Find the best CBSE Class 8 Solutions for RD Sharma Chapter 1. This guide follows the NCERT Pattern to help you solve Exercise 1.1 easily.
Exercise 1.1 Solutions
Question 1: Add the following rational numbers:
(i) \( -5/7 \) and \( 3/7 \)
The denominators are the same (7).
\( \frac{-5}{7} + \frac{3}{7} = \frac{-5 + 3}{7} \)
\( = \frac{-2}{7} \)
Ans: \( -2/7 \)
Explanation: Since the bottom numbers are the same, we just add the top numbers. Quick Check: \( -5 + 3 = -2 \).
Teacher's Tip: If the denominators are already the same, do not waste time finding the LCM.
Exam Tip: Always check if your final answer can be simplified further.
(ii) \( -15/4 \) and \( 7/4 \)
The denominators are the same (4).
\( \frac{-15}{4} + \frac{7}{4} = \frac{-15 + 7}{4} \)
\( = \frac{-8}{4} \)
\( = -2 \)
Ans: \( -2 \)
Explanation: Add the numerators directly. Quick Check: \( -15 + 7 = -8 \). Then divide \( -8 \) by \( 4 \).
Teacher's Tip: Always divide to the lowest form to get full marks.
Exam Tip: Watch the signs! A negative number plus a smaller positive number stays negative.
(iii) \( -8/11 \) and \( -4/11 \)
The denominators are the same (11).
\( \frac{-8}{11} + \frac{-4}{11} = \frac{-8 + (-4)}{11} \)
\( = \frac{-12}{11} \)
Ans: \( -12/11 \)
Explanation: Adding two negative numbers gives a bigger negative number. Quick Check: \( -8 - 4 = -12 \).
Teacher's Tip: Think of it like debt. If you owe 8 and then owe 4 more, you owe 12.
Exam Tip: Keep the negative sign clearly in front of the fraction.
(iv) \( 6/13 \) and \( -9/13 \)
The denominators are the same (13).
\( \frac{6}{13} + \frac{-9}{13} = \frac{6 - 9}{13} \)
\( = \frac{-3}{13} \)
Ans: \( -3/13 \)
Explanation: Subtract the numbers because one is positive and one is negative. Quick Check: \( 6 - 9 = -3 \).
Teacher's Tip: The sign of the bigger number (9) stays with the answer.
Exam Tip: Double-check the addition of integers before writing the numerator.
Question 2: Add the following rational numbers:
(i) \( 3/4 \) and \( -5/8 \)
The denominators are 4 and 8. The LCM is 8.
\( \frac{3 \times 2}{4 \times 2} = \frac{6}{8} \)
\( \frac{6}{8} + \frac{-5}{8} = \frac{6 - 5}{8} \)
\( = \frac{1}{8} \)
Ans: \( 1/8 \)
Explanation: Change the fractions so they both have the bottom number 8. Quick Check: \( 6/8 \) is the same as \( 3/4 \).
Teacher's Tip: Multiply both top and bottom by the same number to keep the fraction equal.
Exam Tip: Incorrect LCM is a common mistake. Verify that 8 is divisible by both 4 and 8.
(ii) \( 5/-9 \) and \( 7/3 \)
First, make the denominator positive: \( \frac{5}{-9} = \frac{-5}{9} \).
The LCM of 9 and 3 is 9.
\( \frac{7 \times 3}{3 \times 3} = \frac{21}{9} \)
\( \frac{-5}{9} + \frac{21}{9} = \frac{-5 + 21}{9} \)
\( = \frac{16}{9} \)
Ans: \( 16/9 \)
Explanation: We moved the minus sign to the top first. Then we made the bottoms equal to 9. Quick Check: \( 21 - 5 = 16 \).
Teacher's Tip: Always move the minus sign from the denominator to the numerator before solving.
Exam Tip: Students often forget to change the second fraction's denominator. Be careful!
(iii) \( -3 \) and \( 3/5 \)
Write \( -3 \) as \( \frac{-3}{1} \). The LCM is 5.
\( \frac{-3 \times 5}{1 \times 5} = \frac{-15}{5} \)
\( \frac{-15}{5} + \frac{3}{5} = \frac{-15 + 3}{5} \)
\( = \frac{-12}{5} \)
Ans: \( -12/5 \)
Explanation: Every whole number has a denominator of 1. Quick Check: \( -15/5 = -3 \).
Teacher's Tip: Treat whole numbers like fractions by putting them over 1.
Exam Tip: Don't just add 3 to the numerator; you must use the LCM.
Question 3: Simplify:
(i) \( 8/9 + -11/6 \)
The LCM of 9 and 6 is 18.
\( \frac{8 \times 2}{9 \times 2} + \frac{-11 \times 3}{6 \times 3} \)
\( \frac{16}{18} + \frac{-33}{18} = \frac{16 - 33}{18} \)
\( = \frac{-17}{18} \)
Ans: \( -17/18 \)
Explanation: We made the denominators 18. Quick Check: \( 16 - 33 = -17 \).
Teacher's Tip: Find the smallest number that both 9 and 6 go into.
Exam Tip: Be very careful when subtracting a larger number from a smaller one.
(ii) \( 3 + 5/-7 \)
First, rewrite as \( \frac{3}{1} + \frac{-5}{7} \). The LCM is 7.
\( \frac{3 \times 7}{1 \times 7} + \frac{-5}{7} = \frac{21}{7} + \frac{-5}{7} \)
\( = \frac{21 - 5}{7} \)
\( = \frac{16}{7} \)
Ans: \( 16/7 \)
Explanation: Move the minus sign up and use 7 as the common bottom number. Quick Check: \( 21 - 5 = 16 \).
Teacher's Tip: Multiplication tables help you find LCM faster.
Exam Tip: Never leave a negative sign in the denominator in your final step.
Question 4: Add and express the sum as a mixed fraction:
(i) \( -12/5 \) and \( 43/10 \)
The LCM of 5 and 10 is 10.
\( \frac{-12 \times 2}{5 \times 2} = \frac{-24}{10} \)
\( \frac{-24}{10} + \frac{43}{10} = \frac{-24 + 43}{10} \)
\( = \frac{19}{10} \)
Convert to mixed fraction: \( 19 \div 10 = 1 \) remainder \( 9 \).
\( = 1 \frac{9}{10} \)
Ans: \( 1 \frac{9}{10} \)
Explanation: We added the fractions and then divided 19 by 10 to get the mixed form. Quick Check: \( 10 \times 1 + 9 = 19 \).
Teacher's Tip: Mixed fractions are written as \( Quotient \frac{Remainder}{Divisor} \).
Exam Tip: Read the question carefully; if it asks for a mixed fraction, don't leave it as \( 19/10 \).