---|---|
| 0 + 100 = 100 | 0 + 10 = 10 |
| 10 + 90 = 100 | 1 + 9 = 10 |
| 20 + 80 = 100 | 2 + 8 = 10 |
| 30 + 70 = 100 | 3 + 7 = 10 |
| 40 + 60 = 100 | 4 + 6 = 10 |
| 50 + 50 = 100 | 5 + 5 = 10 |
| 60 + 40 = 100 | 6 + 4 = 10 |
| 70 + 30 = 100 | 7 + 3 = 10 |
| 80 + 20 = 100 | 8 + 2 = 10 |
| 90 + 10 = 100 | 9 + 1 = 10 |
| 100 + 0 = 100 | 10 + 0 = 10 |
And the other 45 pairs, where the ones are not 0. Each one turned round is a bond too, so with the 11 tens bonds these make all 101.
- 1 + 99
- 2 + 98
- 3 + 97
- 4 + 96
- 5 + 95
- 6 + 94
- 7 + 93
- 8 + 92
- 9 + 91
- 11 + 89
- 12 + 88
- 13 + 87
- 14 + 86
- 15 + 85
- 16 + 84
- 17 + 83
- 18 + 82
- 19 + 81
- 21 + 79
- 22 + 78
- 23 + 77
- 24 + 76
- 25 + 75
- 26 + 74
- 27 + 73
- 28 + 72
- 29 + 71
- 31 + 69
- 32 + 68
- 33 + 67
- 34 + 66
- 35 + 65
- 36 + 64
- 37 + 63
- 38 + 62
- 39 + 61
- 41 + 59
- 42 + 58
- 43 + 57
- 44 + 56
- 45 + 55
- 46 + 54
- 47 + 53
- 48 + 52
- 49 + 51
Try it on a hundred grid
37 + 63 = 100
Each time one part goes up, the other goes down by the same amount, so the total stays 100.
The rule for any pair
Make the ones add to 10 and the tens add to 90. For 37: the ones need 3 more to make 10, and the tens need 60 more to make 90, so the partner is 63. Check: the tens make 90 and the ones make 10, and 90 + 10 = 100.
The tens make 90, not 100, because the ones carry the last 10. When the ones are 0, as in 40 + 60, there is nothing to carry and the tens make 100 on their own.
The slip to watch for: 37 + 73. The tens bonds make it look right, but 30 + 70 = 100 and 7 + 3 = 10, so it comes to 110. Checking the tens make 90 catches it.
The same idea works with money. Change from £1 for something costing 37p is 63p, because 37 + 63 = 100.
Using the bonds
A bond with two different numbers gives four facts. Knowing 45 + 55 = 100 also gives 55 + 45 = 100, 100 − 45 = 55 and 100 − 55 = 45. A double such as 50 + 50 gives only two: 50 + 50 = 100 and 100 − 50 = 50.
In the 11+, bonds to 100 speed up working out change from £1, taking a number away from 100 in one step (100 − 37 = 63), and checking that the percentages in a pie chart add up to 100%.
More number bonds and mental maths
Questions parents ask
What goes with 28 to make 100?
72. The ones need 2 more to make 10, and the tens need 70 more to make 90, so 28 + 72 = 100.
What are the number bonds to 1?
The bonds to 10 written as tenths: 0.3 + 0.7 = 1, 0.4 + 0.6 = 1 and so on. The same idea with hundredths gives pairs such as 0.37 + 0.63 = 1.
What are the number bonds to 1000?
The bonds to 10 made a hundred times bigger: 300 + 700 = 1000. For a number such as 370, use the bond to 100 and multiply by 10: 37 + 63 = 100, so 370 + 630 = 1000.
When do children learn number bonds to 100?
The tens pairs build on bonds to 10 in Year 2, when the national curriculum asks children to derive and use related facts up to 100. Pairs such as 37 + 63 are practised through Years 3 and 4.
Quick mental maths starts with number bonds
11+ maths is timed, and number bonds are behind fast adding, subtracting and working out change. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.