Respuesta :
Answer:
#a
[tex] \implies\displaystyle{ \frac{3}{4} + \frac{5}{6} + \frac{7}{8}}[/tex]
- LCM of 4,6 and 8=2×2×3×2=24
Converting each of them into equivalent like fractions,
[tex] \implies{ \displaystyle \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} }[/tex]
[tex] \implies{ \displaystyle{ \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} }}[/tex]
[tex] \implies{ \displaystyle{ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} }}[/tex]
[tex]{ \displaystyle{ \frac{3}{4} + \frac{5}{6} + \frac{7}{8} = \frac{18}{24} + \frac{20}{24} + \frac{21}{24} = \frac{59}{24} = 2\frac{11}{24} }}[/tex]
Shortcut method:-
[tex]\implies{ \displaystyle{ \frac{3}{4} + \frac{5}{6} + \frac{7}{8} }}[/tex]
[tex]\implies{ \displaystyle{ \frac{3 \times 6 + 5 \times 4 + 7 \times 3}{24} }}[/tex]
[tex]\implies{ \displaystyle{ \frac{18 + 20 + 21}{24} }}[/tex]
[tex]\implies{ \displaystyle{ \frac{59}{24} = 2 \frac{11}{24} }}[/tex]
Remarks:-
- Whenever the answer is an improper fractions we should convert the answer into mixed number.
- Always reduce the answer to the lowest terms.
- You should try to do mental work and apply the shortcut method.
#b
[tex]\implies{ \displaystyle{6 \frac{1}{3} + 2 \frac{5}{6} + 3 \frac{7}{9} }}[/tex]
- Convert to improper fractions,
[tex]\implies{ \displaystyle{ \frac{19}{3} + \frac{17}{6} + \frac{34}{9} }}[/tex]
- LCM of 3,6,9=3×3×2=18
[tex]{ \displaystyle{ \frac{19}{3} + \frac{17}{6} + \frac{34}{9} = \frac{19 \times 6 + 17 \times 3 + 34 \times 2}{18} }}[/tex]
[tex]\implies{ \displaystyle{ \frac{144 + 51 + 68}{18} }}[/tex]
[tex]\implies{ \displaystyle{ \frac{233}{18} = 12 \frac{17}{18} }}[/tex]
Alternatively,
[tex]\implies{ \displaystyle{6 \frac{1}{3} + 2 \frac{5}{6} + 3 \frac{7}{9} }}[/tex]
[tex]\implies{ \displaystyle{(6 + 2 + 3) + \frac{1}{3} + \frac{5}{6} + \frac{7}{9} }}[/tex]
[tex]\implies{ \displaystyle{11 + \frac{1 \times 6 + 5 \times 3 + 7 \times 2}{18} }}[/tex]
[tex]\implies{ \displaystyle{11 + \frac{35}{18} }}[/tex]
[tex]\implies{ \displaystyle{11 + 1 \frac{17}{18} }}[/tex]
[tex]\implies{ \displaystyle{12 + \frac{17}{18} }}[/tex]
[tex]\implies{ \displaystyle{12 \frac{17}{18} }}[/tex]
#a
[tex] \large \sf \frac{3}{4} + \frac{5}{6} + \frac{7}{8} [/tex]
Write all numerators above the least common denominator 24
[tex] \large \sf \frac{3 \times 6 +5 \times 4 + 7 \times 3 }{24} [/tex]
Multiply the numbers
[tex] \large \sf \frac{18 +20 + 21 }{24} [/tex]
Add the numbers
[tex] \large \sf \frac{59 }{24} [/tex]
[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]
#b
[tex] \large \sf 6\frac{1}{3} + 2 \frac{5}{6} + 3 \frac{7}{9} [/tex]
Convert the mixed number to an improper fraction
[tex] \large \sf \frac{19}{3} + \frac{17}{6} + \frac{34}{9} [/tex]
Write all numerators above the least common denominator 18
[tex] \large \sf \frac{19 \times 6 + 17 \times 3 + 34 \times 2}{18} [/tex]
Multiply the numbers
[tex] \large \sf \frac{114+ 51 + 68}{18} [/tex]
Add the numbers
[tex] \large \sf \frac{233}{18} [/tex]
