In each case, determine whether the given ratios are equivalent.
\dfrac{4}{9} and \dfrac{9}{38}
Let's determine if we can simplify the ratios:
\dfrac{4}{9}=\dfrac{2\times2}{3\times3}
\dfrac{4}{9} cannot be simplified, it is in simplest form.
\dfrac{9}{38}=\dfrac{3\times3}{2\times19}
\dfrac{9}{38} cannot be simplified, it is in simplest form.
\dfrac{4}{9} and \dfrac{9}{38} are not equivalent.
\dfrac {2} {3} and \dfrac{9}{12}
Let's determine if we can simplify the ratios:
\dfrac {2} {3} cannot be simplified, it is in simplest form.
\dfrac {9} {12} = \dfrac {3 \times3} {3 \times 4}=\dfrac{3}{4}
\dfrac {9} {12} can be simplified to \dfrac{3}{4}.
\dfrac{2}{3} \neq \dfrac{3}{4}
\dfrac{2}{3} and \dfrac {9} {12} are not equivalent.
\dfrac{3}{9} and \dfrac{2}{6}
Let's determine if we can simplify the ratios:
\dfrac {3} {9} =\dfrac{3\times 1}{3 \times 3}=\dfrac{1}{3}
\dfrac {2} {6} = \dfrac {2 \times1} {2 \times 3} = \dfrac {1} {3}
\dfrac{3}{9} and \dfrac{2}{6} are equivalent.
\dfrac {12} {27} and \dfrac {8} {18}
Let's determine if we can simplify the ratios:
\dfrac {12} {27} = \dfrac {3 \times 4} {3 \times 9} = \dfrac {4} {9}
\dfrac {8} {18} = \dfrac {2 \times 4} {2 \times 9} = \dfrac {4} {9}
\dfrac {12} {27} and \dfrac {8} {18} are equivalent.
\dfrac {5} {12} and \dfrac {7} {13}
Let's determine if we can simplify the ratios:
\dfrac{5}{12} is simplified.
\dfrac{7}{13} is simplified.
\dfrac{5}{12} \neq \dfrac {7} {13}
\dfrac {5} {12} and \dfrac {7} {13} are not equivalent.
\dfrac {25} {45} and \dfrac {5} {9}
Let's determine if we can simplify the ratios:
\dfrac {25} {45} = \dfrac {5 \times 5} {5 \times 9} = \dfrac {5} {9}
\dfrac {25} {45} and \dfrac {5} {9} are equivalent.
\dfrac {15} {105} and \dfrac {3} {21}
Let's determine if we can simplify the ratios:
\dfrac {15} {105} = \dfrac {15 \times 1} {15 \times 7} = \dfrac {1} {7}
\dfrac {3} {21} = \dfrac {3 \times 1} {3 \times 7} = \dfrac {1} {7}
\dfrac {15} {105} and \dfrac {3} {21} are equivalent.