Decimal Subtraction

Directions: Use the digits 1 to 9, at most one time each, to make two true statements.

Hint

How do you place digits so the difference is less than ten?

Answer

Number of Unique Solutions: 132
1: 3.9 – 1.4 = 2.5
2: 3.9 – 1.5 = 2.4
3: 3.9 – 2.4 = 1.5
4: 3.9 – 2.5 = 1.4
5: 4.3 – 1.5 = 2.8
6: 4.3 – 1.8 = 2.5
7: 4.3 – 2.8 = 1.5
8: 4.5 – 1.6 = 2.9
9: 4.5 – 1.7 = 2.8
10: 4.5 – 1.8 = 2.7
11: 4.5 – 1.9 = 2.6
12: 4.5 – 2.6 = 1.9
13: 4.5 – 2.9 = 1.6
14: 4.7 – 1.2 = 3.5
15: 4.7 – 1.5 = 3.2
16: 4.7 – 3.2 = 1.5
17: 4.9 – 1.2 = 3.7
18: 4.9 – 1.7 = 3.2
19: 5.7 – 2.1 = 3.6
20: 5.7 – 2.6 = 3.1
21: 5.7 – 3.1 = 2.6
22: 5.7 – 3.6 = 2.1
23: 5.8 – 1.2 = 4.6
24: 5.9 – 1.2 = 4.7
25: 5.9 – 1.7 = 4.2
26: 6.2 – 1.3 = 4.9
27: 6.2 – 1.5 = 4.7
28: 6.2 – 1.7 = 4.5
29: 6.2 – 4.7 = 1.5
30: 6.3 – 1.5 = 4.8
31: 6.3 – 1.8 = 4.5
32: 6.3 – 4.8 = 1.5
33: 6.5 – 1.7 = 4.8
34: 6.5 – 1.8 = 4.7
35: 6.5 – 2.7 = 3.8
36: 6.5 – 2.8 = 3.7
37: 6.5 – 3.7 = 2.8
38: 6.5 – 3.8 = 2.7
39: 6.7 – 1.3 = 5.4
40: 6.7 – 1.8 = 4.9
41: 6.8 – 2.3 = 4.5
42: 6.8 – 2.5 = 4.3
43: 6.8 – 2.7 = 4.1
44: 6.8 – 4.1 = 2.7
45: 6.8 – 4.3 = 2.5
46: 6.8 – 4.5 = 2.3
47: 6.9 – 1.2 = 5.7
48: 6.9 – 1.7 = 5.2
49: 7.1 – 2.3 = 4.8
50: 7.1 – 2.5 = 4.6
51: 7.1 – 2.6 = 4.5
52: 7.1 – 2.8 = 4.3
53: 7.1 – 4.3 = 2.8
54: 7.1 – 4.6 = 2.5
55: 7.1 – 4.8 = 2.3
56: 7.2 – 1.3 = 5.9
57: 7.2 – 1.8 = 5.4
58: 7.3 – 1.4 = 5.9
59: 7.3 – 1.9 = 5.4
60: 7.3 – 2.5 = 4.8
61: 7.3 – 2.8 = 4.5
62: 7.3 – 4.5 = 2.8
63: 7.3 – 4.8 = 2.5
64: 7.5 – 1.2 = 6.3
65: 7.5 – 1.3 = 6.2
66: 7.5 – 2.6 = 4.9
67: 7.5 – 2.9 = 4.6
68: 7.6 – 3.1 = 4.5
69: 7.6 – 3.5 = 4.1
70: 7.6 – 4.1 = 3.5
71: 7.8 – 1.3 = 6.5
72: 7.8 – 1.5 = 6.3
73: 7.8 – 3.2 = 4.6
74: 7.8 – 4.6 = 3.2
75: 7.8 – 6.3 = 1.5
76: 7.9 – 1.4 = 6.5
77: 7.9 – 1.5 = 6.4
78: 7.9 – 6.4 = 1.5
79: 8.1 – 3.5 = 4.6
80: 8.1 – 3.6 = 4.5
81: 8.1 – 4.6 = 3.5
82: 8.3 – 1.4 = 6.9
83: 8.3 – 1.9 = 6.4
84: 8.3 – 2.4 = 5.9
85: 8.3 – 2.9 = 5.4
86: 8.4 – 1.5 = 6.9
87: 8.4 – 1.9 = 6.5
88: 8.4 – 6.9 = 1.5
89: 8.5 – 1.2 = 7.3
90: 8.5 – 1.3 = 7.2
91: 8.5 – 2.1 = 6.4
92: 8.5 – 2.4 = 6.1
93: 8.5 – 3.6 = 4.9
94: 8.5 – 3.9 = 4.6
95: 8.7 – 3.1 = 5.6
96: 8.7 – 3.6 = 5.1
97: 8.9 – 1.4 = 7.5
98: 8.9 – 1.5 = 7.4
99: 8.9 – 2.4 = 6.5
100: 8.9 – 2.5 = 6.4
101: 8.9 – 3.2 = 5.7
102: 8.9 – 3.7 = 5.2
103: 8.9 – 5.2 = 3.7
104: 8.9 – 5.7 = 3.2
105: 8.9 – 6.4 = 2.5
106: 8.9 – 7.4 = 1.5
107: 9.1 – 2.3 = 6.8
108: 9.1 – 2.8 = 6.3
109: 9.1 – 6.3 = 2.8
110: 9.1 – 6.8 = 2.3
111: 9.5 – 1.2 = 8.3
112: 9.5 – 1.3 = 8.2
113: 9.5 – 2.1 = 7.4
114: 9.5 – 2.4 = 7.1
115: 9.5 – 2.7 = 6.8
116: 9.5 – 2.8 = 6.7
117: 9.5 – 3.1 = 6.4
118: 9.5 – 3.4 = 6.1
119: 9.5 – 6.7 = 2.8
120: 9.5 – 6.8 = 2.7
121: 9.6 – 1.2 = 8.4
122: 9.6 – 1.4 = 8.2
123: 9.6 – 2.1 = 7.5
124: 9.6 – 2.5 = 7.1
125: 9.6 – 7.1 = 2.5
126: 9.7 – 1.2 = 8.5
127: 9.7 – 1.5 = 8.2
128: 9.7 – 4.1 = 5.6
129: 9.7 – 4.6 = 5.1
130: 9.7 – 5.1 = 4.6
131: 9.7 – 5.6 = 4.1
132: 9.7 – 8.2 = 1.5

Source: Owen Kaplinsky

Tags 5.NBT.7 DOK 2: Skill / Concept Owen Kaplinsky

Check Also

Add Fractions with Decimal Sums

Directions: Using the digits 1 to 9 at most one time each, place a digit …

11 comments

Mrs. Elliott's 5th Graders
October 18, 2018 at 11:09 am

5.9-1.2=4.7
7.9-8.3=1.6
3.9-1.5=2.4
8.7-2.3=6.4
9.8-6.1=2.7
8.1-4.6=3.5
9.5-8.3=1.2
9.7-8.5=1.2

Reply
labron
August 24, 2020 at 5:31 am

8.6-4.3=4.3

Reply
Raeonnie mcginnist
August 24, 2020 at 5:35 am

1.38-1.3=0.35

Reply
- RaeOnnie
  September 29, 2022 at 2:43 pm
  
  Sorry it’s 0.38
  
  Reply
  - rae
    September 29, 2022 at 2:44 pm
    
    Sorry it’s0.03
    
    Reply
olivia
August 24, 2020 at 5:45 am

9.2-8.3=0.9

Reply
olivia
August 24, 2020 at 5:47 am

6.7-5.4=1.3

Reply
Ethan
October 7, 2021 at 7:22 am

8.3-6.2=2.1

Reply
Bryson
September 30, 2022 at 6:54 am

0.0-0.0

Reply
Rudolf Österreicher
July 9, 2023 at 10:58 am

The “solution”-section is missing a lot of solutions. There are 400 solutions, not just 132:

3.9 – 1.4 = 2.5
3.9 – 1.5 = 2.4
3.9 – 2.4 = 1.5
3.9 – 2.5 = 1.4
4.3 – 1.5 = 2.8
4.3 – 1.6 = 2.7
4.3 – 1.7 = 2.6
4.3 – 1.8 = 2.5
4.3 – 2.5 = 1.8
4.3 – 2.6 = 1.7
4.3 – 2.7 = 1.6
4.3 – 2.8 = 1.5
4.5 – 1.6 = 2.9
4.5 – 1.7 = 2.8
4.5 – 1.8 = 2.7
4.5 – 1.9 = 2.6
4.5 – 2.6 = 1.9
4.5 – 2.7 = 1.8
4.5 – 2.8 = 1.7
4.5 – 2.9 = 1.6
4.6 – 1.7 = 2.9
4.6 – 1.9 = 2.7
4.6 – 2.7 = 1.9
4.6 – 2.9 = 1.7
4.7 – 1.2 = 3.5
4.7 – 1.5 = 3.2
4.7 – 1.8 = 2.9
4.7 – 1.9 = 2.8
4.7 – 2.8 = 1.9
4.7 – 2.9 = 1.8
4.7 – 3.2 = 1.5
4.7 – 3.5 = 1.2
4.8 – 1.2 = 3.6
4.8 – 1.6 = 3.2
4.8 – 3.2 = 1.6
4.8 – 3.6 = 1.2
4.9 – 1.2 = 3.7
4.9 – 1.7 = 3.2
4.9 – 3.2 = 1.7
4.9 – 3.7 = 1.2
5.2 – 1.4 = 3.8
5.2 – 1.8 = 3.4
5.2 – 3.4 = 1.8
5.2 – 3.8 = 1.4
5.4 – 1.6 = 3.8
5.4 – 1.8 = 3.6
5.4 – 3.6 = 1.8
5.4 – 3.8 = 1.6
5.6 – 1.7 = 3.9
5.6 – 1.9 = 3.7
5.6 – 3.7 = 1.9
5.6 – 3.9 = 1.7
5.7 – 1.8 = 3.9
5.7 – 1.9 = 3.8
5.7 – 2.1 = 3.6
5.7 – 2.6 = 3.1
5.7 – 3.1 = 2.6
5.7 – 3.6 = 2.1
5.7 – 3.8 = 1.9
5.7 – 3.9 = 1.8
5.8 – 1.2 = 4.6
5.8 – 1.6 = 4.2
5.8 – 2.1 = 3.7
5.8 – 2.7 = 3.1
5.8 – 3.1 = 2.7
5.8 – 3.7 = 2.1
5.8 – 4.2 = 1.6
5.8 – 4.6 = 1.2
5.9 – 1.2 = 4.7
5.9 – 1.3 = 4.6
5.9 – 1.6 = 4.3
5.9 – 1.7 = 4.2
5.9 – 2.1 = 3.8
5.9 – 2.8 = 3.1
5.9 – 3.1 = 2.8
5.9 – 3.8 = 2.1
5.9 – 4.2 = 1.7
5.9 – 4.3 = 1.6
5.9 – 4.6 = 1.3
5.9 – 4.7 = 1.2
6.1 – 2.4 = 3.7
6.1 – 2.7 = 3.4
6.1 – 3.4 = 2.7
6.1 – 3.7 = 2.4
6.2 – 1.3 = 4.9
6.2 – 1.5 = 4.7
6.2 – 1.7 = 4.5
6.2 – 1.9 = 4.3
6.2 – 4.3 = 1.9
6.2 – 4.5 = 1.7
6.2 – 4.7 = 1.5
6.2 – 4.9 = 1.3
6.3 – 1.5 = 4.8
6.3 – 1.8 = 4.5
6.3 – 4.5 = 1.8
6.3 – 4.8 = 1.5
6.4 – 2.5 = 3.9
6.4 – 2.9 = 3.5
6.4 – 3.5 = 2.9
6.4 – 3.9 = 2.5
6.5 – 1.7 = 4.8
6.5 – 1.8 = 4.7
6.5 – 2.7 = 3.8
6.5 – 2.8 = 3.7
6.5 – 3.7 = 2.8
6.5 – 3.8 = 2.7
6.5 – 4.7 = 1.8
6.5 – 4.8 = 1.7
6.7 – 1.3 = 5.4
6.7 – 1.4 = 5.3
6.7 – 1.8 = 4.9
6.7 – 1.9 = 4.8
6.7 – 2.8 = 3.9
6.7 – 2.9 = 3.8
6.7 – 3.8 = 2.9
6.7 – 3.9 = 2.8
6.7 – 4.8 = 1.9
6.7 – 4.9 = 1.8
6.7 – 5.3 = 1.4
6.7 – 5.4 = 1.3
6.8 – 2.1 = 4.7
6.8 – 2.3 = 4.5
6.8 – 2.5 = 4.3
6.8 – 2.7 = 4.1
6.8 – 4.1 = 2.7
6.8 – 4.3 = 2.5
6.8 – 4.5 = 2.3
6.8 – 4.7 = 2.1
6.9 – 1.2 = 5.7
6.9 – 1.7 = 5.2
6.9 – 2.1 = 4.8
6.9 – 2.8 = 4.1
6.9 – 4.1 = 2.8
6.9 – 4.8 = 2.1
6.9 – 5.2 = 1.7
6.9 – 5.7 = 1.2
7.1 – 2.3 = 4.8
7.1 – 2.5 = 4.6
7.1 – 2.6 = 4.5
7.1 – 2.8 = 4.3
7.1 – 4.3 = 2.8
7.1 – 4.5 = 2.6
7.1 – 4.6 = 2.5
7.1 – 4.8 = 2.3
7.2 – 1.3 = 5.9
7.2 – 1.4 = 5.8
7.2 – 1.8 = 5.4
7.2 – 1.9 = 5.3
7.2 – 5.3 = 1.9
7.2 – 5.4 = 1.8
7.2 – 5.8 = 1.4
7.2 – 5.9 = 1.3
7.3 – 1.4 = 5.9
7.3 – 1.9 = 5.4
7.3 – 2.5 = 4.8
7.3 – 2.8 = 4.5
7.3 – 4.5 = 2.8
7.3 – 4.8 = 2.5
7.3 – 5.4 = 1.9
7.3 – 5.9 = 1.4
7.4 – 1.6 = 5.8
7.4 – 1.8 = 5.6
7.4 – 2.1 = 5.3
7.4 – 2.3 = 5.1
7.4 – 5.1 = 2.3
7.4 – 5.3 = 2.1
7.4 – 5.6 = 1.8
7.4 – 5.8 = 1.6
7.5 – 1.2 = 6.3
7.5 – 1.3 = 6.2
7.5 – 2.6 = 4.9
7.5 – 2.9 = 4.6
7.5 – 4.6 = 2.9
7.5 – 4.9 = 2.6
7.5 – 6.2 = 1.3
7.5 – 6.3 = 1.2
7.6 – 3.1 = 4.5
7.6 – 3.5 = 4.1
7.6 – 4.1 = 3.5
7.6 – 4.5 = 3.1
7.8 – 1.3 = 6.5
7.8 – 1.5 = 6.3
7.8 – 3.2 = 4.6
7.8 – 3.6 = 4.2
7.8 – 4.2 = 3.6
7.8 – 4.6 = 3.2
7.8 – 6.3 = 1.5
7.8 – 6.5 = 1.3
7.9 – 1.4 = 6.5
7.9 – 1.5 = 6.4
7.9 – 2.1 = 5.8
7.9 – 2.3 = 5.6
7.9 – 2.6 = 5.3
7.9 – 2.8 = 5.1
7.9 – 3.1 = 4.8
7.9 – 3.8 = 4.1
7.9 – 4.1 = 3.8
7.9 – 4.8 = 3.1
7.9 – 5.1 = 2.8
7.9 – 5.3 = 2.6
7.9 – 5.6 = 2.3
7.9 – 5.8 = 2.1
7.9 – 6.4 = 1.5
7.9 – 6.5 = 1.4
8.1 – 2.4 = 5.7
8.1 – 2.7 = 5.4
8.1 – 3.2 = 4.9
8.1 – 3.5 = 4.6
8.1 – 3.6 = 4.5
8.1 – 3.9 = 4.2
8.1 – 4.2 = 3.9
8.1 – 4.5 = 3.6
8.1 – 4.6 = 3.5
8.1 – 4.9 = 3.2
8.1 – 5.4 = 2.7
8.1 – 5.7 = 2.4
8.2 – 1.3 = 6.9
8.2 – 1.5 = 6.7
8.2 – 1.7 = 6.5
8.2 – 1.9 = 6.3
8.2 – 3.5 = 4.7
8.2 – 3.7 = 4.5
8.2 – 4.5 = 3.7
8.2 – 4.7 = 3.5
8.2 – 6.3 = 1.9
8.2 – 6.5 = 1.7
8.2 – 6.7 = 1.5
8.2 – 6.9 = 1.3
8.3 – 1.4 = 6.9
8.3 – 1.9 = 6.4
8.3 – 2.4 = 5.9
8.3 – 2.6 = 5.7
8.3 – 2.7 = 5.6
8.3 – 2.9 = 5.4
8.3 – 5.4 = 2.9
8.3 – 5.6 = 2.7
8.3 – 5.7 = 2.6
8.3 – 5.9 = 2.4
8.3 – 6.4 = 1.9
8.3 – 6.9 = 1.4
8.4 – 1.5 = 6.9
8.4 – 1.9 = 6.5
8.4 – 2.1 = 6.3
8.4 – 2.3 = 6.1
8.4 – 6.1 = 2.3
8.4 – 6.3 = 2.1
8.4 – 6.5 = 1.9
8.4 – 6.9 = 1.5
8.5 – 1.2 = 7.3
8.5 – 1.3 = 7.2
8.5 – 2.1 = 6.4
8.5 – 2.4 = 6.1
8.5 – 3.6 = 4.9
8.5 – 3.9 = 4.6
8.5 – 4.6 = 3.9
8.5 – 4.9 = 3.6
8.5 – 6.1 = 2.4
8.5 – 6.4 = 2.1
8.5 – 7.2 = 1.3
8.5 – 7.3 = 1.2
8.6 – 1.2 = 7.4
8.6 – 1.4 = 7.2
8.6 – 2.7 = 5.9
8.6 – 2.9 = 5.7
8.6 – 3.2 = 5.4
8.6 – 3.4 = 5.2
8.6 – 3.7 = 4.9
8.6 – 3.9 = 4.7
8.6 – 4.7 = 3.9
8.6 – 4.9 = 3.7
8.6 – 5.2 = 3.4
8.6 – 5.4 = 3.2
8.6 – 5.7 = 2.9
8.6 – 5.9 = 2.7
8.6 – 7.2 = 1.4
8.6 – 7.4 = 1.2
8.7 – 2.3 = 6.4
8.7 – 2.4 = 6.3
8.7 – 3.1 = 5.6
8.7 – 3.6 = 5.1
8.7 – 5.1 = 3.6
8.7 – 5.6 = 3.1
8.7 – 6.3 = 2.4
8.7 – 6.4 = 2.3
8.9 – 1.3 = 7.6
8.9 – 1.4 = 7.5
8.9 – 1.5 = 7.4
8.9 – 1.6 = 7.3
8.9 – 2.4 = 6.5
8.9 – 2.5 = 6.4
8.9 – 3.2 = 5.7
8.9 – 3.7 = 5.2
8.9 – 5.2 = 3.7
8.9 – 5.7 = 3.2
8.9 – 6.4 = 2.5
8.9 – 6.5 = 2.4
8.9 – 7.3 = 1.6
8.9 – 7.4 = 1.5
8.9 – 7.5 = 1.4
8.9 – 7.6 = 1.3
9.1 – 2.3 = 6.8
9.1 – 2.4 = 6.7
9.1 – 2.7 = 6.4
9.1 – 2.8 = 6.3
9.1 – 3.4 = 5.7
9.1 – 3.7 = 5.4
9.1 – 5.4 = 3.7
9.1 – 5.7 = 3.4
9.1 – 6.3 = 2.8
9.1 – 6.4 = 2.7
9.1 – 6.7 = 2.4
9.1 – 6.8 = 2.3
9.2 – 1.4 = 7.8
9.2 – 1.8 = 7.4
9.2 – 3.4 = 5.8
9.2 – 3.8 = 5.4
9.2 – 5.4 = 3.8
9.2 – 5.8 = 3.4
9.2 – 7.4 = 1.8
9.2 – 7.8 = 1.4
9.3 – 1.5 = 7.8
9.3 – 1.8 = 7.5
9.3 – 2.5 = 6.8
9.3 – 2.8 = 6.5
9.3 – 4.1 = 5.2
9.3 – 4.2 = 5.1
9.3 – 5.1 = 4.2
9.3 – 5.2 = 4.1
9.3 – 6.5 = 2.8
9.3 – 6.8 = 2.5
9.3 – 7.5 = 1.8
9.3 – 7.8 = 1.5
9.4 – 1.6 = 7.8
9.4 – 1.8 = 7.6
9.4 – 2.1 = 7.3
9.4 – 2.3 = 7.1
9.4 – 3.6 = 5.8
9.4 – 3.8 = 5.6
9.4 – 5.6 = 3.8
9.4 – 5.8 = 3.6
9.4 – 7.1 = 2.3
9.4 – 7.3 = 2.1
9.4 – 7.6 = 1.8
9.4 – 7.8 = 1.6
9.5 – 1.2 = 8.3
9.5 – 1.3 = 8.2
9.5 – 2.1 = 7.4
9.5 – 2.4 = 7.1
9.5 – 2.7 = 6.8
9.5 – 2.8 = 6.7
9.5 – 3.1 = 6.4
9.5 – 3.4 = 6.1
9.5 – 6.1 = 3.4
9.5 – 6.4 = 3.1
9.5 – 6.7 = 2.8
9.5 – 6.8 = 2.7
9.5 – 7.1 = 2.4
9.5 – 7.4 = 2.1
9.5 – 8.2 = 1.3
9.5 – 8.3 = 1.2
9.6 – 1.2 = 8.4
9.6 – 1.4 = 8.2
9.6 – 2.1 = 7.5
9.6 – 2.5 = 7.1
9.6 – 7.1 = 2.5
9.6 – 7.5 = 2.1
9.6 – 8.2 = 1.4
9.6 – 8.4 = 1.2
9.7 – 1.2 = 8.5
9.7 – 1.3 = 8.4
9.7 – 1.4 = 8.3
9.7 – 1.5 = 8.2
9.7 – 3.2 = 6.5
9.7 – 3.5 = 6.2
9.7 – 4.1 = 5.6
9.7 – 4.6 = 5.1
9.7 – 5.1 = 4.6
9.7 – 5.6 = 4.1
9.7 – 6.2 = 3.5
9.7 – 6.5 = 3.2
9.7 – 8.2 = 1.5
9.7 – 8.3 = 1.4
9.7 – 8.4 = 1.3
9.7 – 8.5 = 1.2
9.8 – 2.3 = 7.5
9.8 – 2.5 = 7.3
9.8 – 3.1 = 6.7
9.8 – 3.7 = 6.1
9.8 – 4.1 = 5.7
9.8 – 4.2 = 5.6
9.8 – 4.6 = 5.2
9.8 – 4.7 = 5.1
9.8 – 5.1 = 4.7
9.8 – 5.2 = 4.6
9.8 – 5.6 = 4.2
9.8 – 5.7 = 4.1
9.8 – 6.1 = 3.7
9.8 – 6.7 = 3.1
9.8 – 7.3 = 2.5
9.8 – 7.5 = 2.3

Granted, you could say “9.8 – 7.5 = 2.3” and “9.8 – 2.3 = 7.5” are equivalent. But this still only cuts down the number of solutions in half. The “solution”-section is missing, for example, all solutions that begin with 9.8.

Is it because you count 9.8 – 7.5 = 2.3 as the same solution as 8.9 – 5.7 = 3.2 (because the digits in each number are just swapped)?

I then thought, maybe you counted the different results on both sides of the equation, but there are 59 different results:
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.1
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3.1
3.2
3.4
3.5
3.6
3.7
3.8
3.9
4.1
4.2
4.3
4.5
4.6
4.7
4.8
4.9
5.1
5.2
5.3
5.4
5.6
5.7
5.8
5.9
6.1
6.2
6.3
6.4
6.5
6.7
6.8
6.9
7.1
7.2
7.3
7.4
7.5
7.6
7.8
8.2
8.3
8.4
8.5

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- Rudolf Österreicher
  July 9, 2023 at 11:00 am
  
  Also, the directions say to make “two true statements”, but it’s not possible to make two such statements each using 6 digits and have no digit be repeated. I guess the directions should say “to make *a* true statement”
  
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