Express the following ratios in simplest form.
1. 6:15
2. 22:67
3. 25:55
4. 45:165
5. 33:54
6. 13:39
7. 132:440
8. 4:21
9. 48:160
10. 63:7
1. 6:15
2. 22:67
3. 25:55
4. 45:165
5. 33:54
6. 13:39
7. 132:440
8. 4:21
9. 48:160
10. 63:7
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answer:
1. 2:5
2. 22:67
3. 2:5
4. 3:11
5. 11:18
6. 1:3
7. 3:10
8. 4:21
9. 3:10
10. 9:1
explanation:
1. Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 6 and 15 is 3
Divide both terms by the GCF, 3:
6 ÷ 3 = 2
15 ÷ 3 = 5
The ratio 6 : 15 can be reduced to lowest terms by dividing both terms by the GCF = 3 :
6 : 15 = 2 : 5
Therefore:
6 : 15 = 2 : 5
2. Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 22 and 67 is 1
Divide both terms by the GCF, 1:
22 ÷ 1 = 22
67 ÷ 1 = 67
The ratio 22 : 67 cannot be reduced further by dividing both terms by the GCF = 1 :
This ratio is already in lowest terms.
Therefore:
22 : 67 = 22 : 67
3. Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 22 and 55 is 11
Divide both terms by the GCF, 11:
22 ÷ 11 = 2
55 ÷ 11 = 5
The ratio 22 : 55 can be reduced to lowest terms by dividing both terms by the GCF = 11 :
22 : 55 = 2 : 5
Therefore:
22 : 55 = 2 : 5
4. Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 45 and 165 is 15
Divide both terms by the GCF, 15:
45 ÷ 15 = 3
165 ÷ 15 = 11
The ratio 45 : 165 can be reduced to lowest terms by dividing both terms by the GCF = 15 :
45 : 165 = 3 : 11
Therefore:
45 : 165 = 3 : 11
5. Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 33 and 54 is 3
Divide both terms by the GCF, 3:
33 ÷ 3 = 11
54 ÷ 3 = 18
The ratio 33 : 54 can be reduced to lowest terms by dividing both terms by the GCF = 3 :
33 : 54 = 11 : 18
Therefore:
33 : 54 = 11 : 18
6. Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 13 and 39 is 13
Divide both terms by the GCF, 13:
13 ÷ 13 = 1
39 ÷ 13 = 3
The ratio 13 : 39 can be reduced to lowest terms by dividing both terms by the GCF = 13 :
13 : 39 = 1 : 3
Therefore:
13 : 39 = 1 : 3
7. Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 132 and 440 is 44
Divide both terms by the GCF, 44:
132 ÷ 44 = 3
440 ÷ 44 = 10
The ratio 132 : 440 can be reduced to lowest terms by dividing both terms by the GCF = 44 :
132 : 440 = 3 : 10
Therefore:
132 : 440 = 3 : 10
8. Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 4 and 21 is 1
Divide both terms by the GCF, 1:
4 ÷ 1 = 4
21 ÷ 1 = 21
The ratio 4 : 21 cannot be reduced further by dividing both terms by the GCF = 1 :
This ratio is already in lowest terms.
Therefore:
4 : 21 = 4 : 21
9. Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 48 and 160 is 16
Divide both terms by the GCF, 16:
48 ÷ 16 = 3
160 ÷ 16 = 10
The ratio 48 : 160 can be reduced to lowest terms by dividing both terms by the GCF = 16 :
48 : 160 = 3 : 10
Therefore:
48 : 160 = 3 : 10
10. Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 63 and 7 is 7
Divide both terms by the GCF, 7:
63 ÷ 7 = 9
7 ÷ 7 = 1
The ratio 63 : 7 can be reduced to lowest terms by dividing both terms by the GCF = 7 :
63 : 7 = 9 : 1
Therefore:
63 : 7 = 9 : 1