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After reading \[\dfrac{7}{9}\] of a book, 40 pages are left. How many pages are there in the book?

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Last updated date: 20th Jul 2024
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Answer
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Hint: Here the question is related to fraction, we have to find the total number of pages in the book. To find this first we have to Subtract fraction \[\dfrac{7}{9}\] from 1 to get the remaining part of the book which is not read. On equating a resultant fraction with the number of pages left to read we get the total pages in the book.

Complete step-by-step solution:
Consider the given question:
The part of the book which completed the reading is \[\dfrac{7}{9}\].
The pages left to read are 40.
We have to find the total number of pages in a book.
Now, find the fraction of remaining part of the book which is not read, by subtracting \[\dfrac{7}{9}\] from 1 i.e.,
\[ \Rightarrow \,\,1 - \dfrac{7}{9}\]
Now take 9 as LCM, then we have
\[ \Rightarrow \,\,\dfrac{{9 - 7}}{9}\]
On simplification, we get
\[ \Rightarrow \,\,\dfrac{2}{9}\]
The \[\dfrac{2}{9}\] part of the book which is not read.
Now, find the total number of pages in a book i.e., \[\dfrac{2}{9}\] the part of total pages equal to pages left in the book.
\[ \Rightarrow \,\,number\,of\,pages\,left = \dfrac{2}{9}\, \times total\,pages\]
Let us take total number of pages is \[x\], then
\[ \Rightarrow \,\,40 = \dfrac{2}{9}\, \times x\]
Divide both side by \[\dfrac{2}{9}\], then we have
\[ \Rightarrow \,\,x = 40 \div \dfrac{2}{9}\,\]
Or
\[ \Rightarrow \,\,x = 40 \times \dfrac{9}{2}\,\]
\[ \Rightarrow \,\,x = 20 \times 9\,\]
On multiplication, we get
\[\therefore \,\,x = 180\]
Therefore, the total number of pages in the book is 180.

Note: The number 1 will represent the whole book or whole thing or part, by seeing this students may not be confused why the number 1 has taken to solve the problem. The student must know about the addition and subtraction of like and unlike fractions and table of multiplication.