Class 6 › Mathematics › Ganita Prakash Fractions Class 6 Mathematics · Ganita Prakash · Chapter 7
Practice all → Summary Questions & answers Practise this chapter → This chapter develops fractions as equal shares. When one whole is divided into equal parts, each part is a fractional unit, such as \(\tfrac{1}{2}, \tfrac{1}{3}, \tfrac{1}{4}, \tfrac{1}{5}\); the more parts the whole is split into, the smaller each share, so \(\tfrac{1}{9} < \tfrac{1}{5}\). A fraction \(\tfrac{a}{b}\) has a numerator \(a\) and denominator \(b\), and fractions can be shown on the number line. The chapter explains equivalent fractions \u2014 different fractions that represent the same amount, such as \(\tfrac{1}{2} = \tfrac{2}{4} = \tfrac{3}{6}\) \u2014 obtained by multiplying or dividing numerator and denominator by the same number, and shows how to reduce a fraction to its simplest form. Fractions are compared by making denominators equal. Mixed numbers like \(2\tfrac{1}{3}\) are converted to and from improper fractions. Finally, the chapter teaches adding and subtracting fractions: like fractions are added directly, while unlike fractions are first rewritten with a common denominator. Real-life sharing situations with rotis and lengths run throughout to keep the meaning of fractions concrete.
Fraction
A number \(\dfrac{a}{b}\) representing equal parts of a whole, with numerator \(a\) and denominator \(b\).
Fractional unit
One equal part of a whole, such as \(\tfrac{1}{2}, \tfrac{1}{3}\) or \(\tfrac{1}{4}\).
Numerator and denominator
In \(\dfrac{a}{b}\), \(a\) is the numerator (parts taken) and \(b\) is the denominator (equal parts of the whole).
Equivalent fractions
Different fractions that represent the same value, e.g. \(\tfrac{1}{2} = \tfrac{2}{4} = \tfrac{3}{6}\).
Mixed number
A number with a whole part and a fractional part, such as \(2\tfrac{1}{3}\).
Like fractions
Fractions having the same denominator, which can be added or subtracted directly.
Q1 What is a fractional unit? Answer Q2 Which is greater, \(\tfrac{1}{5}\) or \(\tfrac{1}{9}\)? Answer Q3 What are the numerator and denominator of \(\tfrac{3}{4}\)? Answer Q4 What are equivalent fractions? Answer Q5 How do you get an equivalent fraction? Answer Q6 What is the simplest form of \(\tfrac{6}{8}\)? Answer Q7 What is a mixed number? Answer Q8 How do you convert \(2\tfrac{1}{3}\) to an improper fraction? Answer Q9 How do you add two fractions with the same denominator? Answer Q10 How do you add fractions with different denominators? Answer Q1 Fill in the blanks with fractions. 1. Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh ____ kg. Answer Q2 Fill in the blanks with fractions. 2. A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ___ kg. Answer Q3 Fill in the blanks with fractions. 3. Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank ____ glass of sugarcane juice. Answer Q4 Fill in the blanks with fractions. 4. The big fish weighs \( \frac{1}{2} \) kg. The small one weighs \( \frac{1}{4} \) kg. Together they weigh ____ kg. Answer Q5 5. Arrange these fraction words in order of size from the smallest to the biggest in the empty box below: One and a half, three quarters, one and a quarter, half, quarter, two and a half. Answer Q1 The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? a. Answer Q2 The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? b. Answer Q3 The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? c. Answer Q4 The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? d. Answer Q5 The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? e. Answer Q6 The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? f. Answer Q7 The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? g. Answer Q8 The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece? h. Answer Q1 2 times \( \frac{1}{8} \) = ____ Answer Q2 4 times \( \frac{1}{8} \) = ____ Answer Q3 6 times \( \frac{1}{8} \) = ____ Answer Q4 8 times \( \frac{1}{8} \) = \( \frac{8}{8} \) = 1 Answer Q1 1. Continue this table of \( \frac{1}{2} \) for 2 more steps. Answer Q2 2. Can you create a similar table for \( \frac{1}{4} \)? Answer Q3 3. Make \( \frac{1}{3} \) using a paper strip. Can you use this to also make \( \frac{1}{6} \)? Answer Q4 4. Draw a picture and write an addition statement as above to show: a. 5 times \( \frac{1}{4} \) of a roti Answer Q5 4. Draw a picture and write an addition statement as above to show: b. 9 times \( \frac{1}{4} \) of a roti Answer Q6 5. Match each fractional unit with the correct picture: \( \frac{1}{3} \) Answer Q7 5. Match each fractional unit with the correct picture: \( \frac{1}{5} \) Answer Q8 5. Match each fractional unit with the correct picture: \( \frac{1}{8} \) Answer Q9 5. Match each fractional unit with the correct picture: \( \frac{1}{6} \) Answer Q1 1. Here, the fractional unit is dividing a length of 1 unit into three equal parts. Write the fraction that gives the length of the blue line in the box or in your notebook. Answer Q2 2. Here, a unit is divided into 5 equal parts. Write the fraction that gives the length of the blue lines in the respective boxes or in your notebook. Answer Q3 3. Now, a unit is divided into 8 equal parts. Write the appropriate fractions in your notebook. Answer Q1 1. On a number line, draw lines of lengths \( \frac{1}{10} \), \( \frac{3}{10} \), and \( \frac{4}{5} \). Answer Q2 2. Write five more fractions of your choice and mark them on the number line. Answer Q3 3. How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer. Answer Q4 4. What is the length of the blue line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is \( \frac{1}{2} \). So the blue line is \( \frac{1}{2} \) units long. Write the fraction that gives the length of the black line in the box. Answer Q5 5. Write the fraction that gives the lengths of the black lines in the respective boxes. Answer Q1 1. How many whole units are there in \( \frac{7}{2} \)? Answer Q2 2. How many whole units are there in \( \frac{4}{3} \) and in \( \frac{7}{3} \)? Answer Q1 1. Figure out the number of whole units in each of the following fractions: a. \( \frac{8}{3} \) Answer Q2 1. Figure out the number of whole units in each of the following fractions: b. \( \frac{11}{5} \) Answer Q3 1. Figure out the number of whole units in each of the following fractions: c. \( \frac{9}{4} \) Answer Q4 2. Can all fractions greater than 1 be written as such mixed numbers? Answer Q5 3. Write the following fractions as mixed fractions (e.g., \( \frac{9}{2} = 4\frac{1}{2} \)): a. \( \frac{9}{2} \) Answer Q6 3. Write the following fractions as mixed fractions (e.g., \( \frac{9}{2} = 4\frac{1}{2} \)): b. \( \frac{9}{5} \) Answer Q7 3. Write the following fractions as mixed fractions (e.g., \( \frac{9}{2} = 4\frac{1}{2} \)): c. \( \frac{21}{19} \) Answer Q8 3. Write the following fractions as mixed fractions (e.g., \( \frac{9}{2} = 4\frac{1}{2} \)): d. \( \frac{47}{9} \) Answer Q9 3. Write the following fractions as mixed fractions (e.g., \( \frac{9}{2} = 4\frac{1}{2} \)): e. \( \frac{12}{11} \) Answer Q10 3. Write the following fractions as mixed fractions (e.g., \( \frac{9}{2} = 4\frac{1}{2} \)): f. \( \frac{19}{6} \) Answer Q1 Write the following mixed numbers as fractions: a. \( 3\frac{1}{4} \) Answer Q2 Write the following mixed numbers as fractions: b. \( 7\frac{2}{3} \) Answer Q3 Write the following mixed numbers as fractions: c. \( 9\frac{4}{9} \) Answer Q4 Write the following mixed numbers as fractions: d. \( 3\frac{1}{6} \) Answer Q5 Write the following mixed numbers as fractions: e. \( 2\frac{3}{11} \) Answer Q6 Write the following mixed numbers as fractions: f. \( 3\frac{9}{10} \) Answer Q1 1. Are the lengths \( \frac{1}{2} \) and \( \frac{3}{6} \) equal? Answer Q2 2. Are \( \frac{2}{3} \) and \( \frac{4}{6} \) equivalent fractions? Why? Answer Q3 3. How many pieces of length \( \frac{1}{6} \) will make a length of \( \frac{1}{2} \)? Answer Q4 4. How many pieces of length \( \frac{1}{6} \) will make a length of \( \frac{1}{3} \)? Answer Q1 1. Are \( \frac{3}{6} \), \( \frac{4}{8} \), \( \frac{5}{10} \) equivalent fractions? Why? Answer Q2 2. Write two equivalent fractions for \( \frac{2}{6} \). Answer Q3 3. \( \frac{4}{6} = \) ____ = ____ = ____ = ............ (Write as many as you can) Answer Q1 1. Three rotis are shared equally by four children. Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts, and multiplication facts. Fraction of roti each child gets is ______. Answer Q2 2. Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts. Answer Q3 3. Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get? Answer Q1 Find the missing numbers: a. 5 glasses of juice shared equally among 4 friends is the same as ____ glasses of juice shared equally among 8 friends. So, \( \frac{5}{4} = \frac{}{8} \). Answer Q2 Find the missing numbers: b. 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in ___ bags. So, \( \frac{4}{3} = \frac{12}{} \). Answer Q3 Find the missing numbers: c. 7 rotis divided among 5 children is the same as ____ rotis divided among _____ children. So, \( \frac{7}{5} = \frac{}{} \). Answer Q1 Suppose the number of children is kept the same, but the number of units that are being shared is increased? What can you say about each child’s share now? Why? Discuss how your reasoning explains \( \frac{1}{5} < \frac{2}{5} \), \( \frac{3}{7} < \frac{4}{7} \), and \( \frac{1}{2} < \frac{5}{8} \). Answer Q2 Now, decide in which of the two groups will each child get a larger share: 1. Group 1 : 3 glasses of sugarcane juice divided equally among 4 children. Group 2: 7 glasses of sugarcane juice divided equally among 10 children. Answer Q3 Now, decide in which of the two groups will each child get a larger share: 2. Group 1 : 4 glasses of sugarcane juice divided equally among 7 children. Group 2: 5 glasses of sugarcane juice divided equally among 7 children. Which groups were easier to compare? Why? Answer Q1 Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. a. \( \frac{7}{2} \) and \( \frac{3}{5} \) Answer Q2 Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. b. \( \frac{8}{3} \) and \( \frac{5}{6} \) Answer Q3 Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. c. \( \frac{3}{4} \) and \( \frac{3}{5} \) Answer Q4 Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. d. \( \frac{6}{7} \) and \( \frac{8}{5} \) Answer Q5 Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. e. \( \frac{9}{4} \) and \( \frac{5}{2} \) Answer Q6 Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. f. \( \frac{1}{10} \) and \( \frac{2}{9} \) Answer Q7 Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. g. \( \frac{8}{3} \) and \( \frac{11}{4} \) Answer Q8 Find equivalent fractions for the given pairs of fractions such that the fractional units are the same. h. \( \frac{13}{6} \) and \( \frac{1}{9} \) Answer Q1 Express the following fractions in lowest terms: a. \( \frac{17}{51} \) Answer Q2 Express the following fractions in lowest terms: b. \( \frac{64}{144} \) Answer Q3 Express the following fractions in lowest terms: c. \( \frac{126}{147} \) Answer Q4 Express the following fractions in lowest terms: d. \( \frac{525}{112} \) Answer Q1 1. Compare the following fractions and justify your answers: a. \( \frac{8}{3} \), \( \frac{5}{2} \) Answer Q2 1. Compare the following fractions and justify your answers: b. \( \frac{4}{9} \), \( \frac{3}{7} \) Answer Q3 1. Compare the following fractions and justify your answers: c. \( \frac{7}{10} \), \( \frac{9}{14} \) Answer Q4 1. Compare the following fractions and justify your answers: d. \( \frac{12}{5} \), \( \frac{8}{5} \) Answer Q5 1. Compare the following fractions and justify your answers: e. \( \frac{9}{4} \), \( \frac{5}{2} \) Answer Q6 2. Write the following fractions in ascending order. a. \( \frac{7}{10} \), \( \frac{11}{15} \), \( \frac{2}{5} \) Answer Q7 2. Write the following fractions in ascending order. b. \( \frac{19}{24} \), \( \frac{5}{6} \), \( \frac{7}{12} \) Answer Q8 3. Write the following fractions in descending order. a. \( \frac{25}{16} \), \( \frac{7}{8} \), \( \frac{13}{4} \), \( \frac{17}{32} \) Answer Q9 3. Write the following fractions in descending order. b. \( \frac{3}{4} \), \( \frac{12}{5} \), \( \frac{7}{12} \), \( \frac{5}{4} \) Answer Q1 1. Add the following fractions using Brahmagupta’s method: a. \( \frac{2}{7} + \frac{5}{7} + \frac{6}{7} \) Answer Q2 1. Add the following fractions using Brahmagupta’s method: b. \( \frac{3}{4} + \frac{1}{3} \) Answer Q3 1. Add the following fractions using Brahmagupta’s method: c. \( \frac{2}{3} + \frac{5}{6} \) Answer Q4 1. Add the following fractions using Brahmagupta’s method: d. \( \frac{2}{3} + \frac{2}{7} \) Answer Q5 1. Add the following fractions using Brahmagupta’s method: e. \( \frac{3}{4} + \frac{1}{3} + \frac{1}{5} \) Answer Q6 1. Add the following fractions using Brahmagupta’s method: f. \( \frac{2}{3} + \frac{4}{5} \) Answer Q7 1. Add the following fractions using Brahmagupta’s method: g. \( \frac{4}{5} + \frac{2}{3} \) Answer Q8 1. Add the following fractions using Brahmagupta’s method: h. \( \frac{3}{5} + \frac{5}{8} \) Answer Q9 1. Add the following fractions using Brahmagupta’s method: i. \( \frac{9}{2} + \frac{5}{4} \) Answer Q10 1. Add the following fractions using Brahmagupta’s method: j. \( \frac{8}{3} + \frac{2}{7} \) Answer Q11 1. Add the following fractions using Brahmagupta’s method: k. \( \frac{3}{4} + \frac{1}{3} + \frac{1}{5} \) Answer Q12 1. Add the following fractions using Brahmagupta’s method: l. \( \frac{2}{3} + \frac{4}{5} + \frac{3}{7} \) Answer Q13 1. Add the following fractions using Brahmagupta’s method: m. \( \frac{9}{2} + \frac{5}{4} + \frac{7}{6} \) Answer Q14 2. Rahim mixes \( \frac{2}{3} \) litres of yellow paint with \( \frac{3}{4} \) litres of blue paint to make green paint. What is the volume of green paint he has made? Answer Q15 3. Geeta bought \( \frac{2}{5} \) meter of lace and Shamim bought \( \frac{3}{4} \) meter of the same lace to put a complete border on a table cloth whose perimeter is 1 meter long. Find the total length of the lace they both have bought. Will the lace be sufficient to cover the whole border? Answer Q1 1. \( \frac{5}{8} - \frac{3}{8} \) Answer Q2 2. \( \frac{7}{9} - \frac{5}{9} \) Answer Q3 3. \( \frac{10}{27} - \frac{1}{27} \) Answer Q1 1. Carry out the following subtractions using Brahmagupta’s method: a. \( \frac{8}{15} - \frac{3}{15} \) Answer Q2 1. Carry out the following subtractions using Brahmagupta’s method: b. \( \frac{2}{5} - \frac{4}{15} \) Answer Q3 1. Carry out the following subtractions using Brahmagupta’s method: c. \( \frac{5}{6} - \frac{4}{9} \) Answer Q4 1. Carry out the following subtractions using Brahmagupta’s method: d. \( \frac{2}{3} - \frac{1}{2} \) Answer Q5 2. Subtract as indicated: a. \( \frac{13}{4} \) from \( \frac{10}{3} \) Answer Q6 2. Subtract as indicated: b. \( \frac{18}{5} \) from \( \frac{23}{3} \) Answer Q7 2. Subtract as indicated: c. \( \frac{29}{7} \) from \( \frac{45}{7} \) Answer Q8 3. Solve the following problems: a. Jaya’s school is \( \frac{7}{10} \) km from her home. She takes an auto for \( \frac{1}{2} \) km from her home daily, and then walks the remaining distance to reach her school. How much does she walk daily to reach the school? Answer Q9 3. Solve the following problems: b. Jeevika takes \( \frac{10}{3} \) minutes to take a complete round of the park and her friend Namit takes \( \frac{13}{4} \) minutes to do the same. Who takes less time and by how much? Answer
When one whole is divided into equal parts, each part is called a
A factor B whole number C fractional unit D multiple
Flashcards & interactive practice 
5
