9514 1404 393
Answer:
1/2, 3/10
1/21, 8/27
Step-by-step explanation:
Fractions are multiplied by multiplying the numerators and expressing that product over the product of the denominators:
[tex]\dfrac{a}{b}\times\dfrac{c}{d}=\dfrac{ac}{bd}[/tex]
In several cases here, the numerator product has factors in common with the denominator product. Those can be cancelled, reducing the product fraction to lowest terms.
[tex]\dfrac{3}{4}\times\dfrac{2}{3}=\dfrac{3\cdot2}{4\cdot3}=\dfrac{3\cdot2}{3\cdot2\cdot2}=\boxed{\dfrac{1}{2}}\\\\\dfrac{4}{5}\times\dfrac{3}{8}=\dfrac{4\cdot3}{5\cdot8}=\dfrac{4\cdot3}{4\cdot2\cdot5}=\boxed{\dfrac{3}{10}}\\\\\dfrac{1}{6}\times\dfrac{2}{7}=\dfrac{1\cdot2}{6\cdot7}=\dfrac{2}{2\cdot3\cdot7}=\boxed{\dfrac{1}{21}}\\\\\dfrac{4}{9}\times\dfrac{2}{3}=\dfrac{4\cdot2}{9\cdot3}=\boxed{\dfrac{8}{27}}[/tex]
