Question

Solve the following;
I. \[\dfrac{2}{7}+\dfrac{6}{7}\]
II. \[\dfrac{6}{10}-\dfrac{8}{15}\]
III.. \[4-\dfrac{3}{7}\]
IV. \[9+\dfrac{5}{11}\]

Answer 1

Hint: In the given question, we have been asked to add or to subtract the given fraction. In order to add or subtract the fraction, the first thing we need to do is to equal the denominator of all terms contained in the question by taking the LCM of the denominators. Then we will simply add the numerators of the given fractions with the same denominator.

Complete step-by-step answer:
I. \[\dfrac{2}{7}+\dfrac{6}{7}\]
As the denominator of both the fraction is the same.
Adding the given fraction, we will get
 \[\Rightarrow \dfrac{2}{7}+\dfrac{6}{7}=\dfrac{2+6}{7}=\dfrac{8}{7}\]
Therefore,
 \[\Rightarrow \dfrac{2}{7}+\dfrac{6}{7}=\dfrac{8}{7}\] .

II. \[\dfrac{6}{10}-\dfrac{8}{15}\]
Taking the LCM of the denominator,
LCM of 10 and 15 = 30
Therefore,
 \[\Rightarrow \dfrac{6}{10}-\dfrac{8}{15}=\dfrac{6\times 3}{10\times 3}-\dfrac{8\times 2}{15\times 2}=\dfrac{18}{30}-\dfrac{16}{30}\]
Now,
We have,
 \[\Rightarrow \dfrac{18}{30}-\dfrac{16}{30}\]
Subtracting the given fraction, we will get
 \[\Rightarrow \dfrac{18}{30}-\dfrac{16}{30}=\dfrac{18-16}{30}=\dfrac{2}{30}\]
Reducing it into simplest form,
 \[\Rightarrow \dfrac{18}{30}-\dfrac{16}{30}=\dfrac{2}{30}=\dfrac{1}{15}\]
Therefore,
 \[\Rightarrow \dfrac{6}{10}-\dfrac{8}{15}=\dfrac{1}{15}\] .

III. \[4-\dfrac{3}{7}\]
It can be rewrite as,
 \[\Rightarrow \dfrac{4}{1}-\dfrac{3}{7}\]
Taking the LCM of the denominator,
LCM of 1 and 7 = 7
Therefore,
 \[\Rightarrow \dfrac{4}{1}-\dfrac{3}{7}=\dfrac{4\times 7}{1\times 7}-\dfrac{3}{7}=\dfrac{28}{7}-\dfrac{3}{7}\]
Now,
We have,
 \[\Rightarrow \dfrac{28}{7}-\dfrac{3}{7}\]
Subtracting the given fraction, we will get
 \[\Rightarrow \dfrac{28}{7}-\dfrac{3}{7}=\dfrac{28-3}{7}=\dfrac{25}{7}\]
Therefore,
 \[\Rightarrow 4-\dfrac{3}{7}=\dfrac{25}{7}\] .

IV. \[9+\dfrac{5}{11}\]
It can be rewrite as,
 \[\Rightarrow \dfrac{9}{1}+\dfrac{5}{11}\]
Taking the LCM of the denominator,
LCM of 1 and 11 = 11
Therefore,
 \[\Rightarrow \dfrac{9}{1}+\dfrac{5}{11}=\dfrac{9\times 11}{1\times 11}+\dfrac{5}{11}=\dfrac{99}{11}+\dfrac{5}{11}\]
Now,
We have,
 \[\Rightarrow \dfrac{99}{11}+\dfrac{5}{11}\]
Adding the given fraction, we will get
 \[\Rightarrow \dfrac{99}{11}+\dfrac{5}{11}=\dfrac{99+5}{11}=\dfrac{104}{11}\]
Therefore,
 \[\Rightarrow 9+\dfrac{5}{11}=\dfrac{104}{11}\]

Note: Students should need to remember that for adding and subtraction of fraction, we are required to equal the denominators of all the terms given in the question. Then we will simply add or subtract the numerator of the fraction that contains the same denominator.
If mixed fraction is given in the question, first we need to represent it in the form of proper fraction. We express the process in the form of variables. Let the mixed fraction be \[x\dfrac{c}{b}\] . The improper fraction form will look like \[x+\dfrac{c}{b}=\dfrac{bx+c}{b}\] .