Respuesta :
In order to find those quotients, we can use the following rules for multiplying two fractions:
We keep the first fraction and multiply it by the inverse of the second fraction:
[tex]\frac{a}{b}\colon\frac{c}{d}=\frac{a}{b}\cdot\frac{d}{c}[/tex]Then, the numerator of the result will equal the product of the new numerators, and the denominator of the result will equal the product of the new denominators:
[tex]\frac{a}{b}\cdot\frac{d}{c}=\frac{ad}{bc}[/tex]Writing both rules together, we obtain:
[tex]\frac{a}{b}\colon\frac{c}{d}=\frac{ad}{bc}[/tex]Now, using the given fractions, we have:
1. We keep the first fraction (3/4) as it is, change the sign of division (:) by the sign of multiplication (.), and exchange the numerator and the denominator of the second fraction (11/10), so it becomes 10/11:
[tex]\frac{3}{4}\colon\frac{11}{10}=\frac{3}{4}\cdot\frac{10}{11}=\frac{3\cdot10}{4\cdot11}=\frac{30}{44}[/tex]Notice we can simplify this result by dividing both the numerator and the denominator by the factor 2:
[tex]\frac{30}{44}=\frac{15}{22}[/tex]
2. Now, we can use the same steps. First, though, let's rewrite the mixed number 5 1/2 as a fraction:
[tex]5\frac{1}{2}=5+\frac{1}{2}=\frac{2\cdot5+1}{2}=\frac{10+1}{2}=\frac{11}{2}[/tex]Now, we can proceed with the division:
[tex]\frac{11}{2}\colon6=\frac{11}{2}\cdot\frac{1}{6}=\frac{11\cdot1}{2\cdot6}=\frac{11}{12}[/tex]3. Again, we need to rewrite the mixed number 1 2/15 as a fraction:
[tex]1\frac{2}{15}=\frac{1\cdot15+2}{15}=\frac{15+2}{15}=\frac{17}{15}[/tex]Now, we need to divide this by 1/5:
[tex]\frac{17}{15}\colon\frac{1}{5}=\frac{17}{15}\cdot\frac{5}{1}=\frac{17\cdot5}{15\cdot1}=\frac{17\cdot5}{15}[/tex]Notice that both the factor 5 in the numerator and 15 in the denominator are multiples of the number 5. So, we can divide them both by 5 in order to simplify the fraction:
[tex]\frac{17\cdot5}{15}=\frac{17}{3}[/tex]