Addition of Mixed Fractions
Addition of fractions is adding the numerators for similar fractions and copying the denominator. Express the answer in lowest term. For dissimilar fractions, addition can only be done when changed to similar. This is done by using the least common denominator of the given fractions to be added. Answers are expressed in lowest form.
Answers:
- 1 [tex]\frac{9}{10}[/tex]
- 1 [tex]\frac{8}{15}[/tex]
- 2 [tex]\frac{1}{6}[/tex]
- 2 [tex]\frac{5}{12}[/tex]
- 2 [tex]\frac{13}{20}[/tex]
- 3 [tex]\frac{1}{8}[/tex]
- 3 [tex]\frac{1}{28}[/tex]
- 4 [tex]\frac{3}{10}[/tex]
- 3 [tex]\frac{41}{42}[/tex]
- 3 [tex]\frac{7}{9}[/tex]
Solutions:
- Express mixed numbers as improper fractions.
- Express the addends as similar fractions using the LCD.
- Proceed with the addition.
- Simplify the answer.
1. [tex]\frac{1}{2}[/tex] + 1 [tex]\frac{2}{5}[/tex] = [tex]\frac{1}{2}[/tex] + [tex]\frac{7}{5}[/tex] = [tex]\frac{5}{10}[/tex] + [tex]\frac{14}{10}[/tex] = [tex]\frac{19}{10}[/tex] = 1 [tex]\frac{9}{10}[/tex]
2. 1 [tex]\frac{1}{3}[/tex] + [tex]\frac{1}{5}[/tex] = [tex]\frac{4}{3}[/tex] + [tex]\frac{1}{5}[/tex] = [tex]\frac{20}{15}[/tex] + [tex]\frac{3}{15}[/tex] = [tex]\frac{23}{15}[/tex] = 1 [tex]\frac{8}{15}[/tex]
3. 1 [tex]\frac{1}{2}[/tex] + [tex]\frac{2}{3}[/tex] = [tex]\frac{3}{2}[/tex] + [tex]\frac{2}{3}[/tex] = [tex]\frac{9}{6}[/tex] + [tex]\frac{4}{6}[/tex] = [tex]\frac{13}{6}[/tex] = 2 [tex]\frac{1}{6}[/tex]
4. [tex]\frac{1}{4}[/tex] + 2 [tex]\frac{1}{6}[/tex] = [tex]\frac{1}{4}[/tex] + [tex]\frac{13}{6}[/tex] = [tex]\frac{3}{12}[/tex] + [tex]\frac{26}{12}[/tex] = [tex]\frac{29}{12}[/tex] = 2 [tex]\frac{5}{12}[/tex]
5. [tex]\frac{2}{5}[/tex] + 2 [tex]\frac{1}{4}[/tex] = [tex]\frac{2}{5}[/tex] + [tex]\frac{9}{4}[/tex] = [tex]\frac{8}{20}[/tex] + [tex]\frac{45}{20}[/tex] = [tex]\frac{53}{20}[/tex] = 2 [tex]\frac{13}{20}[/tex]
6. [tex]\frac{5}{8}[/tex] + 2 [tex]\frac{1}{2}[/tex] = [tex]\frac{5}{8}[/tex] + [tex]\frac{5}{2}[/tex] = [tex]\frac{5}{8}[/tex] + [tex]\frac{20}{8}[/tex] = [tex]\frac{25}{8}[/tex] = 3 [tex]\frac{1}{8}[/tex]
7. 2 [tex]\frac{3}{4}[/tex] + [tex]\frac{2}{7}[/tex] = [tex]\frac{11}{4}[/tex] + [tex]\frac{2}{7}[/tex] = [tex]\frac{77}{28}[/tex] + [tex]\frac{8}{28}[/tex] = [tex]\frac{85}{28}[/tex] = 3 [tex]\frac{1}{28}[/tex]
8. 3 [tex]\frac{1}{2}[/tex] + [tex]\frac{4}{5}[/tex] = [tex]\frac{7}{2}[/tex] + [tex]\frac{4}{5}[/tex] = [tex]\frac{35}{10}[/tex] + [tex]\frac{8}{10}[/tex] = [tex]\frac{43}{10}[/tex] = 4 [tex]\frac{3}{10}[/tex]
9. [tex]\frac{5}{6}[/tex] + 3 [tex]\frac{1}{7}[/tex] = [tex]\frac{5}{6}[/tex] + [tex]\frac{22}{7}[/tex] = [tex]\frac{35}{42}[/tex] + [tex]\frac{132}{42}[/tex] = [tex]\frac{167}{42}[/tex] = 3 [tex]\frac{41}{42}[/tex]
10. 3 [tex]\frac{1}{9}[/tex] + [tex]\frac{2}{3}[/tex] = [tex]\frac{28}{9}[/tex] + [tex]\frac{2}{3}[/tex] = [tex]\frac{28}{9}[/tex] + [tex]\frac{6}{9}[/tex] = [tex]\frac{34}{9}[/tex] = 3 [tex]\frac{7}{9}[/tex]
How to add fractions: https://brainly.ph/question/6358313
#BrainlyEveryday
