Arithmetic Notes

Addition of Single-Digit Numbers
Mixed Numbers

The following table lists basic addition facts.

Basic Addition Facts

0 + 0 = 0	1 + 0 = 1	2 + 0 = 2	3 + 0 = 3	4 + 0 = 4	5 + 0 = 5	6 + 0 = 6	7 + 0 = 7	8 + 0 = 8	9 + 0 = 9
0 + 1 = 1	1 + 1 = 2	2 + 1 = 3	3 + 1 = 4	4 + 1 = 5	5 + 1 = 6	6 + 1 = 7	7 + 1 = 8	8 + 1 = 9	9 + 1 = 10
0 + 2 = 2	1 + 2 = 3	2 + 2 = 4	3 + 2 = 5	4 + 2 = 6	5 + 2 = 7	6 + 2 = 8	7 + 2 = 9	8 + 2 = 10	9 + 2 = 11
0 + 3 = 3	1 + 3 = 4	2 + 3 = 5	3 + 3 = 6	4 + 3 = 7	5 + 3 = 8	6 + 3 = 9	7 + 3 = 10	8 + 3 = 11	9 + 3 = 12
0 + 4 = 4	1 + 4 = 5	2 + 4 = 6	3 + 4 = 7	4 + 4 = 8	5 + 4 = 9	6 + 4 = 10	7 + 4 = 11	8 + 4 = 12	9 + 4 = 13
0 + 5 = 5	1 + 5 = 6	2 + 5 = 7	3 + 5 = 8	4 + 5 = 9	5 + 5 = 10	6 + 5 = 11	7 + 5 = 12	8 + 5 = 13	9 + 5 = 14
0 + 6 = 6	1 + 6 = 7	2 + 6 = 8	3 + 6 = 9	4 + 6 = 10	5 + 6 = 11	6 + 6 = 12	7 + 6 = 13	8 + 6 = 14	9 + 6 = 15
0 + 7 = 7	1 + 7 = 8	2 + 7 = 9	3 + 7 = 10	4 + 7 = 11	5 + 7 = 12	6 + 7 = 13	7 + 7 = 14	8 + 7 = 15	9 + 7 = 16
0 + 8 = 8	1 + 8 = 9	2 + 8 = 10	3 + 8 = 11	4 + 8 = 12	5 + 8 = 13	6 + 8 = 14	7 + 8 = 15	8 + 8 = 16	9 + 8 = 17
0 + 9 = 9	1 + 9 = 10	2 + 9 = 11	3 + 9 = 12	4 + 9 = 13	5 + 9 = 14	6 + 9 = 15	7 + 9 = 16	8 + 9 = 17	9 + 9 = 18

EXERCISE

Add the following pairs of numbers.
(a) 3 + 7
(b) 5 + 3
(c) 4 + 9
(d) 7 + 4
(e) 8 + 2
(f) 5 + 1
(g) 9 + 8
(h) 2 + 6
(i) 8 + 5
(j) 6 + 9

ANSWERS

(a) 3 + 7 = 10
(b) 5 + 3 = 8
(c) 4 + 9 = 13
(d) 7 + 4 = 11
(e) 8 + 2 = 10
(f) 5 + 1 = 6
(g) 9 + 8 = 17
(h) 2 + 6 = 8
(i) 8 + 5 = 13
(j) 6 + 9 = 15

PROBLEM

Evaluate each of the following:
(a) (3 2/3 - 5 1/2) + 7 7/8
(b) 7 - (3 5/8 - 2 4/5)
(c) 5 - (2 1/8 + 1 3/5)

SOLUTION

(a) (3 2/3 - 5 1/2) + 7 7/8 = 3 2/3 - 5 1/2 + 7 7/8 = 3 - 5 + 7 + 2/3 - 1/2 + 7/8 = 5 + 2/3 - 1/2 + 7/8
= 5 + (16 - 12 + 21) / 24 = 5 + 25/24 = 5 + 1 + 1/24 = 6 1/24

(b) 7 - (3 5/8 - 2 4/5) = 7 - 3 5/8 + 2 4/5 = 7 - 3 + 2 - 5/8 + 4/5 = 6 - 5/8 + 4/5 = 6 + (-25 + 32) / 40
= 6 + 7/40 = 6 7/40

(c) 5 - (2 1/8 + 1 3/5) = 5 - 2 1/8 - 1 3/5 = 5 - 2 - 1 - 1/8 - 3/5 = 2 - 1/8 - 3/5 = 2 - (5 + 24) / 40
= 2 - 29/40 = 1 11/40