CBSE Class 6 Mathematics Fraction Worksheet Set 02

Very Short Answer Questions

Question 1. What is a fractional unit? Give one example.
Answer:
When one whole is divided into equal parts, each part is called a fractional unit.
Example: \( \frac{1}{4} \) is the fractional unit we get when a whole is cut into 4 equal parts.

Teacher's Note:
1. The parts must be equal.
2. Any fraction with 1 on top is a fractional unit.

Question 2. One roti is shared equally among 3 children. Write the fraction of a roti that each child gets.
Answer:
One whole roti is cut into 3 equal shares, so each child gets \( \frac{1}{3} \) roti.

Teacher's Note:
1. Number of children goes in the denominator.
2. One roti gives 1 on top.

Question 3. Which is greater, \( \frac{1}{6} \) or \( \frac{1}{11} \)? Write the correct sign between them.
Answer:
Fewer sharers means a bigger share, so \( \frac{1}{6} \) is greater.
\( \frac{1}{6} \) > \( \frac{1}{11} \)

Teacher's Note:
1. For fractional units, the smaller denominator wins.
2. Think of 1 roti among 6 and among 11 children.

Question 4. A bar of chikki is broken into 4 equal pieces. How much of the whole chikki is one piece?
Answer:
The chikki is broken into 4 equal pieces, so one piece is \( \frac{1}{4} \) of the chikki.

Teacher's Note:
1. 4 equal pieces, so the unit is a quarter.
2. Equal size is what makes it \( \frac{1}{4} \).

Question 5. Name the numerator and the denominator of the fraction \( \frac{7}{12} \).
Answer:
In \( \frac{7}{12} \), the numerator is 7 and the denominator is 12.

Teacher's Note:
1. Numerator on top, denominator below.
2. The denominator names the unit \( \frac{1}{12} \).

Question 6. Complete the sentence: \( \frac{5}{6} \) means ___ times \( \frac{1}{6} \).
Answer:
\( \frac{5}{6} \) means 5 times \( \frac{1}{6} \).

Teacher's Note:
1. The numerator counts the fractional units.
2. \( \frac{5}{6} \) = \( \frac{1}{6} \) + \( \frac{1}{6} \) + \( \frac{1}{6} \) + \( \frac{1}{6} \) + \( \frac{1}{6} \).

Question 7. To mark \( \frac{1}{5} \) on the number line, into how many equal parts must the length from 0 to 1 be divided?
Answer:
The length from 0 to 1 must be divided into 5 equal parts; the first mark after 0 then shows \( \frac{1}{5} \).

Teacher's Note:
1. The denominator tells how many parts to make.
2. Parts must be of equal length.

Question 8. Write the mixed fraction \( 1\frac{3}{4} \) as a fraction.
Answer:
\( 1\frac{3}{4} \) = 1 + \( \frac{3}{4} \) = \( \frac{4}{4} \) + \( \frac{3}{4} \) = \( \frac{7}{4} \)

Teacher's Note:
1. One whole is \( \frac{4}{4} \).
2. Add the fractional units.

Question 9. Is \( \frac{5}{8} \) less than 1 or greater than 1? Give the reason.
Answer:
\( \frac{5}{8} \) is less than 1, because the numerator 5 is smaller than the denominator 8; we have only 5 of the 8 eighths needed for a whole.

Teacher's Note:
1. Numerator smaller than denominator: less than 1.
2. \( \frac{8}{8} \) would be exactly 1.

Question 10. Write any one fraction that is equivalent to \( \frac{1}{3} \).
Answer:
\( \frac{1\times 2}{3\times 2} \) = \( \frac{2}{6} \), so \( \frac{2}{6} \) is equivalent to \( \frac{1}{3} \). (Others: \( \frac{3}{9} \), \( \frac{4}{12} \), …)

Teacher's Note:
1. Multiply top and bottom by the same number.
2. Many answers are correct.

Question 11. Which is greater, \( \frac{5}{9} \) or \( \frac{7}{9} \)? Why?
Answer:
\( \frac{7}{9} \) is greater. Both use the same fractional unit \( \frac{1}{9} \), and 7 such units are more than 5.

Teacher's Note:
1. Same denominator: compare the numerators.
2. 7 ninths beat 5 ninths.

Question 12. What was a fraction called in Sanskrit in ancient India?
Answer:
A fraction was called bhinna, meaning “broken”. It was also called bhaga or ansha, meaning “part” or “piece”.

Teacher's Note:
1. Bhinna = broken.
2. Bhaga and ansha = part or piece.

Question 13. Five laddus of the same size together weigh 1 kg. What is the weight of one laddu?
Answer:
1 kg is shared equally by 5 laddus, so one laddu weighs \( \frac{1}{5} \) kg.

Teacher's Note:
1. Same size means equal shares.
2. 1 whole shared by 5 gives \( \frac{1}{5} \).

Question 14. A paper strip is folded into 8 equal parts. What fraction of the strip do 5 such parts make?
Answer:
Each part is \( \frac{1}{8} \) of the strip, so 5 parts make 5 times \( \frac{1}{8} \) = \( \frac{5}{8} \) of the strip.

Teacher's Note:
1. Count units of \( \frac{1}{8} \).
2. Numerator = parts taken.

Question 15. How many pieces of length \( \frac{1}{4} \) unit are needed to make a length of 2 units?
Answer:
4 pieces of \( \frac{1}{4} \) make 1 unit, so 2 units need 2 × 4 = 8 pieces.

Teacher's Note:
1. First find how many make 1 unit.
2. Then multiply by the number of units.

Question 16. Between which two whole numbers does the fraction \( \frac{7}{5} \) lie on the number line?
Answer:
\( \frac{7}{5} \) = 1 + \( \frac{2}{5} \), so it lies between 1 and 2.

Teacher's Note:
1. Write it as a mixed fraction to locate it.
2. The whole part is the lower whole number.

Question 17. Write \( \frac{23}{4} \) as a mixed fraction.
Answer:
23 = 5 × 4 + 3, so \( \frac{23}{4} \) = 5 + \( \frac{3}{4} \) = \( 5\frac{3}{4} \).

Teacher's Note:
1. Divide 23 by 4.
2. The remainder becomes the numerator.

Question 18. Write the mixed fraction \( 3\frac{2}{7} \) as a fraction.
Answer:
\( 3\frac{2}{7} \) = \( \frac{21}{7} \) + \( \frac{2}{7} \) = \( \frac{23}{7} \)

Teacher's Note:
1. 3 wholes = 3 × 7 = 21 sevenths.
2. Add the 2 extra sevenths.

Question 19. Express \( \frac{24}{36} \) in its lowest terms.
Answer:
The HCF of 24 and 36 is 12, so \( \frac{24\div 12}{36\div 12} \) = \( \frac{2}{3} \).

Teacher's Note:
1. Divide both by the HCF.
2. 2 and 3 have no common factor, so we stop.

Question 20. Write a fraction equivalent to \( \frac{3}{5} \) whose denominator is 20.
Answer:
20 = 5 × 4, so \( \frac{3\times 4}{5\times 4} \) = \( \frac{12}{20} \).

Teacher's Note:
1. Find what 5 is multiplied by to get 20.
2. Multiply the numerator by the same number.

Question 21. Which is greater, \( \frac{3}{4} \) or \( \frac{5}{7} \)? Show the fractional unit you used.
Answer:
Using the fractional unit \( \frac{1}{28} \): \( \frac{3}{4} \) = \( \frac{21}{28} \) and \( \frac{5}{7} \) = \( \frac{20}{28} \).
21 > 20, so \( \frac{3}{4} \) is greater.

Teacher's Note:
1. 4 × 7 = 28 is a common denominator.
2. Then compare numerators.

Question 22. Add \( \frac{1}{8} \) and \( \frac{1}{2} \).
Answer:
\( \frac{1}{8} \) + \( \frac{1}{2} \) = \( \frac{1}{8} \) + \( \frac{4}{8} \) = \( \frac{5}{8} \)

Teacher's Note:
1. Change \( \frac{1}{2} \) into eighths.
2. Add only the numerators.

Question 23. Subtract \( \frac{1}{4} \) from \( \frac{7}{10} \).
Answer:
\( \frac{7}{10} \) − \( \frac{1}{4} \) = \( \frac{14}{20} \) − \( \frac{5}{20} \) = \( \frac{9}{20} \)

Teacher's Note:
1. 'Subtract \( \frac{1}{4} \) from \( \frac{7}{10} \)' means \( \frac{7}{10} \) − \( \frac{1}{4} \).
2. 20 is the smallest common denominator.

Question 24. Name the Indian mathematician who first set down the general rules for adding and subtracting fractions in their modern form.
Answer:
Brahmagupta (628 CE) first set down these general rules in the modern form we still use.

Teacher's Note:
1. Brahmagupta: 628 CE.
2. His method: make the units the same, then add.

Question 25. Write \( \frac{2}{3} \), \( \frac{5}{8} \) and \( \frac{3}{4} \) in ascending order.
Answer:
Using the fractional unit \( \frac{1}{24} \): \( \frac{2}{3} \) = \( \frac{16}{24} \), \( \frac{5}{8} \) = \( \frac{15}{24} \), \( \frac{3}{4} \) = \( \frac{18}{24} \).
Ascending order: \( \frac{5}{8} \), \( \frac{2}{3} \), \( \frac{3}{4} \)

Teacher's Note:
1. Ascending means smallest first.
2. 24 is a common multiple of 3, 8 and 4.

Question 26. Sana buys \( \frac{3}{5} \) m of red ribbon and \( \frac{1}{2} \) m of blue ribbon. What is the total length of ribbon she buys? Write the answer as a mixed fraction.
Answer:
\( \frac{3}{5} \) + \( \frac{1}{2} \) = \( \frac{6}{10} \) + \( \frac{5}{10} \) = \( \frac{11}{10} \) = \( 1\frac{1}{10} \) m

Teacher's Note:
1. Use tenths as the common unit.
2. 11 tenths is 1 whole and 1 tenth.

Question 27. Jeevika takes \( \frac{11}{4} \) minutes to walk once around a park and Namit takes \( \frac{5}{3} \) minutes. How much longer does Jeevika take?
Answer:
\( \frac{11}{4} \) − \( \frac{5}{3} \) = \( \frac{33}{12} \) − \( \frac{20}{12} \) = \( \frac{13}{12} \) minutes.
Jeevika takes \( \frac{13}{12} \) = \( 1\frac{1}{12} \) minutes longer.

Teacher's Note:
1. 'How much longer' means subtract.
2. 12 is the common denominator of 4 and 3.

Question 28. Write \( \frac{3}{4} \) as the sum of two different fractional units.
Answer:
\( \frac{3}{4} \) = \( \frac{2}{4} \) + \( \frac{1}{4} \) = \( \frac{1}{2} \) + \( \frac{1}{4} \), a sum of the two different fractional units \( \frac{1}{2} \) and \( \frac{1}{4} \).

Teacher's Note:
1. \( \frac{2}{4} \) is the same as \( \frac{1}{2} \).
2. Check by adding back: \( \frac{2}{4} \) + \( \frac{1}{4} \) = \( \frac{3}{4} \).

Question 29. Jaya wrote \( \frac{1}{2} \) + \( \frac{1}{3} \) = \( \frac{2}{5} \). Is she correct? Write the correct sum.
Answer:
No. She added the denominators, which is never allowed.
Correct sum: \( \frac{1}{2} \) + \( \frac{1}{3} \) = \( \frac{3}{6} \) + \( \frac{2}{6} \) = \( \frac{5}{6} \).

Teacher's Note:
1. \( \frac{2}{5} \) is less than \( \frac{1}{2} \), so it cannot be the sum.
2. Always make the units the same first.

Question 30. A wall is painted \( \frac{1}{3} \) on Monday and \( \frac{2}{5} \) on Tuesday. What fraction of the wall is still unpainted?
Answer:
Painted = \( \frac{1}{3} \) + \( \frac{2}{5} \) = \( \frac{5}{15} \) + \( \frac{6}{15} \) = \( \frac{11}{15} \).
Unpainted = 1 − \( \frac{11}{15} \) = \( \frac{15}{15} \) − \( \frac{11}{15} \) = \( \frac{4}{15} \) of the wall.

Teacher's Note:
1. The whole wall is 1 = \( \frac{15}{15} \).
2. Add first, then subtract from 1.