Respuesta :
To determine which expression gives as a result 3/4 you have to solve them:
When you divide two fractions, you have to invert the denominator of the division (reciprocal fraction) and multiply the numerator of the division by the reciprocal fraction.
a.
[tex]\frac{2}{8}\div\frac{1}{3}[/tex]Reverse the denominator
[tex]\frac{1}{3}\to\frac{3}{1}[/tex]And multiply both fractions
[tex]\frac{2}{8}\cdot\frac{3}{1}=\frac{2\cdot3}{8\cdot1}=\frac{6}{8}[/tex]Both 6 and 8 are divisible by 2, so you can simplify the result as
[tex]\frac{6\div2}{8\div2}=\frac{3}{4}[/tex]b.
[tex]\frac{2}{3}\div2[/tex]Determine the reciprocal of the denominator
[tex]\frac{2}{1}=\frac{1}{2}[/tex]And multiply it by the numerator of the division
[tex]\frac{2}{3}\cdot\frac{1}{2}=\frac{2\cdot1}{3\cdot2}=\frac{2}{6}[/tex]Both values are divisible by 2, so you can simplify the result as:
[tex]\frac{2\div2}{6\div2}=\frac{1}{3}[/tex]c.
[tex]\frac{1}{2}\div\frac{3}{8}[/tex]Determine the reciprocal fraction
[tex]\frac{3}{8}\to\frac{8}{3}[/tex]Multiply both fractions
[tex]\frac{1}{2}\cdot\frac{8}{3}=\frac{1\cdot8}{2\cdot3}=\frac{8}{6}[/tex]Divide the numerator and denominator by 2 to simplify the fractions
[tex]\frac{8\div2}{6\div2}=\frac{4}{3}[/tex]d.
[tex]1\frac{1}{4}\div1\frac{2}{3}[/tex]Express both mixed fractions as improper fractions
[tex]1\frac{1}{4}=\frac{4}{4}+\frac{1}{4}=\frac{5}{4}[/tex][tex]1\frac{2}{3}=\frac{3}{3}+\frac{2}{3}=\frac{5}{3}[/tex]So the division is
[tex]\frac{5}{4}\div\frac{5}{3}[/tex]Determine the reciprocal fraction
[tex]\frac{5}{3}\to\frac{3}{5}[/tex]And multiply both fractions
[tex]\frac{5}{4}\cdot\frac{3}{5}=\frac{5\cdot3}{4\cdot5}=\frac{15}{20}[/tex]Both values 15 and 20 are divisible by 5, you can simplify the result
[tex]\frac{15\div5}{20\div5}=\frac{3}{4}[/tex]e.
[tex]4\frac{2}{3}\div3\frac{1}{2}[/tex]Convert the fractions from mixed to improper
[tex]\frac{4\cdot3}{1\cdot3}+\frac{2}{3}=\frac{12}{3}+\frac{2}{3}=\frac{14}{3}[/tex][tex]\frac{3\cdot2}{1\cdot2}+\frac{1}{2}=\frac{6}{2}+\frac{1}{2}=\frac{7}{2}[/tex][tex]\frac{14}{3}\div\frac{7}{2}[/tex]Determine the reciprocal fraction
[tex]\frac{7}{2}\to\frac{2}{7}[/tex]And multiply both fractions
[tex]\frac{14}{3}\cdot\frac{2}{7}=\frac{14\cdot2}{3\cdot7}=\frac{28}{21}=\frac{4}{3}[/tex]From the given quotients, those that have 3/4, as a result, are "a." and "d."
