Respuesta :
To divide the given fractions, we first write each of them as improper fractions.
4 1/4 ÷ 3 1/2
Now,
[tex]4\frac{1}{4}=4+\frac{1}{4}[/tex][tex]=\frac{4\cdot4}{4}+\frac{1}{4}[/tex][tex]=\frac{16}{4}+\frac{1}{4}=\frac{17}{4}[/tex][tex]\therefore4\frac{1}{4}=\frac{17}{4}[/tex]And
[tex]3\frac{1}{2}=3+\frac{1}{2}[/tex][tex]=\frac{2\cdot3}{2}+\frac{1}{2}[/tex][tex]\therefore3\frac{1}{2}=\frac{7}{2}[/tex]Now the division becomes
[tex]\frac{17}{4}\div\frac{7}{2}[/tex]Taking the reciprocal of the left-hand fraction and converting division into multiplication gives
[tex]\frac{17}{4}\times\frac{2}{7}[/tex][tex]=\frac{17}{14}[/tex]Hence,
[tex]4\frac{1}{4}\div3\frac{1}{2}=\frac{17}{14}[/tex]-3.5 ÷ 0.675
We first convert the decimals to fractions.
[tex]-3.5=-\lbrack3+\frac{1}{2}\rbrack[/tex]Converting this to an improper fraction gives
[tex]-\lbrack\frac{3\cdot2}{2}+\frac{1}{2}\rbrack=-\lbrack\frac{7}{2}\rbrack[/tex]Now, 0.675 can be written as
[tex]\frac{675}{1000}[/tex]Therefore, the division can be written as
[tex]-\frac{7}{2}\div\frac{675}{1000}[/tex]Talking the reciprocal of the right-hand fraction gives
[tex]-\frac{7}{2}\times\frac{1000}{675}[/tex][tex]=-7\times\frac{500}{675}=-\frac{140}{27}[/tex]Hence,
[tex]-3.5\div0.675=-\frac{140}{27}[/tex]-2/9 ÷ -3/8
Taking the reciprocal of the right-hand fraction and converting the division into multiplication gives
[tex]-\frac{2}{9}\times\frac{-8}{3}[/tex][tex]=\frac{16}{27}[/tex][tex]\therefore-\frac{2}{9}\div\frac{-3}{8}=\frac{16}{27}[/tex]
