Question

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

Answer 1

QUESTION A

We want to simplify,

$\frac{13}{41}+\frac{27}{82}$

The least common denominator is $82$.

We collect LCM for the denominators to obtain an expression which is,

$=\frac{2\times13 +27}{82}$

We simplify the product in the numerator to get,

$=\frac{26 +27}{82}$

We now simplify the numerator to obtain,

$=\frac{53}{82}$

QUESTION B

We want to simplify

$3\frac{5}{24}+6\frac{7}{24}+4\frac{9}{24}$

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.

$=(3+6+4)+(\frac{5}{24}+\frac{7}{24}+\frac{9}{24})$

$=13+\frac{5+7+9}{24}$

This gives us,

$=13+\frac{21}{24}$

$=13+\frac{7}{8}$

$=13\frac{7}{8}$

QUESTION C

The given problem is

$5\frac{2}{3} +\frac{29}{69}+6\frac{21}{23}$

We change improper fractions to mixed numbers to get,

$\frac{17}{3} +\frac{29}{69}+\frac{159}{23}$

The least common denominator is $69$

We now collect LCM to obtain,

$\frac{17\times 23+1\times 29+3\times159}{69}$

$=\frac{391+29+477}{69}$

This simplifies to,

$=\frac{897}{69}$

This will give us

$=13$

QUESTION D

We want to simplify

$3\frac{9}{10}+\frac{4}{9}+\frac{7}{45}+4$

We change the improper fractions to mixed numbers to get,

$\frac{39}{10}+\frac{4}{9}+\frac{7}{45}+4$

The least common denominator is $90$.

We collect LCM to get,

$\frac{39\times9+4\times 10+2\times7}{90}$

We simplify to get,

$=\frac{351+40+16}{90}$

this gives us,

$=\frac{405}{90}$

$=4\frac{1}{2}$

QUESTION E

The given expression is

$6-\frac{7}{15}$

The least common denominator is $15$.

We collect LCM to obtain,

$=\frac{6\times15-7}{15}$

This simplifies to

$=\frac{90-7}{15}$

$=\frac{83}{15}$

$=5\frac{8}{15}$

QUESTION F

The given problem is

$11\frac{3}{8}-\frac{7}{8}$

Let us change the mixed number to improper fraction to obtain,

$=\frac{91}{8}-\frac{7}{8}$

The least common denominator is $8$.

We collect LCM to obtain,

$=\frac{91-7}{8}$

This simplifies to,

$=\frac{84}{8}$

We write back as a mixed number to get,

$=10\frac{1}{2}$

QUESTION G

The given problem is

$7\frac{1}{6}-3\frac{4}{9}$

Let us convert the mixed number to improper fraction to obtain,

$=\frac{43}{6}-\frac{31}{9}$

The least common denominator is $18$.

We collect LCM to get,

$=\frac{3\times43-2\times31}{18}$

$=\frac{129-62}{18}$

We simplify the numerator to obtain,

$=\frac{67}{18}$

We convert back to mixed numbers to obtain,

$=3\frac{13}{18}$

QUESTION H

The problem given to us is

$5\frac{3}{8}-3\frac{2}{5}$

We convert the improper fractions to mixed numbers to get,

$=\frac{43}{8}-\frac{17}{5}$

The least common denominator is $40$.

We collect LCM to obtain,

$=\frac{5\times43-8\times17}{40}$

This gives us,

$=\frac{215-136}{40}$

We subtract in the numerator to get,

$=\frac{79}{40}$

We convert to mixed numbers to get,

$=1\frac{39}{40}$

Answer 2

13⁄41 + 27⁄82 = 26/82 + 27/82 = 53/82

3 5/24 + 6 7/24 + 4 9/24 = 13 20/24 = 13 5/6

5 2⁄3 + 29⁄69 + 6 21⁄23 = 5 46/69 + 29/69 + 6 63/69 = 11 138/69 = 13

3 9⁄10 + 4⁄9 + 7⁄45 + 4 = 3 81/90 + 40/90 + 14/90 + 4 = 7 135/90 = 8 1/2

6 – 7⁄15 = 5 15/15 - 7/15 = 5 6/15

11 3⁄8 – 7⁄8 = 10 11/8 - 7/8 = 10 4/8 = 10 1/2

 7 1⁄6 – 3 4⁄9 = 7 9/54 - 3 18/54 = 6 63/54 - 3 18/54 = 3 45/54 = 3 5/6

5 3⁄8 – 3 2⁄5 = 5 15/40 - 3 16/40 = 4 55/40 - 3 16/40 = 1 39/40