Solve the following problems. Reduce your answers to their simplest form. a. 13⁄41 + 27⁄82 b. 3 5⁄24 + 6 7⁄24 + 4 9⁄24 c. 5 2⁄3 + 29⁄69 + 6 21⁄23 d. 3 9⁄10 + 4⁄9 + 7⁄45 + 4 e. 6 – 7⁄15 f. 11 3⁄8 – 7⁄8 g. 7 1⁄6 – 3 4⁄9 h. 5 3⁄8 – 3 2⁄5

QUESTION AWe want to simplify,[tex]\frac{13}{41}+\frac{27}{82}[/tex]
The least common denominator is [tex]82[/tex].
We collect LCM for the denominators to obtain an expression which is,
[tex]=\frac{2\times13 +27}{82}[/tex]
We simplify the product in the numerator to get,
[tex]=\frac{26 +27}{82}[/tex]
We now simplify the numerator to obtain,[tex]=\frac{53}{82}[/tex]
QUESTION BWe want to simplify [tex]3\frac{5}{24}+6\frac{7}{24}+4\frac{9}{24}[/tex]
We can add the whole number parts separately and the fractional parts also separately and the simplify of change the improper fractions to mixed numbers.
[tex]=(3+6+4)+(\frac{5}{24}+\frac{7}{24}+\frac{9}{24})[/tex]

[tex]=13+\frac{5+7+9}{24}[/tex]This gives us,[tex]=13+\frac{21}{24}[/tex]
[tex]=13+\frac{7}{8}[/tex]

[tex]=13\frac{7}{8}[/tex]
QUESTION CThe given problem is [tex]5\frac{2}{3} +\frac{29}{69}+6\frac{21}{23}[/tex]
We change improper fractions to mixed numbers to get,[tex]\frac{17}{3} +\frac{29}{69}+\frac{159}{23}[/tex]The least common denominator is [tex]69[/tex]We now collect LCM to obtain,
[tex]\frac{17\times 23+1\times 29+3\times159}{69}[/tex]
[tex]=\frac{391+29+477}{69}[/tex]
This simplifies to,[tex]=\frac{897}{69}[/tex]This will give us[tex]=13[/tex]
QUESTION DWe want to simplify[tex]3\frac{9}{10}+\frac{4}{9}+\frac{7}{45}+4[/tex]
We change the improper fractions to mixed numbers to get,[tex]\frac{39}{10}+\frac{4}{9}+\frac{7}{45}+4[/tex]The least common denominator is [tex]90[/tex].
We collect LCM to get,
[tex]\frac{39\times9+4\times 10+2\times7}{90}[/tex]We simplify to get,[tex]=\frac{351+40+16}{90}[/tex]this gives us,[tex]=\frac{405}{90}[/tex]
[tex]=4\frac{1}{2}[/tex]
QUESTION EThe given expression is [tex]6-\frac{7}{15}[/tex]
The least common denominator is [tex]15[/tex].
We collect LCM to obtain,[tex]=\frac{6\times15-7}{15}[/tex]This simplifies to
[tex]=\frac{90-7}{15}[/tex]
[tex]=\frac{83}{15}[/tex][tex]=5\frac{8}{15}[/tex]
QUESTION FThe given problem is [tex]11\frac{3}{8}-\frac{7}{8}[/tex]Let us change the mixed number to improper fraction to obtain,[tex]=\frac{91}{8}-\frac{7}{8}[/tex]The least common denominator is [tex]8[/tex].
We collect LCM to obtain,[tex]=\frac{91-7}{8}[/tex]This simplifies to,[tex]=\frac{84}{8}[/tex]
We write back as a mixed number to get,[tex]=10\frac{1}{2}[/tex]
QUESTION GThe given problem is [tex]7\frac{1}{6}-3\frac{4}{9}[/tex]Let us convert the mixed number to improper fraction to obtain,[tex]=\frac{43}{6}-\frac{31}{9}[/tex]The least common denominator is [tex]18[/tex].We collect LCM to get,[tex]=\frac{3\times43-2\times31}{18}[/tex]
[tex]=\frac{129-62}{18}[/tex]
We simplify the numerator to obtain,[tex]=\frac{67}{18}[/tex]We convert back to mixed numbers to obtain,[tex]=3\frac{13}{18}[/tex]
QUESTION HThe problem given to us is
[tex]5\frac{3}{8}-3\frac{2}{5}[/tex]
We convert the improper fractions to mixed numbers to get,[tex]=\frac{43}{8}-\frac{17}{5}[/tex]
The least common denominator is [tex]40[/tex].
We collect LCM to obtain,[tex]=\frac{5\times43-8\times17}{40}[/tex]
This gives us,[tex]=\frac{215-136}{40}[/tex]
We subtract in the numerator to get,[tex]=\frac{79}{40}[/tex]
We convert to mixed numbers to get,[tex]=1\frac{39}{40}[/tex]