Fractions and Decimals

This chapter extends what you know about fractions and decimals to multiplication and division. To multiply two fractions, multiply the numerators and multiply the denominators, so 2/3 x 4/5 = 8/15. The word "of" means multiplication: 1/4 of 20 is 1/4 x 20 = 5. The product of two proper fractions is smaller than each of them, while the product with an improper fraction is greater than the other fraction. To divide by a fraction, multiply by its reciprocal; the reciprocal of 3/7 is 7/3, because their product is 1. So 2/5 divided by 3/7 is 2/5 x 7/3 = 14/15. For decimals, multiply the numbers as whole numbers and then place the decimal point so that the answer has as many decimal places as both numbers together, so 0.3 x 0.02 = 0.006. Multiplying by 10, 100 or 1000 shifts the decimal point to the right by one, two or three places, and dividing shifts it to the left. These skills are used to calculate areas, costs, distances and quantities in daily life.

Detailed Worksheet: Fractions and Decimals Section A - Definitions (10 marks) 1. What is the reciprocal of a fraction? Write the reciprocals of 5/8 and 7. (2 marks) 2. State the rule for multiplying two fractions with an example. (2 marks) 3. What does "of" mean when used with fractions? Find 3/4 of 60. (2 marks) 4. How does the decimal point move when a decimal is multiplied by 100 and divided by 100? Give examples. (2 marks) 5. Distinguish between proper, improper and mixed fractions with one example of each. (2 marks) Section B - Calculations and Applications (15 marks) 6. Multiply and reduce to lowest form: (i) 2/3 x 2 2/3 (ii) 6/5 x 5/7 (iii) 4/9 x 15/16. (3 marks) 7. Divide: (i) 6 divided by 2/3 (ii) 3/4 divided by 9/16 (iii) 2 1/2 divided by 5/6. (3 marks) 8. Find: (i) 5.6 x 10 (ii) 2.5 x 0.3 (iii) 1.07 x 0.02 (iv) 76.1 divided by 10 (v) 0.6 divided by 0.2 (vi) 7.75 divided by 0.25. (3 marks) 9. A car runs 16 km using 1 litre of petrol. How far will it go using 2 3/4 litres? Also, a vehicle covers 55.3 km in one litre; how far will it cover in 10 litres? (3 marks) 10. Find the area of a rectangle whose length is 5.7 cm and breadth is 3 cm. Also find the area of a rectangle with sides 4 1/2 m and 2 2/3 m. (3 marks) Section C - Diagrams (10 marks) 11. Using a rectangle divided into a grid, show pictorially that 1/2 x 1/3 = 1/6 and that 2/3 x 3/4 = 1/2. (4 marks) 12. Draw a number line from 0 to 2 and use jumps to show how many 1/4 are there in 1 1/2, that is, 1 1/2 divided by 1/4. (3 marks) 13. Draw a 10 by 10 grid and shade it to show 0.3 x 0.4 = 0.12. (3 marks) Section D - Analysis and Higher-order Thinking (15 marks) 14. Lipika reads a book for 1 3/4 hours every day. She reads the entire book in 6 days. (i) How many hours did she take in all? (ii) If she read 2 1/3 hours a day, would she finish faster? (iii) How many hours more per day is that? (iv) Explain why multiplying by a fraction less than 1 gives a smaller number. (5 marks) 15. Ramu finished 1/3 of a book in one week. Seema finished 2/5 of the same book. (i) Who read more? (ii) By what fraction of the book? (iii) If the book has 300 pages, how many pages did each read? (iv) What fraction is still left for Ramu? (5 marks) 16. Saili plants 4 saplings in a row in her garden. The distance between two adjacent saplings is 3/4 m. (i) Find the distance between the first and last sapling. (ii) If she plants 10 saplings, what will this distance be? (iii) A rod of 18 m is cut into pieces of 0.75 m; how many pieces are obtained? (iv) Explain why dividing by 0.75 gives a number greater than 18. (5 marks) Instructions: Time allowed 2 hours. Attempt all sections. Convert mixed fractions to improper fractions before multiplying or dividing, and write answers in lowest terms.