Answer:
1a) [tex]-\frac{15}{4}[/tex]
1b) [tex]\frac{95}{33}[/tex]
2a) [tex]-84[/tex]
2b) 1
3a) [tex]\frac{171}{550}[/tex]
3b) [tex]4\frac{2}{7}[/tex]
Step-by-step explanation:
For the first equation, let's use [tex]\frac{-a}{b} =\frac{a}{-b} =-\frac{a}{b}[/tex] to right a new fraction.
Step 1- Reduce the fraction with 4.
[tex]-\frac{\frac{12/4}{4/4} }{\frac{4}{5} } = -\frac{3}{\frac{4}{5} }[/tex]
Step 2- Simplify the complex fraction(LCD or Least Common Denominator).
[tex]-\frac{3}{\frac{4}{5} } = -\frac{15}{4}[/tex]
An alternative form for this fraction is [tex]-3\frac{3}{4} or -3.75[/tex].
For the second equation..
Step 1- Convert the mixed number to an improper fraction.
[tex]\frac{6\frac{3}{9} }{\frac{11}{5} } = \frac{\frac{57}{9} }{\frac{11}{5} }[/tex]
Step 2- Simplify the complex fraction.
[tex]\frac{\frac{57}{9} }{\frac{11}{5} } = \frac{95}{33}[/tex]
An alternative form for this fraction is [tex]2\frac{29}{33} or 2.87[/tex].
For the third equation use [tex]\frac{-a}{b} =\frac{a}{-b} =-\frac{a}{b}[/tex]...
Step 1- Simplify the complex fraction(LCD).
[tex]-\frac{7}{\frac{1}{12} } = -84[/tex]
For the fourth equation...
Write the fraction as a division.
[tex]\frac{12}{8}[/tex]÷[tex]\frac{3}{2}[/tex]
To divide a fraction, multiply by the reciprocal of that fraction.
[tex]\frac{12}{8} *\frac{2}{3} = \frac{12*2}{8*3}[/tex]
Reduce the fraction with 3.
[tex]\frac{4*2}{8}= \frac{4}{4} = 1[/tex]
For the fifth equation...
Convert the mixed number to an improper fraction.
[tex]\frac{-1\frac{8}{11} }{-5\frac{5}{9} } = \frac{-\frac{19}{11} }{-\frac{50}{9} }[/tex]
Reduce the fraction with -1, this eliminates the negative sign.
Simplify the complex fraction.
[tex]\frac{\frac{19}{11} }{\frac{50}{9} } = \frac{171}{550}[/tex]
An alternative form for this fraction is 0.3109.
For the sixth equation..
Write the fraction as a division.
[tex]\frac{3}{7}[/tex]÷[tex]\frac{1}{10}[/tex]
To divide by a fraction, multiply by the reciprocal of that fraction.
[tex]\frac{3}{7}[/tex]×10= [tex]\frac{3*10}{7}[/tex]
Multiply the numbers.
[tex]\frac{3*10}{7} = \frac{30}{7}[/tex]
Alternative form of this fraction is [tex]4\frac{2}{7}[/tex] or 4.285714.
Hope this helps! :)
