CBSE Class 6 Mathematics Fractions Assignment Set 08

VI - Mathematics Assignments No-03 - Fractions

Question Q1. Find an equivalent fraction of \(\frac{3}{5}\) with numerator as 12
Answer: To find an equivalent fraction with numerator 12, determine what number 3 must be multiplied by to get 12.
\(3 \times 4 = 12\)
Multiply both the numerator and the denominator by 4:
\(\frac{3 \times 4}{5 \times 4} = \frac{12}{20}\)
In simple words: Multiply both top and bottom numbers by 4 to get the new equivalent fraction.

Exam Tip: Always multiply both the numerator and the denominator by the exact same number to keep the fraction's value unchanged.

Question Q2. Find an equivalent fraction of \(\frac{36}{60}\) with numerator as 12
Answer: To find an equivalent fraction with numerator 12, determine what number 36 must be divided by to get 12.
\(36 \div 3 = 12\)
Divide both the numerator and the denominator by 3:
\(\frac{36 \div 3}{60 \div 3} = \frac{12}{20}\)
In simple words: Divide both top and bottom numbers by 3 to reduce the numerator to 12.

Exam Tip: Equivalent fractions can be found by multiplying or dividing both the numerator and the denominator by the same non-zero number.

Question Q3. Among the following set of fractions choose like or unlike fractions:
(i) \(\frac{2}{11}, \frac{4}{11}, \frac{5}{11}, \frac{7}{11}\)
(ii) \(\frac{3}{17}, \frac{5}{11}, \frac{6}{7}, \frac{13}{20}\)
Answer:
(i) Since all the denominators are equal to 11, they are like fractions.
(ii) Since all the denominators are different (17, 11, 7, 20), they are unlike fractions.
In simple words: Fractions with the same bottom numbers are like fractions; different bottom numbers make them unlike fractions.

Exam Tip: Check the denominators first. If all denominators are identical, the fractions are like fractions.

Question Q4. Write any three like and unlike fractions separately.
Answer:
Like fractions: \(\frac{2}{9}, \frac{4}{9}, \frac{7}{9}\)
Unlike fractions: \(\frac{1}{3}, \frac{2}{5}, \frac{3}{7}\)
In simple words: Write down fractions sharing the same denominator for like fractions, and different denominators for unlike fractions.

Exam Tip: You can choose any common denominator for like fractions, such as 9.

Question Q5. Choose like fractions from the following:
(i) \(\frac{1}{13}, \frac{2}{14}, \frac{3}{13}, \frac{5}{13}, \frac{6}{17}\)
(ii) \(\frac{2}{12}, \frac{5}{12}, \frac{7}{17}, \frac{9}{11}, \frac{7}{12}\)
Answer:
(i) Like fractions are \(\frac{1}{13}, \frac{3}{13}, \frac{5}{13}\)
(ii) Like fractions are \(\frac{2}{12}, \frac{5}{12}, \frac{7}{12}\)
In simple words: Group together the fractions that have the same denominator.

Exam Tip: Ignore the numerators when sorting like fractions; only look at the denominators.

Question Q6. Write the next four like fractions:
\(\frac{1}{17}, \frac{3}{17}, \frac{4}{17}, \dots \dots \dots\)
Answer: Observing the pattern in the numerators (1, 3, 4 - note that the sequence in the image shows an implied progression, but looking closely at standard sequence continuation or given answer key: \(\frac{5}{17}, \frac{6}{17}, \frac{7}{17}, \frac{8}{17}\)):
\(\frac{5}{17}, \frac{6}{17}, \frac{7}{17}, \frac{8}{17}\)
In simple words: Keep the denominator 17 the same and increase the numerator by 1 consecutively.

Question Q7. Which of the following are unit fractions:
\(\frac{1}{15}, \frac{15}{7}, \frac{17}{7}, \frac{1}{9}, \frac{1}{13}, \frac{7}{13}, \frac{1}{10}\)
Answer: Unit fractions are fractions with a numerator of 1.
The unit fractions are: \(\frac{1}{15}, \frac{1}{9}, \frac{1}{13}, \frac{1}{10}\)
In simple words: A unit fraction always has 1 as its top number (numerator).

Exam Tip: Always look for 1 in the numerator to identify unit fractions instantly.

Question Q8. Which fraction in each of the following is smaller:
(i) \(\frac{2}{3}\) and \(\frac{1}{3}\)
(ii) \(\frac{5}{6}\) and \(\frac{1}{2}\)
(iii) \(\frac{14}{15}\) and \(\frac{15}{14}\)
(iv) \(\frac{7}{9}\) and \(\frac{5}{12}\)
Answer:
(i) For \(\frac{2}{3}\) and \(\frac{1}{3}\): Since denominators are equal, compare numerators. \(1 < 2\), so \(\frac{1}{3} < \frac{2}{3}\). Smaller fraction is \(\frac{1}{3}\).
(ii) For \(\frac{5}{6}\) and \(\frac{1}{2}\): Convert \(\frac{1}{2}\) to denominator 6: \(\frac{1 \times 3}{2 \times 3} = \frac{3}{6}\). Compare \(\frac{5}{6}\) and \(\frac{3}{6}\). Since \(3 < 5\), \(\frac{3}{6} < \frac{5}{6}\). Smaller fraction is \(\frac{1}{2}\).
(iii) For \(\frac{14}{15}\) and \(\frac{15}{14}\): \(\frac{14}{15}\) is a proper fraction (less than 1) and \(\frac{15}{14}\) is an improper fraction (greater than 1). Thus, \(\frac{14}{15} < \frac{15}{14}\). Smaller fraction is \(\frac{14}{15}\).
(iv) For \(\frac{7}{9}\) and \(\frac{5}{12}\): Convert to a common denominator (LCM of 9 and 12 is 36).
\(\frac{7 \times 4}{9 \times 4} = \frac{28}{36}\)
\(\frac{5 \times 3}{12 \times 3} = \frac{15}{36}\)
Since \(15 < 28\), \(\frac{15}{36} < \frac{28}{36}\). Smaller fraction is \(\frac{5}{12}\).
In simple words: Make denominators the same or convert to decimals/mixed numbers to easily find which fraction is smaller.

Exam Tip: Finding the LCM of denominators is the most reliable method to compare unlike fractions.

Question Q9. Change \(\frac{3}{8}\) and \(\frac{5}{12}\) into equivalent fractions having same denominator. Find the greater fraction.
Answer:
Step 1: Find the LCM of denominators 8 and 12.
Multiples of 8: 8, 16, 24, 32
Multiples of 12: 12, 24, 36
LCM = 24
Step 2: Convert each fraction to have denominator 24.
\(\frac{3 \times 3}{8 \times 3} = \frac{9}{24}\)
\(\frac{5 \times 2}{12 \times 2} = \frac{10}{24}\)
Step 3: Compare the numerators: \(10 > 9\), so \(\frac{10}{24} > \frac{9}{24}\).
Therefore, the greater fraction is \(\frac{5}{12}\) (or \(\frac{10}{24}\)).
In simple words: Make the bottom numbers equal using LCM, then look at the top numbers to see which is bigger.

Exam Tip: The LCM of denominators gives the least common denominator, making calculations simple and accurate.

Question Q10. Arrange the following fractions in descending order:
\(\frac{1}{2}, \frac{1}{4}, \frac{5}{6}, \frac{7}{8}, \frac{3}{4}\)
Answer:
Step 1: Find the LCM of denominators 2, 4, 6, 8, 4.
The denominators are 2, 4, 6, 8. Their LCM is 24.
Step 2: Convert each fraction to an equivalent fraction with denominator 24:
\(\frac{1}{2} = \frac{1 \times 12}{2 \times 12} = \frac{12}{24}\)
\(\frac{1}{4} = \frac{1 \times 6}{4 \times 6} = \frac{6}{24}\)
\(\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}\)
\(\frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24}\)
\(\frac{3}{4} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}\)
Step 3: Compare the numerators in descending order (largest to smallest):
\(21 > 20 > 18 > 12 > 6\)
So, \(\frac{21}{24} > \frac{20}{24} > \frac{18}{24} > \frac{12}{24} > \frac{6}{24}\)
Corresponding original fractions: \(\frac{7}{8}, \frac{5}{6}, \frac{3}{4}, \frac{1}{2}, \frac{1}{4}\)
In simple words: Convert all fractions to the same denominator, then arrange them from largest to smallest based on their top numbers.

Exam Tip: Descending order means arranging items from the greatest to the smallest value.