Respuesta :
QUESTION A
We 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 B
We 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 C
The 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 D
We 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 E
The 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 F
The 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 G
The 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 H
The 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]
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, [tex]A=\dfrac{53}{82}[/tex].
- The simplest form of expression (B) is , [tex]B=\dfrac{57}{6}[/tex].
- The simplest form of expression (C) is, [tex]C=\dfrac{140}{23}[/tex]
- The simplest form of expression (D) is, [tex]D=\dfrac{729}{162}[/tex].
- The simplest form of expression (E) is, [tex]E=\dfrac{83}{15}[/tex].
- The simplest form of expression (F) is, [tex]F=\dfrac{21}{2}[/tex].
- The simplest form of expression (G) is, [tex]F=\dfrac{67}{18}[/tex].
- The simplest form of expression (H) is, [tex]H=\dfrac{79}{40}[/tex].
Given information:
The expressions are given to solve and reduce the answer to their simplest form.
(A)The expression is given as,
[tex]A=\dfrac{13}{41} +\dfrac{27}{82}[/tex]
Solve the above expression by talking least common factor of denominators.
[tex]A=\dfrac{2\times13+27}{82} \\A=\dfrac{26+27}{82} \\A=\dfrac{53}{82}[/tex]
Hence, the simplest form of expression (A) after solving is, [tex]A=\dfrac{53}{82}[/tex].
(B) The expression is given as,
[tex]B=3\dfrac{5}{24}+6\dfrac{7}{24}[/tex]
On solving the above expression by simplifying the fractions,
[tex]B=3\dfrac{5}{24}+6\dfrac{7}{24}\\\\B=\dfrac{77}{24} +\dfrac{151}{24}\\\\B=\dfrac{228}{24} \\\\B=\dfrac{57}{6}[/tex]
Hence, simplest form of expression (B) after solving is, [tex]B=\dfrac{57}{6}[/tex].
(C) The expression is given as,
[tex]C=5\dfrac{2}{3}+\dfrac{29}{69}[/tex]
On solving the above expression by simplifying the fractions,
[tex]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}[/tex]
Hence, the simplest form of expression (C) after solving is, [tex]C=\dfrac{140}{23}[/tex].
(D)The expression is given as,
[tex]D=3\dfrac{9}{10} +\dfrac{4}{9}+\dfrac{7}{45}[/tex]
On solving the above expression by simplifying the fractions,
[tex]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}[/tex]
Hence, the simplest form of expression (D) after solving is, [tex]D=\dfrac{729}{162}[/tex].
(E)The expression is given as,
[tex]E=6 -\dfrac{7}{15}[/tex]
On solving the above expression by simplifying the fractions,
[tex]E=6-\dfrac{7}{15}\\\\E=\dfrac{90-7}{15} \\\\E=\dfrac{83}{15}[/tex]
Hence, the simplest form of expression (E) after solving is, [tex]E=\dfrac{83}{15}[/tex].
(F)The expression is given as,
[tex]F=11\dfrac{3}{8} -\dfrac{7}{8}[/tex]
On solving the above expression by simplifying the fractions,
[tex]F=11\dfrac{3}{8} -\dfrac{7}{8}\\\\F=\dfrac{91-7}{8} \\\\F=\dfrac{84}{8}\\\\F=\dfrac{21}{2}[/tex]
Hence, the simplest form of expression (F) after solving is, [tex]F=\dfrac{21}{2}[/tex].
(G)The expression is given as,
[tex]G=7\dfrac{1}{6} -3\dfrac{4}{9}[/tex]
On solving the above expression by simplifying the fractions,
[tex]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}[/tex]
Hence, the simplest form of expression (G) after solving is, [tex]F=\dfrac{67}{18}[/tex].
(H)The expression is given as,
[tex]H=5\dfrac{3}{8} -3\dfrac{2}{5}[/tex]
On solving the above expression by simplifying the fractions,
[tex]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}[/tex]
Hence, the simplest form of expression (H) after solving is, [tex]H=\dfrac{79}{40}[/tex].
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