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 ![\frac{1}{2} ,\frac{1}{4}](/tpl/images/0029/8245/bfb6c.png)
is 4
This is also not the only common denominator.
QUESTION 3
We were given;
![\frac{8}{9}+\frac{4}{7}](/tpl/images/0029/8245/cf86b.png)
We want to estimate the sum of the given fractions.
We collect LCM to obtain,
![=\frac{8\times 7+9\times4}{63}](/tpl/images/0029/8245/bb1e5.png)
We multiply out in the numerator to obtain,
![=\frac{56+36}{63}](/tpl/images/0029/8245/5e420.png)
We perform the addition in the numerator to obtain,
![=\frac{92}{63}](/tpl/images/0029/8245/77698.png)
We express the final answer as a mixed number to obtain,
![=1\frac{29}{63}](/tpl/images/0029/8245/1681e.png)
QUESTION 4
The given expression is
.
Let us change the first first mixed number into an improper fraction to get,
![=\frac{17}{5}-\frac{5}{8}](/tpl/images/0029/8245/e5e12.png)
We collect LCM of the denominators which is 40 to obtain,
![=\frac{8\times17-5\times5}{40}](/tpl/images/0029/8245/90218.png)
We now multiply out in the numerator to get,
![=\frac{136-25}{40}](/tpl/images/0029/8245/b0486.png)
We carry out the subtraction in the numerator to get,
![=\frac{111}{40}](/tpl/images/0029/8245/32dde.png)
We express the final answer as a mixed number to obtain;
![=2\frac{31}{40}](/tpl/images/0029/8245/2b845.png)
QUESTION 5
The given fraction is
.
Let us first of all change each mixed number to improper fractions
![=\frac{11}{6}+\frac{24}{11}](/tpl/images/0029/8245/99b24.png)
We now collect LCM of the denominators to obtain,
![=\frac{11\times11+24\times6}{66}](/tpl/images/0029/8245/1db53.png)
We multiply in the numerator to get,
![=\frac{121+144}{66}](/tpl/images/0029/8245/5ca4b.png)
This gives,
![=\frac{265}{66}](/tpl/images/0029/8245/41424.png)
![=4\frac{1}{66}](/tpl/images/0029/8245/87198.png)
QUESTION 6
The given fractions are;
.
The least common denominator is
.
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 18 in the denominator.
.
This gives us;
.
QUESTION 7
The given fractions are;
.
The least common denominator is
.
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 24 in the denominator.
.
This gives us;
.
QUESTION 8
The given fractions are;
.
The least common denominator is
.
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 40 in the denominator.
.
This gives us;
.
QUESTION 9
The given fractions are;
.
The least common denominator is
.
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 10 in the denominator.
.
This gives us;
.
QUESTION 10
The given fractions are;
.
The least common denominator is
.
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 36 in the denominator.
.
This gives us;
.
QUESTION 11
The given fractions are;
.
The least common denominator is
.
We obtain the equivalent fraction by multiplying the denominator and numerator of each fraction by a common factor that gives 21 in the denominator.
.
This gives us;
.
QUESTION 12,
The given fraction is
![\frac{11}{18}-\frac{1}{6}](/tpl/images/0029/8245/7b5d5.png)
The least common denominator is
.
We collect LCD to obtain,
![=\frac{11-3\times1}{18}](/tpl/images/0029/8245/ef0f8.png)
This simplifies to;
![=\frac{11-3}{18}](/tpl/images/0029/8245/675ce.png)
![=\frac{8}{18}](/tpl/images/0029/8245/fb800.png)
![=\frac{9}{4}](/tpl/images/0029/8245/e87fc.png)
QUESTION 13
The given fraction is
![\frac{2}{7}+\frac{2}{5}](/tpl/images/0029/8245/c37a0.png)
The least common denominator is
.
We collect LCD to obtain,
![=\frac{2\times5+2\times7}{35}](/tpl/images/0029/8245/e51da.png)
This simplifies to;
![=\frac{10+14}{35}](/tpl/images/0029/8245/41881.png)
![=\frac{24}{35}](/tpl/images/0029/8245/eca48.png)
QUESTION 14
The given fraction is
![\frac{3}{4}-\frac{3}{10}](/tpl/images/0029/8245/5eb1d.png)
The least common denominator is
.
We collect LCD to obtain,
![=\frac{3\times5-3\times2}{20}](/tpl/images/0029/8245/9360e.png)
This simplifies to;
![=\frac{15-6}{20}](/tpl/images/0029/8245/8b2ec.png)
![=\frac{9}{20}](/tpl/images/0029/8245/39e78.png)