CBSE Class 5 Mathematics Fractions Worksheet Set 03

Ln. 4 : Fractions

1. Fill in the blanks :

Question 1.1. If the product of 2 numbers is 1, then one number is called the _________________ of the other number.
Answer: reciprocal
In simple words: Two numbers whose product equals 1 are called reciprocals or multiplicative inverses of each other.

Exam Tip: Remember that the reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\).

Question 1.2. The product of a number and its multiplicative inverse is _________________.
Answer: 1
In simple words: Multiplying any non-zero number by its reciprocal always gives 1.

Exam Tip: For example, \(\frac{2}{3} \times \frac{3}{2} = 1\).

Question 1.3. The product of a fraction and _________________ is the fraction itself.
Answer: 1
In simple words: 1 is the multiplicative identity, so multiplying any fraction by 1 leaves the fraction unchanged.

Exam Tip: Any number multiplied by 1 remains the same number.

Question 1.4. The product of a fraction and 0 is _________________.
Answer: 0
In simple words: Multiplying any number by zero always results in zero.

Exam Tip: This is the zero property of multiplication.

Question 1.5. Every whole number other than _________________ has a reciprocal.
Answer: 0
In simple words: Zero does not have a reciprocal because division by zero is not defined.

Exam Tip: 0 has no reciprocal since \(\frac{1}{0}\) is undefined.

Question 1.6. The number whose reciprocal is the number itself is _________________.
Answer: 1 and -1
In simple words: 1 divided by 1 is 1, and 1 divided by -1 is -1.

Exam Tip: Always check both positive and negative possibilities when applicable.

Question 1.7. When a fraction is divided by 1, the quotient is _________________.
Answer: the fraction itself
In simple words: Dividing any number by 1 does not change its value.

Question 1.8. When 1 is divided by a fraction, the quotient is the _________________ of the fraction.
Answer: reciprocal
In simple words: 1 divided by a fraction flips the fraction to its reciprocal.

Exam Tip: \(1 \div \frac{a}{b} = \frac{b}{a}\).

Question 1.9. 6 x \(\frac{1}{3}\) = \(\frac{1}{3}\) x ________
Answer: 6
In simple words: Multiplication is commutative, meaning changing the order of numbers does not change the product.

Exam Tip: Apply the commutative property of multiplication: \(a \times b = b \times a\).

Question 1.10. \(\frac{5}{7}\) x _______ = \(\frac{5}{7}\)
Answer: 1
In simple words: Multiplying a number by 1 gives the same number back.

Exam Tip: This illustrates the identity property of multiplication.

Question 1.11. 0 x \(\frac{2}{3}\) = __________
Answer: 0
In simple words: Zero multiplied by any fraction equals zero.

Exam Tip: Any quantity multiplied by 0 is 0.

Question 1.12. \(\frac{1}{7}\) x \(\frac{2}{9}\) = ___________ x \(\frac{1}{7}\)
Answer: \(\frac{2}{9}\)
In simple words: Reversing the order of two multiplied fractions keeps the result equal.

Exam Tip: Commutative property holds true for fractions as well.

Question 1.13. The multiplicative inverse of 7 is ____________
Answer: \(\frac{1}{7}\)
In simple words: To find the multiplicative inverse, write the number as a fraction and flip it upside down.

Exam Tip: \(7 = \frac{7}{1}\), so its reciprocal is \(\frac{1}{7}\).

Question 1.14. The multiplicative inverse of \(\frac{1}{3}\) is ___________
Answer: 3
In simple words: Flipping the fraction \(\frac{1}{3}\) gives \(\frac{3}{1}\), which is 3.

Exam Tip: The reciprocal of a unit fraction is the whole denominator.

Question 1.15. 5 x ___________ = 1
Answer: \(\frac{1}{5}\)
In simple words: Multiply a number by its reciprocal to get 1.

Exam Tip: \(5 \times \frac{1}{5} = \frac{5}{5} = 1\).

Question 1.16. \(\frac{1}{3}\) x ___________ = 1
Answer: 3
In simple words: Multiply \(\frac{1}{3}\) by 3 to get 1.

Exam Tip: \(\frac{1}{3} \times 3 = \frac{3}{3} = 1\).

Question 1.17. \(\frac{2}{7}\) x \(\frac{7}{2}\) = __________
Answer: 1
In simple words: A fraction multiplied by its reciprocal always equals 1.

Exam Tip: Numerators and denominators cancel each other out completely.

Question 1.18. When 0 is divided by a non-zero fraction, the quotient is ____________.
Answer: 0
In simple words: Zero divided by any valid number is always zero.

Question 1.19. \(\frac{5}{6}\) ÷ 1 = ___________
Answer: \(\frac{5}{6}\)
In simple words: Any fraction divided by 1 remains unchanged.

Exam Tip: Division by 1 preserves the original number.

Question 1.20. \(\frac{10}{9}\) ÷ \(\frac{10}{9}\) = ____________
Answer: 1
In simple words: Any non-zero number divided by itself is always 1.

Exam Tip: \(\frac{10}{9} \times \frac{9}{10} = 1\).

Question 1.21. 0 ÷ \(\frac{2}{3}\) = ______________
Answer: 0
In simple words: Zero divided by any fraction gives 0.

Exam Tip: Zero divided by anything except zero is zero.

Question 1.22. 1 ÷ \(\frac{4}{5}\) = ______________
Answer: \(\frac{5}{4}\)
In simple words: Dividing 1 by a fraction gives its reciprocal.

Exam Tip: \(1 \div \frac{a}{b} = \frac{b}{a}\).

Question 1.23. ___________ ÷ \(\frac{6}{9}\) = 0
Answer: 0
In simple words: Only 0 divided by a non-zero number can result in 0.

Exam Tip: The dividend must be 0 for the quotient to be 0.

Question 1.24. _____________ ÷ 1 = \(\frac{3}{7}\)
Answer: \(\frac{3}{7}\)
In simple words: The number that when divided by 1 gives \(\frac{3}{7}\) is \(\frac{3}{7}\).

Exam Tip: Working backwards: \(\frac{3}{7} \times 1 = \frac{3}{7}\).

Question 25. Simplify
(a) \(\frac{9}{10}\) x 15
Answer:
\(= \frac{9 \times 15}{10}\)
\(= \frac{135}{10}\)
\(= \frac{27}{2} = 13\frac{1}{2}\)
In simple words: Multiply numerator by whole number and simplify the fraction.

Exam Tip: Reduce fractions by common factors before multiplying to make calculation easier.

Question 25 (cont.). (b) 20 x \(\frac{3}{25}\)
Answer:
\(= \frac{20 \times 3}{25}\)
\(= \frac{60}{25}\)
\(= \frac{12}{5} = 2\frac{2}{5}\)
In simple words: Multiply 20 by 3 and divide by 25, then simplify.

Exam Tip: Cancel common factors between numerator and denominator: 20 and 25 share factor 5.

Question 25 (cont.). (c) 3 x \(\frac{7}{10}\)
Answer:
\(= \frac{3 \times 7}{10}\)
\(= \frac{21}{10} = 2\frac{1}{10}\)
In simple words: Multiply 3 by 7 to get 21 over 10.

Question 25 (cont.). (d) \(\frac{5}{3}\) x \(\frac{9}{13}\)
Answer:
\(= \frac{5 \times 9}{3 \times 13}\)
\(= \frac{45}{39}\)
\(= \frac{15}{13} = 1\frac{2}{13}\)
In simple words: Multiply numerators together and denominators together, then simplify.

Exam Tip: You can cancel 3 and 9 beforehand to get \(\frac{5 \times 3}{1 \times 13} = \frac{15}{13}\).

Question 25 (cont.). (e) \(\frac{13}{5}\) x \(\frac{5}{26}\)
Answer:
\(= \frac{13 \times 5}{5 \times 26}\)
\(= \frac{1}{2}\)
In simple words: Cancel out 5 from numerator and denominator, and simplify 13 and 26.

Exam Tip: Cross-canceling saves time and prevents large numbers.

Question 25 (cont.). (f) \(\frac{12}{18}\) x \(\frac{7}{21}\)
Answer:
Simplify individual fractions first:
\(\frac{12}{18} = \frac{2}{3}\)
\(\frac{7}{21} = \frac{1}{3}\)
\(= \frac{2}{3} \times \frac{1}{3} = \frac{2}{9}\)
In simple words: Reduce each fraction to its simplest form before multiplying.

Exam Tip: Reducing fractions first makes multiplication much simpler.

Question 25 (cont.). (g) 8 x \(4\frac{1}{6}\)
Answer:
Convert mixed fraction to improper fraction:
\(4\frac{1}{6} = \frac{25}{6}\)
\(= 8 \times \frac{25}{6}\)
\(= \frac{200}{6}\)
\(= \frac{100}{3} = 33\frac{1}{3}\)
In simple words: Change the mixed number into an improper fraction and multiply by 8.

Exam Tip: Always convert mixed numbers to improper fractions before performing multiplication or division.

Question 25 (cont.). (h) \(3\frac{1}{7}\) x \(1\frac{1}{7}\)
Answer:
Convert mixed fractions:
\(3\frac{1}{7} = \frac{22}{7}\)
\(1\frac{1}{7} = \frac{8}{7}\)
\(= \frac{22}{7} \times \frac{8}{7}\)
\(= \frac{176}{49} = 3\frac{29}{49}\)
In simple words: Convert both mixed fractions to improper fractions, then multiply.

Exam Tip: Multiply numerators (22 x 8 = 176) and denominators (7 x 7 = 49).

Question 25 (cont.). (i) 9 of \(\frac{6}{15}\)
Answer:
"of" means multiplication:
\(= 9 \times \frac{6}{15}\)
\(= \frac{9 \times 6}{15}\)
\(= \frac{54}{15}\)
\(= \frac{18}{5} = 3\frac{3}{5}\)
In simple words: Replace the word "of" with a multiplication sign and solve.

Exam Tip: "Of" always translates to multiplication in fraction word problems.

Question 25 (cont.). (j) 5 of \(\frac{15}{25}\)
Answer:
\(= 5 \times \frac{15}{25}\)
Simplify \(\frac{15}{25} = \frac{3}{5}\)
\(= 5 \times \frac{3}{5}\)
\(= 3\)
In simple words: Simplify the fraction first, then multiply by 5.

Question 25 (cont.). (k) \(1\frac{2}{3}\) x \(3\frac{4}{5}\)
Answer:
Convert mixed fractions:
\(1\frac{2}{3} = \frac{5}{3}\)
\(3\frac{4}{5} = \frac{19}{5}\)
\(= \frac{5}{3} \times \frac{19}{5}\)
Cancel 5:
\(= \frac{19}{3} = 6\frac{1}{3}\)
In simple words: Convert to improper fractions and cancel common terms.

Exam Tip: Cross-cancellation makes multiplying mixed numbers very fast.

Question 25 (cont.). (l) \(3\frac{1}{3}\) x 12
Answer:
Convert mixed fraction:
\(3\frac{1}{3} = \frac{10}{3}\)
\(= \frac{10}{3} \times 12\)
\(= 10 \times 4 = 40\)
In simple words: Convert to an improper fraction and divide 12 by 3.

Exam Tip: 12 divided by 3 is 4, which multiplied by 10 gives 40.

Question 26. Simplify :
(a) \(\frac{3}{5}\) ÷ \(\frac{1}{2}\)
Answer:
\(= \frac{3}{5} \times \frac{2}{1}\)
\(= \frac{6}{5} = 1\frac{1}{5}\)
In simple words: To divide fractions, multiply the first fraction by the reciprocal of the second fraction.

Exam Tip: Remember the rule: Keep-Change-Flip (Keep the first fraction, change division to multiplication, flip the second fraction).

Question 26 (cont.). (b) \(\frac{15}{17}\) ÷ \(\frac{4}{5}\)
Answer:
\(= \frac{15}{17} \times \frac{5}{4}\)
\(= \frac{75}{68} = 1\frac{7}{68}\)
In simple words: Multiply \(\frac{15}{17}\) by the reciprocal of \(\frac{4}{5}\), which is \(\frac{5}{4}\).

Exam Tip: Multiply numerators together and denominators together.

Question 26 (cont.). (c) \(\frac{6}{11}\) ÷ \(\frac{3}{11}\)
Answer:
\(= \frac{6}{11} \times \frac{11}{3}\)
\(= \frac{6}{3} = 2\)
In simple words: Flip the second fraction and multiply; 11 cancels out.

Exam Tip: When denominators are identical, division simplifies to dividing the numerators.

Question 26 (cont.). (d) \(\frac{4}{5}\) ÷ \(\frac{1}{5}\)
Answer:
\(= \frac{4}{5} \times \frac{5}{1}\)
\(= 4\)
In simple words: 5 cancels out, leaving 4 divided by 1.

Exam Tip: Same denominator shortcut: \(\frac{4}{5} \div \frac{1}{5} = \frac{4}{1} = 4\).

Question 26 (cont.). (e) \(\frac{3}{9}\) ÷ 2\(\frac{2}{3}\)
Answer:
Convert mixed fraction and simplify \(\frac{3}{9}\):
\(\frac{3}{9} = \frac{1}{3}\)
\(2\frac{2}{3} = \frac{8}{3}\)
\(= \frac{1}{3} \div \frac{8}{3}\)
\(= \frac{1}{3} \times \frac{3}{8}\)
\(= \frac{1}{8}\)
In simple words: Convert to improper fractions and multiply by the reciprocal.

Exam Tip: Always simplify fractions before performing division if possible.

Question 26 (cont.). (f) \(\frac{5}{9}\) ÷ 1\(\frac{1}{3}\)
Answer:
Convert mixed fraction:
\(1\frac{1}{3} = \frac{4}{3}\)
\(= \frac{5}{9} \div \frac{4}{3}\)
\(= \frac{5}{9} \times \frac{3}{4}\)
\(= \frac{15}{36} = \frac{5}{12}\)
In simple words: Multiply \(\frac{5}{9}\) by the reciprocal of \(\frac{4}{3}\).

Exam Tip: Reduce \(\frac{15}{36}\) by dividing numerator and denominator by 3.

Question 26 (cont.). (g) \(\frac{6}{13}\) ÷ 2\(\frac{1}{5}\)
Answer:
Convert mixed fraction:
\(2\frac{1}{5} = \frac{11}{5}\)
\(= \frac{6}{13} \div \frac{11}{5}\)
\(= \frac{6}{13} \times \frac{5}{11}\)
\(= \frac{30}{143}\)
In simple words: Multiply the dividend by the reciprocal of the divisor.

Exam Tip: Check if any numbers can be cross-cancelled before final multiplication.

Question 26 (cont.). (h) \(\frac{9}{10}\) ÷ 3\(\frac{1}{3}\)
Answer:
Convert mixed fraction:
\(3\frac{1}{3} = \frac{10}{3}\)
\(= \frac{9}{10} \div \frac{10}{3}\)
\(= \frac{9}{10} \times \frac{3}{10}\)
\(= \frac{27}{100}\)
In simple words: Multiply \(\frac{9}{10}\) by \(\frac{3}{10}\).

Exam Tip: Multiply straight across: 9 x 3 = 27, 10 x 10 = 100.

Question 26 (cont.). (i) \(\frac{7}{35}\) ÷ 4\(\frac{2}{3}\)
Answer:
Simplify \(\frac{7}{35} = \frac{1}{5}\)
Convert mixed fraction:
\(4\frac{2}{3} = \frac{14}{3}\)
\(= \frac{1}{5} \div \frac{14}{3}\)
\(= \frac{1}{5} \times \frac{3}{14}\)
\(= \frac{3}{70}\)
In simple words: Simplify the first fraction, convert the second, and multiply by the reciprocal.

Question I.1. Decimal fractions having equal number of decimal places are called _________________.
Answer: like decimals
In simple words: Decimals with the same number of digits after the decimal point are like decimals.

Exam Tip: Example: 2.34 and 5.67 are like decimals because both have two decimal places.

Question I.2. Decimal fractions having unequal number of decimal places are called ________________.
Answer: unlike decimals
In simple words: Decimals with different numbers of digits after the decimal point are unlike decimals.

Exam Tip: Example: 2.3 and 4.56 are unlike decimals.

Question I.3. Decimal fractions having equal values are called ________________ .
Answer: equivalent decimals
In simple words: Adding trailing zeros to a decimal does not change its value, making them equivalent.

Exam Tip: Example: 0.5, 0.50, and 0.500 are equivalent decimals.

Question I.4. To multiply a decimal fraction by 10 we shift the decimal point to the right by ________________ place.
Answer: one
In simple words: Multiplying by 10 moves the decimal point one place to the right.

Exam Tip: The number of zeros in the multiplier tells you how many places to move the decimal point.

Question I.5. To multiply a decimal fraction by 1000 we shift the decimal point to the ________________ by 3 places.
Answer: right
In simple words: Multiplying by 1000 moves the decimal point three places to the right.

Exam Tip: Add placeholder zeros if there are not enough digits to the right.

Question I.6. 0.9 x 10 = ________________
Answer: 9
In simple words: Move the decimal point one place to the right in 0.9 to get 9.

Exam Tip: 0.9 x 10 = 9.0 = 9.

Question I.7. 6.6 x 100 = ________________
Answer: 660
In simple words: Move the decimal point two places to the right, adding a zero as a placeholder.

Exam Tip: 6.6 x 100 = 660.