Fractions

A fraction is a number that represents a part of a whole or a part of a collection. In 3/8, the denominator 8 tells into how many equal parts the whole is divided and the numerator 3 tells how many parts are taken. In this chapter you will show fractions on a number line, and classify them as proper fractions (numerator less than denominator, such as 4/7), improper fractions (such as 9/4) and mixed fractions (such as 2 and 1/4). You will convert between improper and mixed fractions and find equivalent fractions like 1/2 = 2/4 = 3/6 by multiplying or dividing both terms by the same number. The chapter then explains how to reduce a fraction to its simplest form using the HCF of its numerator and denominator, and how to recognise like and unlike fractions. You will compare fractions with the same denominator, the same numerator, or different terms by converting to equivalent fractions using the LCM, and finally add and subtract like and unlike fractions in real-life problems.

Detailed Worksheet: Fractions Section A - Definitions (10 marks) 1. What is a fraction? Identify the numerator and denominator in 5/9 and state what each means. (2 marks) 2. Distinguish between proper and improper fractions, giving two examples of each. (2 marks) 3. What is a mixed fraction? Write 17/5 as a mixed fraction. (2 marks) 4. What are equivalent fractions? Write three fractions equivalent to 2/3. (2 marks) 5. When is a fraction said to be in its simplest form? Is 14/21 in simplest form? (2 marks) Section B - Calculations and Applications (15 marks) 6. Reduce to simplest form: (i) 48/60 (ii) 150/60 (iii) 84/98 (iv) 12/52 (v) 7/28 (vi) 36/48. (3 marks) 7. Compare the fractions and put the correct sign: (i) 3/8 and 5/8 (ii) 4/9 and 4/7 (iii) 2/3 and 3/4 (iv) 5/6 and 7/9 (v) 3/5 and 9/15 (vi) 1/2 and 4/9. (3 marks) 8. Arrange in ascending order: (i) 1/8, 5/8, 3/8 (ii) 2/5, 2/3, 2/7 (iii) 1/2, 2/3, 3/4, 5/6. (3 marks) 9. Find: (i) 2/3 + 1/7 (ii) 3/10 + 7/15 (iii) 5/8 - 1/6 (iv) 2 and 1/3 + 3 and 1/2 (v) 4 and 2/3 - 3 and 1/4 (vi) 1 - 5/9. (3 marks) 10. Sarita bought 2/5 metre of ribbon and Lalita bought 3/4 metre of ribbon. (i) What is the total length of ribbon they bought? (ii) Who bought the longer ribbon and by how much? (iii) If the ribbon costs Rs 40 per metre, find what Lalita paid. (3 marks) Section C - Diagrams (10 marks) 11. Draw a number line from 0 to 2 and divide each unit into 5 equal parts. Mark 2/5, 4/5, 6/5 and 9/5 on it. Write 6/5 and 9/5 as mixed fractions. (4 marks) 12. Draw three identical rectangles. Shade 1/2 of the first, 2/4 of the second and 4/8 of the third. What do you conclude about these fractions? (3 marks) 13. Draw a circle divided into 6 equal parts and shade 1/3 of it. Draw another circle divided into 4 equal parts and shade 3/4. Use the figures to compare 1/3 and 3/4. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Javed was given 5/7 of a basket of oranges and his sister was given the rest. (i) What fraction did his sister get? (ii) If the basket had 28 oranges, how many oranges did each get? (iii) Who got more and by what fraction of the basket? (iv) Explain why the two fractions add up to 1. (5 marks) 15. Rahul says that 3/4 is less than 4/5 because 3 is less than 4 and 4 is less than 5. (i) Check whether 3/4 is less than 4/5 by converting to like fractions. (ii) Is Rahul's reasoning always correct? Test it with 2/3 and 3/7. (iii) State a correct method for comparing unlike fractions. (5 marks) 16. A cake is shared at a party. Ramesh eats 1/6 of the cake, Sheetal eats 1/4 and Jamaal eats 1/3. (i) What fraction of the cake did the three eat together? (ii) What fraction is left? (iii) Who ate the most? (iv) If the cake weighed 1200 g, how many grams are left? (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Reduce every answer to its simplest form and show the LCM used for unlike fractions.