Home
Class 7
MATHS
Evaluate: |(1)/(3)-(3)/(5)|+|(2)/(9)xx(3...

Evaluate: `|(1)/(3)-(3)/(5)|+|(2)/(9)xx(3)/(4)|-|(5)/(6)-(2)/(3)|`

Text Solution

AI Generated Solution

The correct Answer is:
To evaluate the expression \( \left| \frac{1}{3} - \frac{3}{5} \right| + \left| \frac{2}{9} \times \frac{3}{4} \right| - \left| \frac{5}{6} - \frac{2}{3} \right| \), we will follow these steps: ### Step 1: Evaluate \( \left| \frac{1}{3} - \frac{3}{5} \right| \) 1. Find the LCM of the denominators 3 and 5. - LCM(3, 5) = 15. 2. Convert \( \frac{1}{3} \) and \( \frac{3}{5} \) to have a common denominator of 15: - \( \frac{1}{3} = \frac{5}{15} \) (since \( 1 \times 5 = 5 \) and \( 3 \times 5 = 15 \)). - \( \frac{3}{5} = \frac{9}{15} \) (since \( 3 \times 3 = 9 \) and \( 5 \times 3 = 15 \)). 3. Now, subtract the two fractions: - \( \frac{5}{15} - \frac{9}{15} = \frac{5 - 9}{15} = \frac{-4}{15} \). 4. Take the absolute value: - \( \left| \frac{-4}{15} \right| = \frac{4}{15} \). ### Step 2: Evaluate \( \left| \frac{2}{9} \times \frac{3}{4} \right| \) 1. Multiply the two fractions: - \( \frac{2}{9} \times \frac{3}{4} = \frac{2 \times 3}{9 \times 4} = \frac{6}{36} \). 2. Simplify \( \frac{6}{36} \): - \( \frac{6}{36} = \frac{1}{6} \). 3. Take the absolute value: - \( \left| \frac{1}{6} \right| = \frac{1}{6} \). ### Step 3: Evaluate \( \left| \frac{5}{6} - \frac{2}{3} \right| \) 1. Convert \( \frac{2}{3} \) to have the same denominator as \( \frac{5}{6} \): - \( \frac{2}{3} = \frac{4}{6} \) (since \( 2 \times 2 = 4 \) and \( 3 \times 2 = 6 \)). 2. Now, subtract the two fractions: - \( \frac{5}{6} - \frac{4}{6} = \frac{5 - 4}{6} = \frac{1}{6} \). 3. Take the absolute value: - \( \left| \frac{1}{6} \right| = \frac{1}{6} \). ### Step 4: Combine the results Now, substitute the results back into the original expression: \[ \frac{4}{15} + \frac{1}{6} - \frac{1}{6} \] Since \( \frac{1}{6} - \frac{1}{6} = 0 \), we have: \[ \frac{4}{15} + 0 = \frac{4}{15} \] ### Final Answer The final answer is \( \frac{4}{15} \). ---
Promotional Banner

Similar Questions

Explore conceptually related problems

Evaluate : (i) ((2)/(-3)xx(5)/(4))+((5)/(9)xx(3)/(-10))

Evaluate: g. 5 (1)/(3) xx 8 (1)/(4) xx 2 (3)/(5)

Evaluate : (64)^((2)/(3))-root(3)(125)-(1)/(2^(-5))+(27)^(-(2)/(3))xx((25)/(9))^(-(1)/(2))

-(3)/(5)times(3)/(5)+(5)/(2)-(3)/(5)times(1)/(6)

Evaluate : [(-(2)/(3))^(-2)]^(3)xx((1)/(3))^(-4)xx3^(-1)xx(1)/(6)

Evaluate : ((1)/(4)) ^(-2) - 3 (32)^((2)/(5)) xx ( 7) ^(0) +((9)/(16))^(-(1)/(2))

Evaluate: c. 5 (1)/(4) xx 3 (5)/(6) + 1 (3)/(5) div 5 (1)/(3)

Evaluate : 5^(-4)xx(125)^((5)/(3))+(25)^(-(1)/(2))

Evaluate: (1/2)^3+\ (1/3)^3-\ \ (5/6)^3

Evaluate : a. (-1)^(11) b. (-3)^(2)xx(5)^(3) c. 6^(2)xx3^(3) d. (-2)^(3)xx(-5)^(2) e. (-1)^(7)xx2 f. (-1)^(4)xx(-1)^(5) g. 4^(3)xx3^(4) h. (-2)^(5)xx5^(3) i. (-4)^(3)xx(-6)^(3) j. (-1)^(33)xx(-3)^(1) k. ((-1)/(6))^(2) l. ((2)/(11))^(3)