Answer:
7. -37/36 or -1 1/36
8. -3/10
9. 1/24
10. -118/21 or -5 13/21
11. 97/12 or 8 1/12
12. 49/8 or 6 1/8
Step-by-step explanation:
To subtract fractions, they must have the same denominator. The common denominator will be the LCM (lowest common multiple) of the two denominators. Then, combine the fractions and simplify.
7. [tex]-\frac{1}{4}-\frac{7}{9}[/tex] Find a common denominator
[tex]=-\frac{1*9}{4*9}-\frac{7*4}{9*4}[/tex]
[tex]=-\frac{9}{36}-\frac{28}{36}[/tex]
[tex]=\frac{-9-28}{36}[/tex] Combine the fractions
[tex]=\frac{-37}{36}[/tex] Answer. Already in lowest terms.
[tex]=-1\frac{1}{36}[/tex] Keep a negative number. 37 goes into 36 one time, leaving 1 remainder (becomes numerator)
8. [tex]\frac{3}{5}-\frac{9}{10}[/tex] Find a common denominator
[tex]=\frac{3*2}{5*2}-\frac{9}{10}[/tex]
[tex]=\frac{6}{10}-\frac{9}{10}[/tex]
[tex]=\frac{6-9}{10}[/tex] Combine the fractions
[tex]=\frac{-3}{10}[/tex] Answer in simplest form.
9. [tex]\frac{5}{8}-\frac{7}{12}[/tex] Find common denominator
[tex]=\frac{5*3}{8*3}-\frac{7*2}{12*2}[/tex]
[tex]=\frac{15}{24}-\frac{14}{24}[/tex]
[tex]=\frac{15-14}{24}[/tex] Combine the fractions
[tex]=\frac{1}{24}[/tex] Answer in simplest form
10. [tex]-1\frac{1}{3}-4\frac{2}{7}[/tex] Translate to improper fraction
[tex]=-\frac{4}{3}-\frac{30}{7}[/tex] Multiplied each whole number with base, added to numerator
[tex]=-\frac{28}{21}-\frac{90}{21}[/tex] Found common denominator
[tex]=\frac{-28-90}{21}[/tex] Combined fractions
[tex]=\frac{-118}{21}[/tex] Answer in improper form
[tex]=-5\frac{13}{21}[/tex] Answer as a mixed number
11. [tex]5\frac{5}{6}-(-2\frac{1}{4})[/tex] Convert to improper fraction
[tex]\frac{35}{6}-(-\frac{9}{4})[/tex] Two minuses make a plus
[tex]=\frac{35}{6}+\frac{9}{4}[/tex] Find common denominator
[tex]=\frac{35*2}{6*2}+\frac{9*3}{4*3}[/tex]
[tex]=\frac{70}{12}+\frac{27}{12}[/tex]
[tex]=\frac{70+27}{12}[/tex] Combined fractions
[tex]=\frac{97}{12}[/tex] Answer as improper fraction
[tex]=8\frac{1}{12}[/tex] Answer as mixed fraction
12. [tex]12\frac{1}{2}-6\frac{3}{8}[/tex] Convert to improper fraction
[tex]\frac{25}{2}-\frac{51}{8}[/tex]
[tex]\frac{25*4}{2*4}-\frac{51}{8}[/tex] Find common denominator
[tex]\frac{100}{8}-\frac{51}{8}[/tex]
[tex]\frac{100-51}{8}[/tex] Combined fractions
[tex]\frac{49}{8}[/tex] Answer as improper fraction
[tex]8\frac{1}{8}[/tex] Answer as mixed number
