Find out the digit sums of all the numbers from 40 to 70. Share your observations with the class.

Question

Homi · Accepted Answer

We will add the digits of each number to find its digit sum.

Step 1 — Digit Sums for 40 to 49

We find the digit sum for each number from 40 to 49.

For 40: $4 + 0$ $= 4$

$\boxed{4}$

For 41: $4 + 1$ $= 5$

$\boxed{5}$

For 42: $4 + 2$ $= 6$

$\boxed{6}$

For 43: $4 + 3$ $= 7$

$\boxed{7}$

For 44: $4 + 4$ $= 8$

$\boxed{8}$

For 45: $4 + 5$ $= 9$

$\boxed{9}$

For 46: $4 + 6$ $= 10$

$\boxed{10}$

For 47: $4 + 7$ $= 11$

$\boxed{11}$

For 48: $4 + 8$ $= 12$

$\boxed{12}$

For 49: $4 + 9$ $= 13$

$\boxed{13}$

Step 2 — Digit Sums for 50 to 59

We find the digit sum for each number from 50 to 59.

For 50: $5 + 0$ $= 5$

$\boxed{5}$

For 51: $5 + 1$ $= 6$

$\boxed{6}$

For 52: $5 + 2$ $= 7$

$\boxed{7}$

For 53: $5 + 3$ $= 8$

$\boxed{8}$

For 54: $5 + 4$ $= 9$

$\boxed{9}$

For 55: $5 + 5$ $= 10$

$\boxed{10}$

For 56: $5 + 6$ $= 11$

$\boxed{11}$

For 57: $5 + 7$ $= 12$

$\boxed{12}$

For 58: $5 + 8$ $= 13$

$\boxed{13}$

For 59: $5 + 9$ $= 14$

$\boxed{14}$

Step 3 — Digit Sums for 60 to 70

We find the digit sum for each number from 60 to 70.

For 60: $6 + 0$ $= 6$

$\boxed{6}$

For 61: $6 + 1$ $= 7$

$\boxed{7}$

For 62: $6 + 2$ $= 8$

$\boxed{8}$

For 63: $6 + 3$ $= 9$

$\boxed{9}$

For 64: $6 + 4$ $= 10$

$\boxed{10}$

For 65: $6 + 5$ $= 11$

$\boxed{11}$

For 66: $6 + 6$ $= 12$

$\boxed{12}$

For 67: $6 + 7$ $= 13$

$\boxed{13}$

For 68: $6 + 8$ $= 14$

$\boxed{14}$

For 69: $6 + 9$ $= 15$

$\boxed{15}$

For 70: $7 + 0$ $= 7$

$\boxed{7}$

Step 4 — Observations

We look at the list of digit sums we found.

For numbers from 40 to 49, the digit sums are 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.

For numbers from 50 to 59, the digit sums are 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.

For numbers from 60 to 69, the digit sums are 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.

The digit sum usually goes up by 1 when the number goes up by 1.

But when we reach a new group of ten, the digit sum drops. For example, from 49 (sum 13) to 50 (sum 5).

Answer

The digit sums are:

40: 4

41: 5

42: 6

43: 7

44: 8

45: 9

46: 10

47: 11

48: 12

49: 13

50: 5

51: 6

52: 7

53: 8

54: 9

55: 10

56: 11

57: 12

58: 13

59: 14

60: 6

61: 7

62: 8

63: 9

64: 10

65: 11

66: 12

67: 13

68: 14

69: 15

70: 7

Observations:

For numbers from 40 to 49, the digit sums are 4, 5, 6, 7, 8, 9, 10, 11, 12, 13.

For numbers from 50 to 59, the digit sums are 5, 6, 7, 8, 9, 10, 11, 12, 13, 14.

For numbers from 60 to 69, the digit sums are 6, 7, 8, 9, 10, 11, 12, 13, 14, 15.

The digit sum increases by 1 as the number increases by 1.

The digit sum drops when the number crosses a multiple of 10.

Question 13

Answer

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