Step-by-step explanation:
A. Solution:
Since
5 : 2 = 15 : X
Then we know
2/5 = X/15
Multiplying both sides by 15 cancels on the right
15 × (2/5) = (X/15) × 15
15 × (2/5) = X
Then solving for X
X = 15 × (2/5)
X = 6
Therefore
5 : 2 = 15 : 6
B. Solution:
We can simplify the ratio 2 : 6 by dividing both terms by the greatest common factor (GCF).
The GCF of 2 and 6 is 2.
Divide both terms by 2.
2 ÷ 2 = 1
6 ÷ 2 = 3
Therefore:
2 : 6 = 1 : 3
C. Solution:
Since
2 : 10 = 20 : X
Then we know
10/2 = X/20
Multiplying both sides by 20 cancels on the right
20 × (10/2) = (X/20) × 20
20 × (10/2) = X
Then solving for X
X = 20 × (10/2)
X = 100
Therefore
2 : 10 = 20 : 100
D. Solution:
Since
12 : 4 = 3 : X
Then we know
4/12 = X/3
Multiplying both sides by 3 cancels on the right
3 × (4/12) = (X/3) × 3
3 × (4/12) = X
Then solving for X
X = 3 × (4/12)
X = 1
Therefore
12 : 4 = 3 : 1
E. Solution:
Since
33 : 21 = 11 : X
Then we know
21/33 = X/11
Multiplying both sides by 11 cancels on the right
11 × (21/33) = (X/11) × 11
11 × (21/33) = X
Then solving for X
X = 11 × (21/33)
X = 7
Therefore
33 : 21 = 11 : 7
F. Solution:
Since
21 : 9 = X : 3
Then we know
21/9 = X/3
Multiplying both sides by 3 cancels on the right
3 × (21/9) = (X/3) × 3
3 × (21/9) = X
Then solving for X
X = 3 × (21/9)
X = 7
Therefore
21 : 9 = 7 : 3
G. Solution:
We can simplify the ratio 32 : 12 by dividing both terms by the greatest common factor (GCF).
The GCF of 32 and 12 is 4.
Divide both terms by 4.
32 ÷ 4 = 8
12 ÷ 4 = 3
Therefore:
32 : 12 = 8 : 3
H. Solution:
Since
3 : 4 = X : 8
Then we know
3/4 = X/8
Multiplying both sides by 8 cancels on the right
8 × (3/4) = (X/8) × 8
8 × (3/4) = X
Then solving for X
X = 8 × (3/4)
X = 6
Therefore
3 : 4 = 6 : 8
I. The ratio is already in lowest terms so we found an equivalent ratio by multiplying both terms by 2
Therefore
5 : 2 = 10 : 4
J. Solution:
We can simplify the ratio 25 : 50 by dividing both terms by the greatest common factor (GCF).
The GCF of 25 and 50 is 25.
Divide both terms by 25.
25 ÷ 25 = 1
50 ÷ 25 = 2
Therefore:
25 : 50 = 1 : 2
K. Solution:
We can simplify the ratio 34 : 18 by dividing both terms by the greatest common factor (GCF).
The GCF of 34 and 18 is 2.
Divide both terms by 2.
34 ÷ 2 = 17
18 ÷ 2 = 9
Therefore:
34 : 18 = 17 : 9
I hope this answers your question.
