Mathematics, 02.08.2019 09:30 j015

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

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On solving the given expressions and reducing them into their simplest form, the simplest form of the expressions can be written as:

The simplest form of expression (A) is, $A=\dfrac{53}{82}$ .The simplest form of expression (B) is , $B=\dfrac{57}{6}$ .The simplest form of expression (C) is, $C=\dfrac{140}{23}$ The simplest form of expression (D) is, $D=\dfrac{729}{162}$ .The simplest form of expression (E) is, $E=\dfrac{83}{15}$ .The simplest form of expression (F) is, $F=\dfrac{21}{2}$ .The simplest form of expression (G) is, $F=\dfrac{67}{18}$ .The simplest form of expression (H) is, $H=\dfrac{79}{40}$ .

Given information:

The expressions are given to solve and reduce the answer to their simplest form.

(A)The expression is given as,

$A=\dfrac{13}{41} +\dfrac{27}{82}$

Solve the above expression by talking least common factor of denominators.

$A=\dfrac{2\times13+27}{82} \\A=\dfrac{26+27}{82} \\A=\dfrac{53}{82}$

Hence, the simplest form of expression (A) after solving is, $A=\dfrac{53}{82}$ .

(B) The expression is given as,

$B=3\dfrac{5}{24}+6\dfrac{7}{24}$

On solving the above expression by simplifying the fractions,

$B=3\dfrac{5}{24}+6\dfrac{7}{24}\\\\B=\dfrac{77}{24} +\dfrac{151}{24}\\\\B=\dfrac{228}{24} \\\\B=\dfrac{57}{6}$

Hence, simplest form of expression (B) after solving is, $B=\dfrac{57}{6}$ .

$C=5\dfrac{2}{3}+\dfrac{29}{69}$

On solving the above expression by simplifying the fractions,

$C=5\dfrac{2}{3}+\dfrac{29}{69}\\\\C=\dfrac{17}{3} +\dfrac{29}{69} \\\\C=\dfrac{(23\times17)+(29)}{69} \\\\C=\dfrac{420}{69}\\\\C=\dfrac{140}{23}$

Hence, the simplest form of expression (C) after solving is, $C=\dfrac{140}{23}$ .

(D)The expression is given as,

$D=3\dfrac{9}{10} +\dfrac{4}{9}+\dfrac{7}{45}$

On solving the above expression by simplifying the fractions,

$D=3\dfrac{9}{10}+\dfrac{4}{9}+\dfrac{7}{45} \\\\D=\dfrac{39}{10} +\dfrac{4}{9} +\dfrac{7}{45}\\\\D=\dfrac{15795+1800+630}{4050} \\\\D=\dfrac{18225}{4050}\\\\D=\dfrac{729}{162}$

Hence, the simplest form of expression (D) after solving is, $D=\dfrac{729}{162}$ .

(E)The expression is given as,

$E=6 -\dfrac{7}{15}$

On solving the above expression by simplifying the fractions,

$E=6-\dfrac{7}{15}\\\\E=\dfrac{90-7}{15} \\\\E=\dfrac{83}{15}$

Hence, the simplest form of expression (E) after solving is, $E=\dfrac{83}{15}$ .

(F)The expression is given as,

$F=11\dfrac{3}{8} -\dfrac{7}{8}$

On solving the above expression by simplifying the fractions,

$F=11\dfrac{3}{8} -\dfrac{7}{8}\\\\F=\dfrac{91-7}{8} \\\\F=\dfrac{84}{8}\\\\F=\dfrac{21}{2}$

Hence, the simplest form of expression (F) after solving is, $F=\dfrac{21}{2}$ .

(G)The expression is given as,

$G=7\dfrac{1}{6} -3\dfrac{4}{9}$

On solving the above expression by simplifying the fractions,

$G=7\dfrac{1}{6} -3\dfrac{4}{9}\\\\G=\dfrac{43}{6} -\dfrac{31}{9} \\\\G=\dfrac{129-62}{18} \\\\G=\dfrac{67}{18}$

Hence, the simplest form of expression (G) after solving is, $F=\dfrac{67}{18}$ .

(H)The expression is given as,

$H=5\dfrac{3}{8} -3\dfrac{2}{5}$

On solving the above expression by simplifying the fractions,

$H=5\dfrac{3}{8} -3\dfrac{2}{5}\\\\H=\dfrac{43}{8}-\dfrac{17}{5} \\\\H=\dfrac{215-136}{40}\\\\H=\dfrac{79}{40}$

Hence, the simplest form of expression (H) after solving is, $H=\dfrac{79}{40}$ .

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Answer from: cats0srule

QUESTION A

We want to simplify,

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

The least common denominator is .

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

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 .

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 .

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 .

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 .

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 .

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 from: Quest

answer: 7270

step-by-step explanation:

Answer from: Quest

step-by-step explanation:

it's the only multiple of both and the least

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