# Converting Between Fractions and Decimals

Directions: Using the digits 0 to 9 at most one time each, fill in the boxes so that the fraction equals the decimal.

### Hint

What are easier decimals to find fraction equivalents for?

Number of Unique Solutions: 56
1:  17 / 25 = 0.68
2:  17 / 68 = 0.25
3:  18 / 24 = 0.75
4:  18 / 75 = 0.24
5:  19 / 25 = 0.76
6:  19 / 76 = 0.25
7:  36 / 15 = 2.40
8:  36 / 24 = 1.50
9:  36 / 48 = 0.75
10:  36 / 75 = 0.48
11:  37 / 04 = 9.25
12:  37 / 20 = 1.85
13:  37 / 25 = 1.48
14:  39 / 15 = 2.60
15:  39 / 26 = 1.50
16:  48 / 15 = 3.20
17:  48 / 32 = 1.50
18:  49 / 28 = 1.75
19:  60 / 48 = 1.25
20:  63 / 15 = 4.20
21:  63 / 42 = 1.50
22:  63 / 75 = 0.84
23:  63 / 84 = 0.75
24:  64 / 50 = 1.28
25:  67 / 50 = 1.34
26:  69 / 20 = 3.45
27:  69 / 50 = 1.38
28:  72 / 15 = 4.80
29:  72 / 16 = 4.50
30:  72 / 45 = 1.60
31:  72 / 48 = 1.50
32:  73 / 50 = 1.46
33:  74 / 08 = 9.25
34:  76 / 25 = 3.04
35:  78 / 12 = 6.50
36:  78 / 40 = 1.95
37:  78 / 65 = 1.20
38:  79 / 25 = 3.16
39:  80 / 64 = 1.25
40:  83 / 20 = 4.15
41:  86 / 40 = 2.15
42:  86 / 50 = 1.72
43:  87 / 20 = 4.35
44:  87 / 60 = 1.45
45:  90 / 24 = 3.75
46:  91 / 25 = 3.64
47:  91 / 26 = 3.50
48:  91 / 35 = 2.60
49:  93 / 15 = 6.20
50:  93 / 20 = 4.65
51:  93 / 62 = 1.50
52:  93 / 75 = 1.24
53:  94 / 25 = 3.76
54:  96 / 25 = 3.84
55:  96 / 75 = 1.28
56:  97 / 20 = 4.85

Source: Robert Kaplinsky

## Two Step Inequality with Fractional Coeffcient

Directions: Using the digits 1 to 7 at most one time each, place a digit …

1. Also 36/48 = 0.75

2. I think I found another one…72/16 = 4.50

3. My class found 4 more unless we are making a mistake!!

18/24= 0.75
73/50= 1.46
48/32= 1.50
80/64= 1.25

4. Also
39/26 = 1.50
72/48 = 1.50

I really like that this problem has many solutions that can keep kids thinking. Math often has more than one correct answer.

5. 76/25=3.04

6. Any statement with using the digit 0 on it?

7. My students also found:

78/40=1.95
74/08=9.25
78/65=1.20
86/50=1.72

8. Students found 37/04 = 9.25