Which Ratios for a proportion?
A. 4/9,12/25
B. 3/7,18/42
C. 5/11,20/45
D. 5/8,15/25
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To determine which ratios form a proportion, we need to check if they are equivalent, meaning their values are equal.
Let's calculate the value of each ratio by simplifying them.
A. 4/9, 12/25
To simplify the first ratio, divide both the numerator and the denominator by their greatest common divisor, which is 1 in this case. Thus, the simplified form of 4/9 is 4/9.
Now, simplify the second ratio. By dividing both the numerator and the denominator by their greatest common divisor, which is 1 in this case, the simplified form of 12/25 is 12/25.
Since 4/9 is not equal to 12/25, option A does not form a proportion.
Now let's check the other options.
B. 3/7, 18/42
Simplifying the first ratio, we can divide both the numerator and the denominator by their greatest common divisor, which is 1 in this case. The simplified form of 3/7 is 3/7.
For the second ratio, dividing both numerator and denominator by their greatest common divisor, which is 6 in this case, the simplified form of 18/42 is 3/7.
Since 3/7 is equal to 3/7, option B forms a proportion.
C. 5/11, 20/45
Simplifying the first ratio by dividing both the numerator and the denominator by their greatest common divisor, which is 1 in this case, the simplified form of 5/11 is 5/11.
For the second ratio, dividing both the numerator and the denominator by 5, their greatest common divisor, the simplified form of 20/45 is 4/9.
Since 5/11 is not equal to 4/9, option C does not form a proportion.
D. 5/8, 15/25
Simplifying the first ratio, we can divide both the numerator and the denominator by their greatest common divisor, which is 1 in this case. The simplified form of 5/8 is 5/8.
For the second ratio, dividing both the numerator and the denominator by their greatest common divisor, which is 5 in this case, the simplified form of 15/25 is 3/5.
Since 5/8 is not equal to 3/5, option D does not form a proportion.
Therefore, the only option that forms a proportion is B. 3/7, 18/42.