Question

QUESTION:-

Answer 1

Answer:

#a

$\implies\displaystyle{ \frac{3}{4} + \frac{5}{6} + \frac{7}{8}}$

• LCM of 4,6 and 8=2×2×3×2=24

Converting each of them into equivalent like fractions,

$\implies{ \displaystyle \frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24} }$

$\implies{ \displaystyle{ \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} }}$

$\implies{ \displaystyle{ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} }}$

${ \displaystyle{ \frac{3}{4} + \frac{5}{6} + \frac{7}{8} = \frac{18}{24} + \frac{20}{24} + \frac{21}{24} = \frac{59}{24} = 2\frac{11}{24} }}$

Shortcut method:-

$\implies{ \displaystyle{ \frac{3}{4} + \frac{5}{6} + \frac{7}{8} }}$

$\implies{ \displaystyle{ \frac{3 \times 6 + 5 \times 4 + 7 \times 3}{24} }}$

$\implies{ \displaystyle{ \frac{18 + 20 + 21}{24} }}$

$\implies{ \displaystyle{ \frac{59}{24} = 2 \frac{11}{24} }}$

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

$\implies{ \displaystyle{6 \frac{1}{3} + 2 \frac{5}{6} + 3 \frac{7}{9} }}$

• Convert to improper fractions,

$\implies{ \displaystyle{ \frac{19}{3} + \frac{17}{6} + \frac{34}{9} }}$

• LCM of 3,6,9=3×3×2=18

${ \displaystyle{ \frac{19}{3} + \frac{17}{6} + \frac{34}{9} = \frac{19 \times 6 + 17 \times 3 + 34 \times 2}{18} }}$

$\implies{ \displaystyle{ \frac{144 + 51 + 68}{18} }}$

$\implies{ \displaystyle{ \frac{233}{18} = 12 \frac{17}{18} }}$

Alternatively,

$\implies{ \displaystyle{6 \frac{1}{3} + 2 \frac{5}{6} + 3 \frac{7}{9} }}$

$\implies{ \displaystyle{(6 + 2 + 3) + \frac{1}{3} + \frac{5}{6} + \frac{7}{9} }}$

$\implies{ \displaystyle{11 + \frac{1 \times 6 + 5 \times 3 + 7 \times 2}{18} }}$

$\implies{ \displaystyle{11 + \frac{35}{18} }}$

$\implies{ \displaystyle{11 + 1 \frac{17}{18} }}$

$\implies{ \displaystyle{12 + \frac{17}{18} }}$

$\implies{ \displaystyle{12 \frac{17}{18} }}$

Answer 2

#a

$\large \sf \frac{3}{4} + \frac{5}{6} + \frac{7}{8}$

Write all numerators above the least common denominator 24

$\large \sf \frac{3 \times 6 +5 \times 4 + 7 \times 3 }{24}$

Multiply the numbers

$\large \sf \frac{18 +20 + 21 }{24}$

Add the numbers

$\large \sf \frac{59 }{24}$

$\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}$

#b

$\large \sf 6\frac{1}{3} + 2 \frac{5}{6} + 3 \frac{7}{9}$

Convert the mixed number to an improper fraction

$\large \sf \frac{19}{3} + \frac{17}{6} + \frac{34}{9}$

Write all numerators above the least common denominator 18

$\large \sf \frac{19 \times 6 + 17 \times 3 + 34 \times 2}{18}$

Multiply the numbers

$\large \sf \frac{114+ 51 + 68}{18}$

Add the numbers

$\large \sf \frac{233}{18}$