Answer:
Step-by-step explanation: We will determine if ratios are proportional using cross multiplication.
first, we will check option (a)
12/15 =5/4
12*4 = 15*5
48 is not equal to 75. So, these are not proportional.
now, we will check option (b)
15/12 = 5/4
15*4 = 12*5
60 = 60.
as the left-hand side is equal to the right-hand side.
So, option (b) is correct.
Answer:
[tex]\textsf{B)} \quad \dfrac{15}{12}\; \textsf{and}\;\dfrac{5}{4}[/tex]
Step-by-step explanation:
If two fractions are equal, they form a proportion.
Therefore, to determine if two ratios form a proportion, rewrite the fractions so that their denominators are the same, then compare.
[tex]\textsf{A)}\quad \dfrac{12}{15}\; \textsf{and}\;\dfrac{5}{4} \implies \dfrac{12 \times 4}{15\times 4}\; \textsf{and}\;\dfrac{5\times 15}{4\times 15}\implies \dfrac{48}{60}\; \textsf{and}\;\dfrac{75}{60}[/tex]
As the two fractions are not equal, they do not form a proportion.
[tex]\textsf{B)} \quad \dfrac{15}{12}\; \textsf{and}\;\dfrac{5}{4}\implies \dfrac{15}{12}\; \textsf{and}\;\dfrac{5 \times 3}{4 \times 3}\implies \dfrac{15}{12}\; \textsf{and}\;\dfrac{15}{12}[/tex]
As the two fractions are equal, they form a proportion.
[tex]\textsf{C)} \quad \dfrac{6}{5}\; \textsf{and}\;\dfrac{4}{5}[/tex]
The denominators of these two fractions are already the same.
Therefore, as the two fractions are not equal, they do not form a proportion.
[tex]\textsf{D)} \quad \dfrac{5}{6} \; \textsf{and}\;\dfrac{4}{5}\implies \dfrac{5\times 5}{6\times 5} \; \textsf{and}\; \dfrac{4\times 6}{5\times 6}\implies \dfrac{25}{30}\; \textsf{and}\;\dfrac{24}{30}[/tex]
As the two fractions are not equal, they do not form a proportion.
