Question
Simplify:
$\frac{-7}{10}+\frac{13}{-15}+\frac{27}{20}$
$\frac{-7}{10}+\frac{13}{-15}+\frac{27}{20}$
✓
Answer
$\frac{-7}{10}+\frac{13}{-15}+\frac{27}{20}$
$\frac{13}{-15}=\frac{13\times(-1)}{-15\times(-1)}=\frac{-13}{15}$
Now LCM of 10, 15, 20 = 60
$\begin{array}{c|c}2&10,15,20\\\hline5&5,15,10\\\hline&1,3,2\end{array}$
$\therefore\text{LCM}=2\times5\times3\times2=60$
$\frac{-7}{10}=\frac{-7\times6}{10\times6}=\frac{-42}{60}$
$\frac{-13}{15}=\frac{-13\times4}{15\times4}=\frac{-52}{60}$
$\frac{27}{20}=\frac{27\times3}{20\times3}=\frac{81}{60}$
$\therefore\frac{-7}{10}+\frac{-13}{15}+\frac{27}{20}$
$=\frac{-42}{60}+\frac{-52}{60}+\frac{81}{60}$
$=\frac{-42+(-52)+81}{60}$
$=\frac{-42-52+81}{60}=\frac{-94+81}{60}$
$=\frac{-13}{60}$
$\frac{13}{-15}=\frac{13\times(-1)}{-15\times(-1)}=\frac{-13}{15}$
Now LCM of 10, 15, 20 = 60
$\begin{array}{c|c}2&10,15,20\\\hline5&5,15,10\\\hline&1,3,2\end{array}$
$\therefore\text{LCM}=2\times5\times3\times2=60$
$\frac{-7}{10}=\frac{-7\times6}{10\times6}=\frac{-42}{60}$
$\frac{-13}{15}=\frac{-13\times4}{15\times4}=\frac{-52}{60}$
$\frac{27}{20}=\frac{27\times3}{20\times3}=\frac{81}{60}$
$\therefore\frac{-7}{10}+\frac{-13}{15}+\frac{27}{20}$
$=\frac{-42}{60}+\frac{-52}{60}+\frac{81}{60}$
$=\frac{-42+(-52)+81}{60}$
$=\frac{-42-52+81}{60}=\frac{-94+81}{60}$
$=\frac{-13}{60}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
By selling 3 6 oranges, a vendor suffers a loss equal to the selling price of 4 oranges. Find his loss percent.
ABCD is quadrilateral.
Prove that (AB + BC + CD + DA) > (AC + BD)
Prove that (AB + BC + CD + DA) > (AC + BD)
Draw $\triangle\text{ABC}$ in which $\angle\text{A}=120^\circ,$ AB = AC = 3cm. Measure $\angle\text{B}$ and $\angle\text{C}.$
→question A wall is 4.5 m long and 3 m high. It has two equal windows, each having form and dimensions as shown in Figure. below. Find the cost of painting the wall (leaving windows) at the rate of Rs. 15 per $m ^2$.
→The length of a side of a square field is 4m. What will be the altitude of the rhombus, if the area of the rhombus is equal to the square field and one of its diagonals is 2m?
Draw triangle with the measures given. In ∆EFG, l(EG) = 6 cm, m∠F = 65°, m∠G = 45°.
How much does $a^2-3 a b+2 b^2$ exceed $2 a^2-7 a b+9 b^2$ ?
→If $P=a^2-b^2+2 a b, Q=a^2+4 b^2-6 a b, R=b^2+b, S=a^2-4 a b$ and $T=-2 a^2+b^2-a b+a$. Find $P+Q+R+S-T$.
→Divide the sum of $\frac{65}{12}$ and $\frac{8}{3}$ by their difference.
→Find the values of n in the following:
If $\frac{9^{\text{n}}\times3^2\times3^{\text{n}}-27^{\text{n}}}{(3^3)^5\times2^3}=\frac{1}{27},$ find the value of n
→If $\frac{9^{\text{n}}\times3^2\times3^{\text{n}}-27^{\text{n}}}{(3^3)^5\times2^3}=\frac{1}{27},$ find the value of n