What is the value of $\frac{7}{9} - \frac{11}{12} + \frac{13}{16} - \frac{1}{8}$?
Solving Fraction Arithmetic: $\frac{7}{9} - \frac{11}{12} + \frac{13}{16} - \frac{1}{8}$
To evaluate the given expression involving fractions, we need to perform addition and subtraction. This requires finding a common denominator for all the fractions.
Finding the Least Common Denominator (LCD)
- The denominators are 9, 12, 16, and 8.
- Find the prime factorization of each denominator:
- $9 = 3^2$
- $12 = 2^2 \times 3$
- $16 = 2^4$
- $8 = 2^3$
- The Least Common Multiple (LCM), which is the LCD, is found by taking the highest power of each prime factor present: $2^4 \times 3^2 = 16 \times 9 = 144$.
Converting Fractions to the Common Denominator
Convert each fraction to an equivalent fraction with a denominator of 144:
- $\frac{7}{9} = \frac{7 \times 16}{9 \times 16} = \frac{112}{144}$
- $\frac{11}{12} = \frac{11 \times 12}{12 \times 12} = \frac{132}{144}$
- $\frac{13}{16} = \frac{13 \times 9}{16 \times 9} = \frac{117}{144}$
- $\frac{1}{8} = \frac{1 \times 18}{8 \times 18} = \frac{18}{144}$
Performing the Calculation
Substitute the equivalent fractions back into the original expression:
$ \frac{112}{144} - \frac{132}{144} + \frac{117}{144} - \frac{18}{144} $Combine the numerators over the common denominator:
$ \frac{112 - 132 + 117 - 18}{144} $Calculate the result:
$ \frac{(112 + 117) - (132 + 18)}{144} = \frac{229 - 150}{144} = \frac{79}{144} $Final Answer
The value of the expression $\frac{7}{9} - \frac{11}{12} + \frac{13}{16} - \frac{1}{8}$ is $\frac{79}{144}$.
Similar Questions
- $1.236576576...$
can be written in the form of: - What is the sum of $\frac{1}{3}$, $\frac{4}{3}$ and $\frac{3}{4}$?
- Four persons A, B, C and D completed a task in $\frac{2}{3} \text{ h}, \frac{3}{4} \text{ h}, \frac{4}{5} \text{ h}$ and $\frac{1}{5} \text{ h}$ respectively. Who among the following took the highest amount of time to complete the task?
- The value of $\frac{4}{3} + \left( \frac{1}{1 + \frac{5}{6}} \right) - \frac{5}{4}$ is
- How much does one need to add to $\frac{1}{2}$ to get $2$?
- The sum of the numerator and denominator of a fraction is 11. If the numerator is decreased by 1, the fraction becomes $\frac{1}{4}$. Find the fraction.
- If the numerator of a fraction is increased by 30% and its denominator is decreased by 35%, the value of the fraction becomes $\frac{3}{15}$. Find the original fraction.
- Two-fifth of seven-seventeenth of three-fifth of a number is 84. Find 40% of that number.
- A beautician's income includes her salary and the tips she gets for her services. During a particular week, if her tips were $\frac{5}{4}$ of her salary, then what fraction of her income came from the tips?
- What smallest fraction should be added to $3\frac{2}{3} + 6\frac{7}{12} + 4\frac{9}{36} + 5 + 7\frac{1}{12}$ to make the sum a whole number?
Important Questions from Fractions
5 \(\frac{3}{4}\) + x + 2 \(\frac{1}{2}\) = 10 \(\frac{1}{8}\) Find the value of x.
Simplify the expression 441 ÷ \(\left[270 \div \frac{3}{7}+\left(17\div \frac{1}{3}\right)-\left(8\frac{1}{2}-\frac{5}{2}\right)\right]\)
Number 0.232323 can be written in rational form as:
Solve: \(\frac{1}{2}\) [{-2(2 + 3)*20}/2]
Match the following.
Column I
Column II
a.
Equivalent fraction of \(\frac{7}{12}\) is
i.
Proper fraction
b.
Equivalent fraction of \(\frac{9}{15}\) is
ii.
Improper fraction
c.
\(\frac{7}{11}\) is
iii.
\(\frac{21}{36}\)
d.
\(\frac{19}{5}\) is
iv.
\(\frac{3}{5}\)
