GSEB Class 6 Maths Solutions Chapter 7 અપૂર્ણાંક સંખ્યાઓ Exercise 7.5

Question 1. નીચેની આકૃતિઓ જોઈ સરવાળા છે કે બાદબાકી એ ચકાસીને અપૂર્ણાંકમાં જવાબ મેળવવાનો પ્રયત્ન કરો: (Observe the figures below and try to determine if they represent addition or subtraction to find the answer in fractions.)
Answer:
(a) The first picture shows \( \frac{1}{5} \), the second picture displays \( \frac{2}{5} \), and the third picture represents \( \frac{3}{5} \). Thus, the pictures demonstrate that adding \( \frac{1}{5} \) and \( \frac{2}{5} \) results in \( \frac{3}{5} \).
\( \frac{1}{5} + \frac{2}{5} = \frac{1+2}{5} = \frac{3}{5} \)
(b) The first picture shows \( \frac{5}{5} = 1 \), the second picture displays \( \frac{3}{5} \), and the third picture represents \( \frac{2}{5} \). Therefore, the pictures indicate that subtracting \( \frac{3}{5} \) from 1 results in \( \frac{2}{5} \).
\( 1 - \frac{3}{5} = \frac{5}{5} - \frac{3}{5} = \frac{5-3}{5} = \frac{2}{5} \)
(c) The first picture shows \( \frac{2}{6} \), the second picture displays \( \frac{3}{6} \), and the third picture represents \( \frac{5}{6} \). Thus, the pictures demonstrate that adding \( \frac{2}{6} \) and \( \frac{3}{6} \) results in \( \frac{5}{6} \).
\( \frac{2}{6} + \frac{3}{6} = \frac{2+3}{6} = \frac{5}{6} \)
In simple words: Look at the pictures to see if the parts are being combined (added) or taken away (subtracted). Then, write down the fractions and perform the calculation.

Exam Tip: Always pay attention to whether the shaded parts are increasing (addition) or decreasing (subtraction) in the sequence of images to determine the correct operation.

Question 2. ઉકેલો: (Solve:)
(a) \( \frac{1}{18} + \frac{1}{18} \)
(b) \( \frac{8}{15} + \frac{3}{15} \)
(c) \( \frac{7}{7} - \frac{5}{7} \)
(d) \( \frac{1}{22} + \frac{21}{22} \)
(e) \( \frac{12}{15} - \frac{7}{15} \)
(f) \( \frac{5}{8} + \frac{3}{8} \)
(g) \( 1 - \frac{2}{3} \)
(h) \( \frac{1}{4} + \frac{0}{4} \)
Answer:
(a) \( \frac{1}{18} + \frac{1}{18} = \frac{1+1}{18} = \frac{2}{18} = \frac{1}{9} \)
(b) \( \frac{8}{15} + \frac{3}{15} = \frac{8+3}{15} = \frac{11}{15} \)
(c) \( \frac{7}{7} - \frac{5}{7} = \frac{7-5}{7} = \frac{2}{7} \)
(d) \( \frac{1}{22} + \frac{21}{22} = \frac{1+21}{22} = \frac{22}{22} = 1 \)
(e) \( \frac{12}{15} - \frac{7}{15} = \frac{12-7}{15} = \frac{5}{15} = \frac{1}{3} \)
(f) \( \frac{5}{8} + \frac{3}{8} = \frac{5+3}{8} = \frac{8}{8} = 1 \)
(g) \( 1 - \frac{2}{3} = \frac{3}{3} - \frac{2}{3} = \frac{3-2}{3} = \frac{1}{3} \)
(h) \( \frac{1}{4} + \frac{0}{4} = \frac{1+0}{4} = \frac{1}{4} \)
In simple words: When adding or subtracting fractions with the same bottom number (denominator), you just add or subtract the top numbers (numerators) and keep the bottom number the same. Always simplify your answer if possible.

Exam Tip: Remember to simplify fractions to their lowest terms after performing addition or subtraction, as this is often required for full marks.

Question 3. શુભમે તેના રૂમની દીવાલના \( \frac{2}{3} \) ભાગ પર રંગ કર્યો અને તેની બહેન માધવીએ તેની રૂમના \( \frac{1}{3} \) ભાગ પર રંગ કરવામાં મદદ કરી, તો બંનેએ સાથે મળીને કુલ કેટલા ભાગ પર રંગ કર્યો? (Shubham painted \( \frac{2}{3} \) of his room's wall, and his sister Madhavi helped him by painting \( \frac{1}{3} \) of his room's wall. So, how much of the wall did both of them paint together?)
Answer:
Shubham's painted portion of the wall \( = \frac{2}{3} \)
Madhavi's painted portion of the wall \( = \frac{1}{3} \)
Total portion of the wall painted by both \( = \frac{2}{3} + \frac{1}{3} \)
\( = \frac{2+1}{3} = \frac{3}{3} = 1 \)
Thus, together they painted the entire wall (whole).
In simple words: To find the total painted area, simply add the parts Shubham and Madhavi each painted. Since their parts add up to 1, they painted the whole wall.

Exam Tip: When combining fractional parts, especially with the same denominator, directly add the numerators. If the sum is \( \frac{n}{n} \), it means the whole object or quantity has been covered.

Question 4. ખૂટતો અપૂર્ણાંક ભરો: (Fill in the missing fraction:)
(a) \( \frac{7}{10} - \Box = \frac{3}{10} \)
(b) \( \Box - \frac{3}{21} = \frac{5}{21} \)
(c) \( \Box - \frac{3}{6} = \frac{3}{6} \)
(d) \( \Box + \frac{5}{27} = \frac{12}{27} \)
Answer:
(a) Here it is clear that the missing fraction is smaller than \( \frac{7}{10} \). Therefore, the missing fraction \( = \frac{7}{10} - \frac{3}{10} = \frac{7-3}{10} = \frac{4}{10} = \frac{2}{5} \) (in simplified form).
So, \( \frac{7}{10} - \frac{2}{5} = \frac{3}{10} \)
(b) Here it is clear that the missing fraction is larger than \( \frac{3}{21} \). The missing fraction is equal to the sum of \( \frac{3}{21} \) and \( \frac{5}{21} \). Therefore, the missing fraction \( = \frac{3}{21} + \frac{5}{21} = \frac{3+5}{21} = \frac{8}{21} \).
So, \( \frac{8}{21} - \frac{3}{21} = \frac{5}{21} \)
(c) Here it is clear that the missing fraction is larger than \( \frac{3}{6} \). The missing fraction is equal to the sum of \( \frac{3}{6} \) and \( \frac{3}{6} \). Therefore, the missing fraction \( = \frac{3}{6} + \frac{3}{6} = \frac{3+3}{6} = \frac{6}{6} = 1 \) (in simplified form).
So, \( 1 - \frac{3}{6} = \frac{3}{6} \)
(d) Here it is clear that the sum of the missing fraction and \( \frac{5}{27} \) is \( \frac{12}{27} \). Therefore, the missing fraction is obtained by subtracting \( \frac{5}{27} \) from \( \frac{12}{27} \). The missing fraction \( = \frac{12}{27} - \frac{5}{27} = \frac{12-5}{27} = \frac{7}{27} \).
So, \( \frac{7}{27} + \frac{5}{27} = \frac{12}{27} \)
In simple words: To find the missing number in fraction problems, you often do the opposite of what's shown. If it's subtraction, you might add; if it's addition, you might subtract. Remember to simplify your final fraction.

Exam Tip: When finding a missing fraction in an equation, treat it like an algebraic variable. If \( x - a = b \), then \( x = a + b \). If \( a - x = b \), then \( x = a - b \). Always isolate the unknown fraction.

Question 5. જાવેદને ટોપલીના \( \frac{5}{7} \) ભાગ જેટલી નારંગી આપવામાં આવી, તો હવે ટોપલીમાં બીજા કેટલા અપૂર્ણાક જેટલા ભાગની નારંગી બાકી હશે? (Javed was given \( \frac{5}{7} \) of a basket of oranges. So, how much of the basket of oranges will be left now?)
Answer:
The whole basket full of oranges \( = 1 \)
The portion of oranges given to Javed from the basket \( = \frac{5}{7} \)
Therefore, the remaining portion of oranges in the basket \( = 1 - \frac{5}{7} \)
\( = \frac{7}{7} - \frac{5}{7} = \frac{7-5}{7} = \frac{2}{7} \)
Thus, \( \frac{2}{7} \) portion of oranges remained in the basket.
In simple words: Imagine the whole basket as '1'. If Javed took \( \frac{5}{7} \) of it, you subtract that from '1' to see how much is still there. Convert '1' to a fraction with the same bottom number as \( \frac{5}{7} \), which is \( \frac{7}{7} \), then subtract.

Exam Tip: For "remaining" problems, always consider the whole as '1'. Convert '1' into a fraction with the same denominator as the given part to easily perform subtraction and find the remaining portion.