CBSE Class 4 Maths Fractions Worksheet Set 03

Fill in the blanks :-

Question 1. A fraction is a part of a whole.
Answer: fraction
In simple words: A fraction represents a portion taken out of a complete object or collection.

Exam Tip: Remember that a whole is always considered as 1 or a complete group.

Question 2. The number above the fractional bar is called numerator.
Answer: numerator
In simple words: The top number tells how many parts are taken.

Exam Tip: Think 'N' for North (top) to remember Numerator.

Question 3. The number below the fractional bar is called denominator.
Answer: denominator
In simple words: The bottom number tells the total equal parts the whole is divided into.

Exam Tip: Think 'D' for Down (bottom) to remember Denominator.

Question 4. Four quarters are there in a whole.
Answer: Four
In simple words: A quarter means one-fourth (\(\frac{1}{4}\)), so four quarters make one whole.

Exam Tip: Four quarters make 1 whole just like four 25-paise coins make 1 rupee.

Question 5. Two halves make a whole.
Answer: Two
In simple words: A half is written as \(\frac{1}{2}\), and two halves combine to form 1.

Exam Tip: \(\frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1\).

Question 6. Two quarters are there in one half.
Answer: Two
In simple words: Two parts of \(\frac{1}{4}\) equal \(\frac{2}{4}\), which simplifies to \(\frac{1}{2}\).

Question 7. Three quarters are there in three-fourths.
Answer: Three
In simple words: Three-fourths means three parts of \(\frac{1}{4}\).

Exam Tip: Three-fourths is written numerically as \(\frac{3}{4}\).

Question 8. Three quarters can be represented as \(\frac{3}{4}\).
Answer: \(\frac{3}{4}\)
In simple words: Three out of four equal parts is written as \(\frac{3}{4}\).

Exam Tip: Quarter always denotes denominator 4.

Question 9. In \(\frac{8}{15}\), numerator is 8 and denominator is 15.
Answer: 8, 15
In simple words: Top number is 8 and bottom number is 15.

Exam Tip: Always state numerator first, then denominator.

Question 10. Fractions which indicate the same value are equivalent fractions.
Answer: equivalent
In simple words: Fractions that look different but represent the same amount are equivalent.

Exam Tip: Multiply or divide numerator and denominator by the same number to find equivalent fractions.

Question 11. Fractions that have the same denominator are called like fractions.
Answer: like
In simple words: Fractions with identical bottom numbers are like fractions.

Exam Tip: Example of like fractions: \(\frac{2}{7}, \frac{4}{7}, \frac{5}{7}\).

Question 12. Fractions that have different denominators are called unlike fractions.
Answer: unlike
In simple words: Fractions with different bottom numbers are unlike fractions.

Exam Tip: Example of unlike fractions: \(\frac{1}{3}, \frac{2}{5}, \frac{3}{7}\).

Question 13. \(\frac{9}{16}\) < \(\frac{10}{16}\)
Answer: <
In simple words: Since denominators are equal, compare numerators: 9 is smaller than 10.

Exam Tip: For like fractions, the fraction with the smaller numerator is smaller.

Question 14. \(\frac{3}{7} + 0 = \frac{3}{7}\)
Answer: \(\frac{3}{7}\)
In simple words: Adding zero to any fraction leaves the fraction unchanged.

Exam Tip: This is the zero property of addition.

Question 15. A fraction with the numerator less than the denominator is a proper fraction.
Answer: proper
In simple words: When the top number is smaller than the bottom number, it is proper.

Exam Tip: Proper fractions are always less than 1.

Question 16. A fraction with the numerator greater than or equal to the denominator is an improper fraction.
Answer: improper
In simple words: When the top number is bigger than or equal to the bottom number, it is improper.

Exam Tip: Improper fractions are greater than or equal to 1.

Question 17. Proper fractions that have 1 as the numerator are called unit fractions.
Answer: unit
In simple words: Fractions with 1 on top are unit fractions.

Exam Tip: Examples of unit fractions: \(\frac{1}{2}, \frac{1}{3}, \frac{1}{8}\).

Question 18. Fractions having a whole number and a fractional number are called mixed fractions (or mixed numbers).
Answer: mixed
In simple words: A combination of a whole number and a proper fraction is a mixed fraction.

Exam Tip: Example: \(2\frac{1}{3}\).

Question 19. \(\frac{1}{2}, \frac{1}{9}, \frac{1}{4}, \frac{1}{8}\), etc. are unit fractions.
Answer: unit
In simple words: All these fractions have 1 as their numerator.

Exam Tip: Check if numerator is 1 for unit fractions.

Question 20. \(\frac{3}{8}, \frac{17}{8}, \frac{11}{8}, \frac{9}{16}, \frac{6}{8}\), etc. are... [Wait, let's look at denominators: 8, 8, 8, 16, 8. They are fractions with common denominators or check next line. Actually \(\frac{3}{8}, \frac{17}{8}, \frac{11}{8}, \frac{6}{8}\) are like fractions, let's classify based on context.]
Answer: unlike (or improper/like depending on exact categorization, here denominators are mixed 8 and 16, so unlike fractions)
In simple words: Fractions with different denominators are unlike fractions.

Exam Tip: Look at the bottom numbers to determine like or unlike.

Question 21. \(\frac{1}{11}, \frac{4}{11}, \frac{5}{11}, \frac{8}{11}\), etc. are like fractions.
Answer: like
In simple words: All these fractions have the same denominator 11.

Exam Tip: Same denominators mean like fractions.

Do the following

Question 1. Study the shaded regions and fill in the blanks.
a) \(\frac{1}{2} = \frac{4}{8}\)
b) \(\frac{2}{3} = \frac{4}{6}\)
c) \(\frac{1}{2} = \frac{3}{6}\)
d) \(\frac{3}{4} = \frac{6}{8}\)
Answer: a) 4, b) 4, c) 3, d) 3
In simple words: Count the shaded parts in the second figure to find the equivalent numerator.

Exam Tip: Ensure numerator and denominator are multiplied by the same number.

Question 2. Colour \(\frac{1}{3}\) of the stars on the left and \(\frac{4}{12}\) of the stars on the right.
Answer: Colour 4 stars in the left group (since \(\frac{1}{3}\) of 12 = 4) and 4 stars in the right group.
In simple words: Divide the total number of items by the denominator and multiply by the numerator.

Exam Tip: Total stars = 12. \(\frac{1}{3} \times 12 = 4\).

Put in the sign (<, > or =) the boxes to show what you observe.
\(\frac{1}{3} \square \frac{4}{12}\)
Answer: \(\frac{1}{3} = \frac{4}{12}\)
In simple words: Simplify \(\frac{4}{12}\) by dividing top and bottom by 4 to get \(\frac{1}{3}\).

Exam Tip: Equivalent fractions are always equal to each other.

Question 3. Colour the following to show equivalent fractions.
a) \(\frac{1}{2} = \frac{2}{4}\)
b) \(\frac{1}{3} = \frac{2}{6}\)
c) \(\frac{2}{4} = \frac{4}{8}\)
d) \(\frac{4}{8} = \frac{8}{16}\)
Answer: Colour the corresponding number of parts in each figure to match the equivalent fraction.
In simple words: Shade the required number of equal segments.

Exam Tip: Verify that the shaded proportion looks identical in both shapes.

Question 4. Identify these as like and unlike fractions.
a. \(\frac{12}{15}, \frac{6}{15}\)
b. \(\frac{1}{6}, \frac{1}{4}, \frac{1}{2}\)
c. \(\frac{3}{11}, \frac{6}{12}, \frac{4}{9}\)
d. \(\frac{7}{10}, \frac{3}{10}, \frac{8}{10}\)
e. \(\frac{1}{16}, \frac{2}{16}, \frac{6}{16}\)
f. \(\frac{2}{5}, \frac{1}{5}\)
Answer:
a. Like fractions
b. Unlike fractions
c. Unlike fractions
d. Like fractions
e. Like fractions
f. Like fractions
In simple words: If denominators are the same, they are like fractions. If different, they are unlike.

Exam Tip: Look only at the denominators to classify.

Question 5. Compare the fractions and fill in the blanks with <, > or =
a. \(\frac{11}{15} \square \frac{2}{15}\)
b. \(\frac{4}{9} \square \frac{4}{9}\)
c. \(\frac{9}{12} \square \frac{6}{12}\)
d. \(\frac{3}{8} \square \frac{7}{8}\)
e. \(\frac{2}{6} \square \frac{2}{8}\)
f. \(\frac{1}{8} \square \frac{1}{6}\)
g. \(\frac{8}{9} \square \frac{7}{10}\)
h. \(\frac{3}{5} \square \frac{3}{5}\)
Answer:
a. \(\frac{11}{15} > \frac{2}{15}\)
b. \(\frac{4}{9} = \frac{4}{9}\)
c. \(\frac{9}{12} > \frac{6}{12}\)
d. \(\frac{3}{8} < \frac{7}{8}\)
e. \(\frac{2}{6} > \frac{2}{8}\)
f. \(\frac{1}{8} < \frac{1}{6}\)
g. \(\frac{8}{9} > \frac{7}{10}\) (Cross multiply: \(8 \times 10 = 80\), \(9 \times 7 = 63\))
h. \(\frac{3}{5} = \frac{3}{5}\)
In simple words: Compare numerators when denominators are equal. For same numerators, the fraction with the smaller denominator is larger.

Exam Tip: Use cross-multiplication for fractions with different numerators and denominators.

Question 6. Arrange the following in ascending order.
a. \(\frac{2}{9}, \frac{7}{9}, \frac{1}{9}, \frac{8}{9}, \frac{5}{9}\)
b. \(\frac{3}{10}, \frac{9}{10}, \frac{6}{10}, \frac{4}{10}\)
c. \(\frac{3}{4}, \frac{1}{4}, \frac{2}{4}\)
d. \(\frac{10}{12}, \frac{7}{12}, \frac{12}{12}, \frac{3}{12}, \frac{6}{12}, \frac{8}{12}\)
Answer:
a. \(\frac{1}{9}, \frac{2}{9}, \frac{5}{9}, \frac{7}{9}, \frac{8}{9}\)
b. \(\frac{3}{10}, \frac{4}{10}, \frac{6}{10}, \frac{9}{10}\)
c. \(\frac{1}{4}, \frac{2}{4}, \frac{3}{4}\)
d. \(\frac{3}{12}, \frac{6}{12}, \frac{7}{12}, \frac{8}{12}, \frac{10}{12}, \frac{12}{12}\)
In simple words: Arrange from smallest to largest numerator since denominators are all equal.

Exam Tip: Ascending means going up (smallest to largest).

Question 7. Arrange the following in descending order.
a. \(\frac{5}{7}, \frac{1}{7}, \frac{6}{7}, \frac{3}{7}, \frac{4}{7}\)
b. \(\frac{8}{16}, \frac{11}{16}, \frac{14}{16}, \frac{10}{16}\)
c. \(\frac{2}{20}, \frac{11}{20}, \frac{15}{20}, \frac{18}{20}, \frac{20}{20}\)
d. \(\frac{1}{8}, \frac{7}{8}, \frac{2}{8}\)
Answer:
a. \(\frac{6}{7}, \frac{5}{7}, \frac{4}{7}, \frac{3}{7}, \frac{1}{7}\)
b. \(\frac{14}{16}, \frac{11}{16}, \frac{10}{16}, \frac{8}{16}\)
c. \(\frac{20}{20}, \frac{18}{20}, \frac{15}{20}, \frac{11}{20}, \frac{2}{20}\)
d. \(\frac{7}{8}, \frac{2}{8}, \frac{1}{8}\)
In simple words: Arrange from largest to smallest numerator.

Exam Tip: Descending means going down (largest to smallest).

Question 8. Add
a. \(\frac{4}{10} + \frac{5}{10}\)
b. \(\frac{14}{17} + \frac{1}{17}\)
c. \(\frac{2}{7} + \frac{5}{7}\)
d. \(\frac{9}{15} + \frac{4}{15}\)
e. \(\frac{8}{13} + \frac{5}{13}\)
f. \(\frac{6}{9} + \frac{2}{9}\)
Answer:
a. \(\frac{4 + 5}{10} = \frac{9}{10}\)
b. \(\frac{14 + 1}{17} = \frac{15}{17}\)
c. \(\frac{2 + 5}{7} = \frac{7}{7} = 1\)
d. \(\frac{9 + 4}{15} = \frac{13}{15}\)
e. \(\frac{8 + 5}{13} = \frac{13}{13} = 1\)
f. \(\frac{6 + 2}{9} = \frac{8}{9}\)
In simple words: Add the numerators together and keep the common denominator the same.

Exam Tip: Never add the denominators together.

Question 9. Subtract
a. \(\frac{8}{10} - \frac{5}{10}\)
b. \(\frac{13}{15} - \frac{9}{15}\)
c. \(\frac{4}{6} - \frac{4}{6}\)
d. \(\frac{12}{14} - \frac{9}{14}\)
e. \(\frac{10}{13} - \frac{8}{13}\)
f. \(\frac{7}{9} - \frac{1}{9}\)
Answer:
a. \(\frac{8 - 5}{10} = \frac{3}{10}\)
b. \(\frac{13 - 9}{15} = \frac{4}{15}\)
c. \(\frac{4 - 4}{6} = \frac{0}{6} = 0\)
d. \(\frac{12 - 9}{14} = \frac{3}{14}\)
e. \(\frac{10 - 8}{13} = \frac{2}{13}\)
f. \(\frac{7 - 1}{9} = \frac{6}{9}\) (or \(\frac{2}{3}\))
In simple words: Subtract the second numerator from the first and keep the denominator the same.

Question 10. Find the fraction in each of the following.
a) \(\frac{7}{9}\) of 36
b) \(\frac{1}{2}\) of 24
c) \(\frac{3}{8}\) of 48
d) \(\frac{4}{7}\) of 49
e) \(\frac{8}{11}\) of 99
f) \(\frac{4}{5}\) of 50
Answer:
a) \(36 \div 9 = 4\)
\(4 \times 7 = 28\)
b) \(24 \div 2 = 12\)
\(12 \times 1 = 12\)
c) \(48 \div 8 = 6\)
\(6 \times 3 = 18\)
d) \(49 \div 7 = 7\)
\(7 \times 4 = 28\)
e) \(99 \div 11 = 9\)
\(9 \times 8 = 72\)
f) \(50 \div 5 = 10\)
\(10 \times 4 = 40\)
In simple words: Divide the whole number by the denominator, then multiply the result by the numerator.

Exam Tip: 'Of' means multiplication.

Question 11. Find the fraction in each of the following.
a) \(\frac{5}{6}\) of a day (in hours)
b) \(\frac{2}{3}\) of a dozen
c) \(\frac{4}{10}\) of an hour (in minutes)
d) \(\frac{3}{7}\) of a week (in days)
e) \(\frac{1}{4}\) of 1kg (in gram)
f) \(\frac{3}{4}\) of 1 litre (in milli litre)
Answer:
a) 1 day = 24 hours
\(24 \div 6 = 4\)
\(4 \times 5 = 20\) hours
b) 1 dozen = 12 items
\(12 \div 3 = 4\)
\(4 \times 2 = 8\)
c) 1 hour = 60 minutes
\(60 \div 10 = 6\)
\(6 \times 4 = 24\) minutes
d) 1 week = 7 days
\(7 \div 7 = 1\)
\(1 \times 3 = 3\) days
e) 1 kg = 1000 g
\(1000 \div 4 = 250\)
\(250 \times 1 = 250\) g
f) 1 litre = 1000 ml
\(1000 \div 4 = 250\)
\(250 \times 3 = 750\) ml
In simple words: Convert the unit first (e.g., day to hours), then calculate the fraction.

Exam Tip: Memorize standard conversions: 1 day = 24 hrs, 1 hour = 60 mins, 1 kg = 1000 g, 1 litre = 1000 ml, 1 dozen = 12.

Question 12. Use the pictures to write the improper fractions and then convert them into mixed numbers.
(Hint: The number of parts in each shape gives you the denominator)
Answer:
a) Improper fraction: \(\frac{3}{2}\), Mixed number: \(1\frac{1}{2}\)
b) Improper fraction: \(\frac{7}{3}\), Mixed number: \(2\frac{1}{3}\)
c) Improper fraction: \(\frac{5}{4}\), Mixed number: \(1\frac{1}{4}\)
In simple words: Count total shaded parts for the numerator and parts in one whole for the denominator.

Exam Tip: Divide the numerator by the denominator to get the whole number and remainder.

Question 13. Convert these improper fractions into mixed numbers.
a) \(\frac{9}{6}\)
b) \(\frac{5}{2}\)
c) \(\frac{14}{8}\)
d) \(\frac{7}{3}\)
e) \(\frac{19}{9}\)
f) \(\frac{17}{5}\)
Answer:
a) \(9 \div 6 = 1\) remainder 3 = \(1\frac{3}{6}\) (or \(1\frac{1}{2}\))
b) \(5 \div 2 = 2\) remainder 1 = \(2\frac{1}{2}\)
c) \(14 \div 8 = 1\) remainder 6 = \(1\frac{6}{8}\) (or \(1\frac{3}{4}\))
d) \(7 \div 3 = 2\) remainder 1 = \(2\frac{1}{3}\)
e) \(19 \div 9 = 2\) remainder 1 = \(2\frac{1}{9}\)
f) \(17 \div 5 = 3\) remainder 2 = \(3\frac{2}{5}\)
In simple words: Quotient is the whole number, remainder is the new numerator, and denominator stays the same.

Exam Tip: Always reduce the fractional part to lowest terms if possible.

Question 14. Convert these improper fractions into whole numbers.
a) \(\frac{12}{3}\)
b) \(\frac{18}{9}\)
c) \(\frac{64}{8}\)
d) \(\frac{27}{3}\)
e) \(\frac{55}{11}\)
f) \(\frac{72}{12}\)
Answer:
a) \(12 \div 3 = 4\)
b) \(18 \div 9 = 2\)
c) \(64 \div 8 = 8\)
d) \(27 \div 3 = 9\)
e) \(55 \div 11 = 5\)
f) \(72 \div 12 = 6\)
In simple words: Divide the numerator by the denominator.

Exam Tip: These fractions divide evenly without any remainder.

Question 15. Convert these mixed numbers into improper fractions.
a) \(4\frac{1}{2}\)
b) \(9\frac{2}{6}\)
c) \(7\frac{1}{4}\)
d) \(3\frac{3}{7}\)
e) \(8\frac{4}{5}\)
f) \(15\frac{1}{2}\)
Answer:
a) \(\frac{(4 \times 2) + 1}{2} = \frac{8 + 1}{2} = \frac{9}{2}\)
b) \(9\frac{2}{6} = 9\frac{1}{3}\), \(\frac{(9 \times 3) + 1}{3} = \frac{28}{3}\) (or \(\frac{(9 \times 6) + 2}{6} = \frac{56}{6}\))
c) \(\frac{(7 \times 4) + 1}{4} = \frac{28 + 1}{4} = \frac{29}{4}\)
d) \(\frac{(3 \times 7) + 3}{7} = \frac{21 + 3}{7} = \frac{24}{7}\)
e) \(\frac{(8 \times 5) + 4}{5} = \frac{40 + 4}{5} = \frac{44}{5}\)
f) \(\frac{(15 \times 2) + 1}{2} = \frac{30 + 1}{2} = \frac{31}{2}\)
In simple words: Multiply the whole number by the denominator, add the numerator, and put it over the same denominator.

Exam Tip: Formula: \(\frac{(\text{Whole} \times \text{Denominator}) + \text{Numerator}}{\text{Denominator}}\).