Fractions with the same denominator can be added easily by copying the denominator and adding the numerator.
[tex] \displaystyle \frac{a}{c} + \frac{b}{c} = \frac{a+b}{c} [/tex]
Fractions with the different denominator can be added by finding their LCD or finding the LCM of the denominator, then dividing the LCD/LCM to the fraction's denominators, leaving their quotients, and multiplying the quotients to their respective numerators. Afterwards, the same steps are taken for adding and subtracting fraction.
[tex] \displaystyle \frac{a}{b} + \frac{c}{d} = \frac{lcm(b,d) \div b \times a}{lcm(b,d) \div b} + \frac{lcm(b,d) \div d \times c}{lcm(b,d) \div d} [/tex]
Fraction with whole numbers can be converted into an improper fraction by multiplying the whole number with the denominator, and adding the product and the current numerator, and copying the denominator.
[tex] \displaystyle a\frac{b}{c} = \frac{a \times c + b}{c} [/tex]
Whole numbers is converted into improper fractions by multiplying them with the denominator of the chosen fraction, placing it as numerator, and copying the denominator.
[tex] \displaystyle a + \frac{b}{c} = \frac{a \times c}{c} + \frac{b}{c} [/tex]
Solutions:
1.
[tex] \displaystyle \frac{4}{10} + \frac{5}{10} [/tex]
[tex] \displaystyle = \frac{4 + 5}{10} [/tex]
[tex] \displaystyle = \frac{9}{10} [/tex]
[tex] \displaystyle = \boxed{\frac{9}{10}} [/tex]
2.
[tex] \displaystyle \frac{2}{5} + \frac{3}{4} [/tex]
[tex] \displaystyle \textsf{ The LCD is 20. } [/tex]
[tex] \displaystyle \frac{8}{20} + \frac{15}{20} [/tex]
[tex] \displaystyle = \frac{8 + 15}{20} [/tex]
[tex] \displaystyle = \frac{23}{20} [/tex]
[tex] \displaystyle = \boxed{\frac{23}{20} \text{\ or\ } 1\frac{3}{20}} [/tex]
3.
[tex] \displaystyle \frac{7}{20} + \frac{11}{20} [/tex]
[tex] \displaystyle = \frac{18}{20} [/tex]
[tex] \displaystyle = \frac{9}{10} [/tex]
[tex] \displaystyle = \boxed{\frac{9}{10}} [/tex]
4.
[tex] \displaystyle \frac{5}{6} - \frac{1}{3} [/tex]
[tex] \displaystyle \textsf{ The LCD is 6. } [/tex]
[tex] \displaystyle \frac{5}{6} - \frac{2}{6} [/tex]
[tex] \displaystyle = \frac{5 - 2}{6} [/tex]
[tex] \displaystyle = \frac{3}{6} [/tex]
[tex] \displaystyle = \boxed{\frac{1}{2}} [/tex]
5.
[tex] \displaystyle \frac{8}{13} - \frac{6}{13} [/tex]
[tex] \displaystyle = \frac{8-6}{13} [/tex]
[tex] \displaystyle = \frac{2}{13} [/tex]
[tex] \displaystyle = \boxed{\frac{2}{13}} [/tex]
6.
[tex] \displaystyle \frac{7}{8} - \frac{4}{8} [/tex]
[tex] \displaystyle = \frac{7 - 4}{8} [/tex]
[tex] \displaystyle = \frac{3}{8} [/tex]
[tex] \displaystyle = \boxed{\frac{3}{8}} [/tex]
7.
[tex] \displaystyle 3 - \frac{2}{9} [/tex]
[tex] \displaystyle \textsf{ Convert 3 to improper fraction. } [/tex]
[tex] \displaystyle \frac{3 \times 9}{9} - \frac{2}{9} [/tex]
[tex] \displaystyle \frac{27}{9} - \frac{2}{9} [/tex]
[tex] \displaystyle = \frac{25}{9} [/tex]
[tex] \displaystyle = \boxed{\frac{25}{9} \text{\ or\ } 2\frac{7}{9}} [/tex]
8.
[tex] \displaystyle 1 - \frac{9}{15} [/tex]
[tex] \displaystyle \textsf{ Convert 1 to improper fraction. } [/tex]
[tex] \displaystyle \frac{1 \times 15}{15} - \frac{9}{15} [/tex]
[tex] \displaystyle \frac{15}{15} - \frac{9}{15} [/tex]
[tex] \displaystyle = \frac{6}{15} [/tex]
[tex] \displaystyle = \boxed{\frac{2}{5}} [/tex]
