Express the following ratios in their simplest form:
a. 20:50
b. 32:12
c. 1/2 : 3/4
d. 1.5 : 4.5
e. 0.6 : 3
Answer (2)
The simplest forms of the ratios are: 2:5 for 20:50, 8:3 for 32:12, 2:3 for 2 1 : 4 3 , 1:3 for 1.5:4.5, and 1:5 for 0.6:3.
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To express the given ratios in their simplest form, we need to divide both terms of each ratio by their greatest common divisor (GCD). Here’s how you can simplify each ratio step-by-step:
a. 20:50
Find the GCD of 20 and 50, which is 10.
Divide both numbers by the GCD:
10 20 : 10 50 = 2 : 5
The simplest form of the ratio 20:50 is 2:5.
b. 32:12
Find the GCD of 32 and 12, which is 4.
Divide both numbers by the GCD:
4 32 : 4 12 = 8 : 3
The simplest form of the ratio 32:12 is 8:3.
c. 1/2 : 3/4
Express as fractions: 1/2 and 3/4.
Find the least common denominator, which is 4.
Convert each fraction:
1/2 = 2/4
Now the ratio is 2/4 : 3/4.
Simplify the ratio by cancelling the common denominator:
2:3
The simplest form of the ratio 1/2 : 3/4 is 2:3.
d. 1.5 : 4.5
Convert decimals to whole numbers by multiplying each by 10:
15:45
Find the GCD, which is 15.
Divide both numbers by the GCD:
15 15 : 15 45 = 1 : 3
The simplest form of the ratio 1.5:4.5 is 1:3.
e. 0.6 : 3
Convert the decimal 0.6 to a whole number by multiplying by 10:
6:30
Find the GCD of 6 and 30, which is 6.
Divide both numbers by the GCD:
6 6 : 6 30 = 1 : 5
The simplest form of the ratio 0.6:3 is 1:5.
