QUESTION 1
A common multiple is a number that is a multiple of two or more numbers.
For instance 18 is a common multiple of 2 and 3.
This is not the only common multiple.
QUESTION 2
A common denominator is a common multiple of two or more denominators.
For instance a common denominator for [tex]\frac{1}{2} ,\frac{1}{4}[/tex]
is 4
This is also not the only common denominator.
QUESTION 3
We were given;
[tex]\frac{8}{9}+\frac{4}{7}[/tex]
We want to estimate the sum of the given fractions.
We collect LCM to obtain,
[tex]=\frac{8\times 7+9\times4}{63}[/tex]
We multiply out in the numerator to obtain,
[tex]=\frac{56+36}{63}[/tex]
We perform the addition in the numerator to obtain,
[tex]=\frac{92}{63}[/tex]
We express the final answer as a mixed number to obtain,
[tex]=1\frac{29}{63}[/tex]
QUESTION 4
The given expression is [tex]3\frac{2}{5}-\frac{5}{8}[/tex].
Let us change the first first mixed number into an improper fraction to get,
[tex]=\frac{17}{5}-\frac{5}{8}[/tex]
We collect LCM of the denominators which is 40 to obtain,
[tex]=\frac{8\times17-5\times5}{40}[/tex]
We now multiply out in the numerator to get,
[tex]=\frac{136-25}{40}[/tex]
We carry out the subtraction in the numerator to get,
[tex]=\frac{111}{40}[/tex]
We express the final answer as a mixed number to obtain;
[tex]=2\frac{31}{40}[/tex]
QUESTION 5
The given fraction is [tex]1\frac{5}{6}+2\frac{2}{11}[/tex].
Let us first of all change each mixed number to improper fractions
[tex]=\frac{11}{6}+\frac{24}{11}[/tex]
We now collect LCM of the denominators to obtain,
[tex]=\frac{11\times11+24\times6}{66}[/tex]
We multiply in the numerator to get,
[tex]=\frac{121+144}{66}[/tex]
This gives,
[tex]=\frac{265}{66}[/tex]
[tex]=4\frac{1}{66}[/tex]
QUESTION 6
The given fractions are;
[tex]\frac{1}{6},\frac{1}{9}[/tex].
The least common denominator is [tex]18[/tex].
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 18 in the denominator.
[tex]\frac{1\times3}{6\times3},\frac{1\times2}{9\times2}[/tex].
This gives us;
[tex]\frac{3}{18},\frac{2}{18}[/tex].
QUESTION 7
The given fractions are;
[tex]\frac{5}{6},\frac{3}{8}[/tex].
The least common denominator is [tex]24[/tex].
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 24 in the denominator.
[tex]\frac{5\times4}{6\times4},\frac{3\times3}{8\times3}[/tex].
This gives us;
[tex]\frac{20}{24},\frac{9}{24}[/tex].
QUESTION 8
The given fractions are;
[tex]\frac{3}{8},\frac{3}{10}[/tex].
The least common denominator is [tex]40[/tex].
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 40 in the denominator.
[tex]\frac{3\times5}{8\times5},\frac{3\times4}{10\times40}[/tex].
This gives us;
[tex]\frac{15}{40},\frac{12}{40}[/tex].
QUESTION 9
The given fractions are;
[tex]\frac{2}{5},\frac{1}{10}[/tex].
The least common denominator is [tex]10[/tex].
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 10 in the denominator.
[tex]\frac{2\times2}{5\times2},\frac{1\times1}{10\times1}[/tex].
This gives us;
[tex]\frac{4}{10},\frac{1}{10}[/tex].
QUESTION 10
The given fractions are;
[tex]\frac{1}{9},\frac{5}{12}[/tex].
The least common denominator is [tex]36[/tex].
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 36 in the denominator.
[tex]\frac{1\times4}{9\times4},\frac{5\times3}{12\times3}[/tex].
This gives us;
[tex]\frac{4}{36},\frac{3}{36}[/tex].
QUESTION 11
The given fractions are;
[tex]\frac{1}{3},\frac{2}{7}[/tex].
The least common denominator is [tex]21[/tex].
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 21 in the denominator.
[tex]\frac{1\times7}{3\times7},\frac{2\times3}{7\times3}[/tex].
This gives us;
[tex]\frac{7}{21},\frac{6}{21}[/tex].
QUESTION 12,
The given fraction is
[tex]\frac{11}{18}-\frac{1}{6}[/tex]
The least common denominator is [tex]18[/tex].
We collect LCD to obtain,
[tex]=\frac{11-3\times1}{18}[/tex]
This simplifies to;
[tex]=\frac{11-3}{18}[/tex]
[tex]=\frac{8}{18}[/tex]
[tex]=\frac{9}{4}[/tex]
QUESTION 13
The given fraction is
[tex]\frac{2}{7}+\frac{2}{5}[/tex]
The least common denominator is [tex]35[/tex].
We collect LCD to obtain,
[tex]=\frac{2\times5+2\times7}{35}[/tex]
This simplifies to;
[tex]=\frac{10+14}{35}[/tex]
[tex]=\frac{24}{35}[/tex]
QUESTION 14
The given fraction is
[tex]\frac{3}{4}-\frac{3}{10}[/tex]
The least common denominator is [tex]20[/tex].
We collect LCD to obtain,
[tex]=\frac{3\times5-3\times2}{20}[/tex]
This simplifies to;
[tex]=\frac{15-6}{20}[/tex]
[tex]=\frac{9}{20}[/tex]
