Which ratios form a proportion?
• 3/15, 12/55
• 8/24, 12/35
• 5/18, 25/90
• 4/11, 16/25
To determine which ratios form a proportion, let's compare the ratios by finding their equivalent fractions with a common denominator.
For the first set of ratios, let's find equivalent fractions with a common denominator:
3/15 = (3 * 11)/(15 * 11) = 33/165
12/55 = (12 * 3)/(55 * 3) = 36/165
Since the equivalent fractions have the same numerator and denominator, they are proportional.
For the second set of ratios:
8/24 = 1/3
12/35 = 12/35
Similarly, since the equivalent fractions have the same numerator and denominator, they are proportional.
For the third set of ratios:
5/18 = (5 * 5)/(18 * 5) = 25/90
25/90 = 25/90
Once again, since the equivalent fractions have the same numerator and denominator, they are proportional.
For the last set of ratios:
4/11 = 4/11
16/25 = (16 * 11)/(25 * 11) = 176/275
In this case, the equivalent fractions do not have the same numerator and denominator, so they are not proportional.
In summary:
• The ratios 3/15 and 12/55 form a proportion.
• The ratios 8/24 and 12/35 form a proportion.
• The ratios 5/18 and 25/90 form a proportion.
• The ratios 4/11 and 16/25 do not form a proportion.