CBSE Class 4 Maths Fractions Worksheet Set 04

I Fill in the answers-

Question a). \(\frac{8}{9}\), \(\frac{4}{5}\) and \(\frac{2}{3}\) are a group of _________ fractions.
Answer: Unlike fractions
In simple words: Fractions with different denominators are called unlike fractions.

Exam Tip: Check the denominators; if they are not the same, the fractions are unlike.

Question b). \(\frac{7}{12} = \frac{\square}{84}\)
Answer: 49
To find the missing numerator, determine what 12 is multiplied by to get 84:
\(84 \div 12 = 7\)
Multiply the numerator 7 by 7:
\(7 \times 7 = 49\)
In simple words: Multiply both the numerator and the denominator by the same number to find the equivalent fraction.

Exam Tip: Always divide the new denominator by the old denominator to find the multiplier.

Question c). \(\frac{9}{15}\) and \(\frac{12}{20}\) _________ (are / are not) equivalent fractions.
Answer: are
Simplify both fractions to their lowest terms:
\(\frac{9}{15} = \frac{9 \div 3}{15 \div 3} = \frac{3}{5}\)
\(\frac{12}{20} = \frac{12 \div 4}{20 \div 4} = \frac{3}{5}\)
Since both fractions simplify to \(\frac{3}{5}\), they are equivalent fractions.
In simple words: Simplify both fractions to check if they represent the same value.

Exam Tip: You can also use cross-multiplication: \(9 \times 20 = 180\) and \(15 \times 12 = 180\). Since products are equal, they are equivalent.

Question d). The improper fraction for \(8\frac{5}{11}\) is _________ .
Answer: \(\frac{93}{11}\)
Multiply the whole number by the denominator and add the numerator:
\((8 \times 11) + 5 = 88 + 5 = 93\)
Place the result over the denominator 11.
In simple words: Whole number times denominator plus numerator gives the new numerator.

Exam Tip: Keep the denominator exactly the same when converting mixed numbers to improper fractions.

Question e). The mixed number for \(\frac{101}{15}\) is _________ .
Answer: \(6\frac{11}{15}\)
Divide 101 by 15:
\(101 \div 15 = 6\) with a remainder of 11.
Write the quotient as the whole number, the remainder as the numerator, and keep the denominator 15.
In simple words: Divide numerator by denominator to get the whole number and remainder.

Exam Tip: Check your answer by converting back: \((6 \times 15) + 11 = 90 + 11 = 101\).

Question f). A fraction with numerator 1 is called _________ fraction.
Answer: unit
In simple words: Any fraction with 1 as the top number is a unit fraction.

Exam Tip: Memorize basic fraction vocabulary terms like unit fraction, proper fraction, and improper fraction.

Question g). 27/35 - 9/35 = ...................
Answer: \(\frac{18}{35}\)
Since denominators are the same, subtract the numerators:
\(27 - 9 = 18\)
Result = \(\frac{18}{35}\)
In simple words: Subtract the top numbers and keep the bottom number the same when denominators match.

Exam Tip: Never subtract the denominators in addition or subtraction of fractions.

Question h). \(\frac{6}{11}\), \(\frac{6}{15}\), \(\frac{6}{19}\) and \(\frac{6}{23}\) are arranged in _________ order.
Answer: descending
In simple words: When numerators are equal, the fraction with the smallest denominator is the largest, making this a descending order.

Exam Tip: For fractions with the same numerator, larger denominator means smaller value.

Question i). \(\frac{9}{10} \square \frac{7}{8}\) (\(>\) or \(<\))
Answer: \(>\)
Cross-multiply to compare:
\(9 \times 8 = 72\)
\(10 \times 7 = 70\)
Since \(72 > 70\), \(\frac{9}{10} > \frac{7}{8}\)
In simple words: Cross-multiplication helps compare two fractions easily.

Exam Tip: Always write the product on the side of the numerator you started with.

Question j). \(\frac{82}{7} = 11\frac{\square}{7}\)
Answer: 5
Divide 82 by 7:
\(11 \times 7 = 77\)
Remainder = \(82 - 77 = 5\)
In simple words: Find the remainder when the numerator is divided by the denominator.

Exam Tip: The denominator in the mixed fraction remains unchanged.

II Find the next four equivalent fractions for-

Question a). \(\frac{9}{14}\)
Answer:
Multiply the numerator and denominator by 2, 3, 4, and 5:
\(\frac{9 \times 2}{14 \times 2} = \frac{18}{28}\)
\(\frac{9 \times 3}{14 \times 3} = \frac{27}{42}\)
\(\frac{9 \times 4}{14 \times 4} = \frac{36}{56}\)
\(\frac{9 \times 5}{14 \times 5} = \frac{45}{70}\)
Next four equivalent fractions are \(\frac{18}{28}, \frac{27}{42}, \frac{36}{56}, \frac{45}{70}\).
In simple words: Multiply top and bottom by 2, 3, 4, and 5 in sequence.

Exam Tip: Show your multiplication clearly for each step to avoid calculation errors.

Question b). \(\frac{1}{20}\)
Answer:
Multiply the numerator and denominator by 2, 3, 4, and 5:
\(\frac{1 \times 2}{20 \times 2} = \frac{2}{40}\)
\(\frac{1 \times 3}{20 \times 3} = \frac{3}{60}\)
\(\frac{1 \times 4}{20 \times 4} = \frac{4}{80}\)
\(\frac{1 \times 5}{20 \times 5} = \frac{5}{100}\)
Next four equivalent fractions are \(\frac{2}{40}, \frac{3}{60}, \frac{4}{80}, \frac{5}{100}\).
In simple words: Multiply both numbers by consecutive whole numbers starting from 2.

Exam Tip: Double-check multiplication tables for the denominator.

III Reduce to the lowest term-

Question a). \(\frac{140}{200}\)
Answer:
Find the Highest Common Factor (HCF) of 140 and 200, or divide by common factors step-by-step:
\(\frac{140 \div 10}{200 \div 10} = \frac{14}{20}\)
\(\frac{14 \div 2}{20 \div 2} = \frac{7}{10}\)
In simple words: Cancel out common zeros and divide by common factors until no more reduction is possible.

Exam Tip: A fraction is in lowest terms when the numerator and denominator have no common factor other than 1.

Question b). \(\frac{96}{124}\)
Answer:
Divide both numerator and denominator by their common factor 4:
\(\frac{96 \div 4}{124 \div 4} = \frac{24}{31}\)
In simple words: Divide top and bottom by the largest number that divides both evenly.

Exam Tip: 31 is a prime number, so \(\frac{24}{31}\) cannot be simplified further.

IV Find any two lower equivalent fractions for-

Question a). \(\frac{200}{300}\)
Answer:
Divide numerator and denominator by common factors like 2 and 10:
1) Divide by 10: \(\frac{200 \div 10}{300 \div 10} = \frac{20}{30}\)
2) Divide by 100: \(\frac{200 \div 100}{300 \div 100} = \frac{2}{3}\)
Lower equivalent fractions are \(\frac{20}{30}\) and \(\frac{2}{3}\).
In simple words: Divide both numbers by the same number to get smaller equivalent fractions.

Exam Tip: Lower equivalent fractions are found by division, whereas higher ones are found by multiplication.

Question b). \(\frac{75}{90}\)
Answer:
1) Divide by 5: \(\frac{75 \div 5}{90 \div 5} = \frac{15}{18}\)
2) Divide by 15: \(\frac{75 \div 15}{90 \div 15} = \frac{5}{6}\)
Lower equivalent fractions are \(\frac{15}{18}\) and \(\frac{5}{6}\).
In simple words: Divide the top and bottom numbers by their common divisors.

Exam Tip: Look for numbers ending in 0 or 5 to quickly spot division by 5.

V Are the following fractions equivalent-

Question a). \(\frac{8}{12}\) and \(\frac{6}{9}\)
Answer:
Simplify both fractions:
\(\frac{8}{12} = \frac{8 \div 4}{12 \div 4} = \frac{2}{3}\)
\(\frac{6}{9} = \frac{6 \div 3}{9 \div 3} = \frac{2}{3}\)
Since both simplify to \(\frac{2}{3}\), they are equivalent fractions.
In simple words: Reduce both fractions to their simplest form to check equality.

Exam Tip: Cross-multiplication check: \(8 \times 9 = 72\) and \(12 \times 6 = 72\). Both products are equal.

Question b). \(\frac{6}{15}\) and \(\frac{4}{12}\)
Answer:
Simplify both fractions:
\(\frac{6}{15} = \frac{6 \div 3}{15 \div 3} = \frac{2}{5}\)
\(\frac{4}{12} = \frac{4 \div 4}{12 \div 4} = \frac{1}{3}\)
Since \(\frac{2}{5} \neq \frac{1}{3}\), they are not equivalent fractions.
In simple words: If simplified forms are different, the fractions are not equivalent.

Exam Tip: Cross-multiplication check: \(6 \times 12 = 72\) and \(15 \times 4 = 60\). Since \(72 \neq 60\), they are not equivalent.

VI Solve-

Question a). \(\frac{8}{15} + \frac{7}{9}\)
Answer:
Find the LCM of 15 and 9, which is 45.
Convert fractions to have the denominator 45:
\(\frac{8 \times 3}{15 \times 3} = \frac{24}{45}\)
\(\frac{7 \times 5}{9 \times 5} = \frac{35}{45}\)
Add the numerators:
\(\frac{24 + 35}{45} = \frac{59}{45} = 1\frac{14}{45}\)
In simple words: Find a common denominator before adding numerators.

Exam Tip: Always find the Least Common Multiple (LCM) of denominators for addition.

Question b). \(3\frac{1}{3} + 2\frac{5}{6} + \frac{5}{8}\)
Answer:
Convert mixed numbers to improper fractions:
\(3\frac{1}{3} = \frac{10}{3}\)
\(2\frac{5}{6} = \frac{17}{6}\)
Find the LCM of denominators 3, 6, and 8, which is 24.
Convert each fraction:
\(\frac{10 \times 8}{3 \times 8} = \frac{80}{24}\)
\(\frac{17 \times 4}{6 \times 4} = \frac{68}{24}\)
\(\frac{5 \times 3}{8 \times 3} = \frac{15}{24}\)
Add the numerators:
\(\frac{80 + 68 + 15}{24} = \frac{163}{24} = 6\frac{19}{24}\)
In simple words: Convert mixed fractions first, make denominators equal, then add.

Exam Tip: Doing LCM for all denominators at once prevents multiple conversion steps.

Question c). \(9 - 3\frac{4}{5}\)
Answer:
Convert whole number 9 into a fraction with denominator 5 or borrow from 9:
\(9 = 8\frac{5}{5}\)
Subtract the mixed number:
\(8\frac{5}{5} - 3\frac{4}{5} = (8 - 3) + \left(\frac{5}{5} - \frac{4}{5}\right) = 5 + \frac{1}{5} = 5\frac{1}{5}\)
In simple words: Borrow 1 from the whole number and write it as a fraction with the same denominator.

Exam Tip: Alternatively, convert 9 to \(\frac{45}{5}\) and \(3\frac{4}{5}\) to \(\frac{19}{5}\), then subtract to get \(\frac{26}{5} = 5\frac{1}{5}\).

Question d). \(7\frac{2}{3} - 2\frac{3}{4}\)
Answer:
Convert mixed numbers to improper fractions:
\(7\frac{2}{3} = \frac{23}{3}\)
\(2\frac{3}{4} = \frac{11}{4}\)
Find the LCM of 3 and 4, which is 12.
Convert fractions:
\(\frac{23 \times 4}{3 \times 4} = \frac{92}{12}\)
\(\frac{11 \times 3}{4 \times 3} = \frac{33}{12}\)
Subtract the numerators:
\(\frac{92 - 33}{12} = \frac{59}{12} = 4\frac{11}{12}\)
In simple words: Convert to improper fractions, find a common denominator, and subtract.

Exam Tip: Converting mixed numbers to improper fractions is usually the safest method for subtraction.

VII Find-

Question a). \(\frac{7}{8}\) of Rs. 560
Answer:
Multiply \(\frac{7}{8}\) by 560:
\(\frac{7}{8} \times 560 = 7 \times (560 \div 8)\)
\(560 \div 8 = 70\)
\(7 \times 70 = 490\)
Result = Rs. 490
In simple words: Divide the number by the denominator and multiply by the numerator.

Exam Tip: Always divide first before multiplying to keep numbers small and manageable.

Question b). \(\frac{3}{4}\) of 1 kg (in grams)
Answer:
1 kg = 1000 grams
\(\frac{3}{4} \times 1000 = 3 \times (1000 \div 4)\)
\(1000 \div 4 = 250\)
\(3 \times 250 = 750 \text{ grams}\)
In simple words: Convert 1 kg to 1000 grams first, then calculate the fraction.

Exam Tip: Pay attention to unit conversion requirements specified in brackets.

Question c). \(\frac{5}{6}\) of 72 km
Answer:
\(\frac{5}{6} \times 72 = 5 \times (72 \div 6)\)
\(72 \div 6 = 12\)
\(5 \times 12 = 60 \text{ km}\)
In simple words: Divide 72 by 6, then multiply the result by 5.

Exam Tip: Include the unit (km) in your final answer.

Question d). \(\frac{9}{13}\) of 104
Answer:
\(\frac{9}{13} \times 104 = 9 \times (104 \div 13)\)
\(104 \div 13 = 8\)
\(9 \times 8 = 72\)
In simple words: Divide 104 by 13 and multiply by 9.

Exam Tip: Memorize multiplication tables up to 15 to quickly calculate division with numbers like 13.

VIII Put the \(>, <\) or \(=\) sign-

Question a). \(\frac{8}{11} \square \frac{7}{12}\)
Answer: \(>\)
Cross-multiply:
\(8 \times 12 = 96\)
\(11 \times 7 = 77\)
Since \(96 > 77\), \(\frac{8}{11} > \frac{7}{12}\)
In simple words: Compare cross-products to determine the larger fraction.

Exam Tip: The larger cross-product indicates the larger fraction.

Question b). \(\frac{20}{30} \square \frac{7}{8}\)
Answer: \(<\)
Simplify \(\frac{20}{30}\) to \(\frac{2}{3}\).
Cross-multiply \(\frac{2}{3}\) and \(\frac{7}{8}\):
\(2 \times 8 = 16\)
\(3 \times 7 = 21\)
Since \(16 < 21\), \(\frac{20}{30} < \frac{7}{8}\)
In simple words: Simplify the fraction first to make cross-multiplication easier.

Exam Tip: Simplifying fractions before comparing always saves time.

Question c). \(\frac{16}{40} \square \frac{8}{20}\)
Answer: \(=\)
Simplify both fractions:
\(\frac{16}{40} = \frac{16 \div 8}{40 \div 8} = \frac{2}{5}\)
\(\frac{8}{20} = \frac{8 \div 4}{20 \div 4} = \frac{2}{5}\)
Since both equal \(\frac{2}{5}\), they are equal.
In simple words: Both fractions represent the exact same value.

Exam Tip: Equivalent fractions always take the equality sign.

IX Arrange in Ascending order - (put the sign)

Question. \(\frac{7}{15}, \frac{7}{20}, \frac{7}{11}, \frac{7}{19}, \frac{7}{13}\)
Answer: \(\frac{7}{20} < \frac{7}{19} < \frac{7}{15} < \frac{7}{13} < \frac{7}{11}\)
In simple words: When numerators are the same, the fraction with the largest denominator is the smallest.

Exam Tip: Order denominators from largest to smallest to write unit-numerator/equal-numerator fractions in ascending order.

X a) Write an equivalent fraction for \(\frac{12}{25}\) with denominator 100.

Question a). Write an equivalent fraction for \(\frac{12}{25}\) with denominator 100.
Answer: \(\frac{48}{100}\)
Determine the multiplier for the denominator:
\(100 \div 25 = 4\)
Multiply both numerator and denominator by 4:
\(\frac{12 \times 4}{25 \times 4} = \frac{48}{100}\)
In simple words: Multiply top and bottom by 4 to get 100 in the denominator.

Exam Tip: Always multiply both the top and bottom numbers by the same factor.

X b) Write an equivalent fraction for \(\frac{5}{9}\) with numerator 40.

Question b). Write an equivalent fraction for \(\frac{5}{9}\) with numerator 40.
Answer: \(\frac{40}{72}\)
Determine the multiplier for the numerator:
\(40 \div 5 = 8\)
Multiply both numerator and denominator by 8:
\(\frac{5 \times 8}{9 \times 8} = \frac{40}{72}\)
In simple words: Find what number multiplies 5 to make 40, then multiply 9 by that same number.

Exam Tip: The multiplier is found by dividing the target numerator by the given numerator.