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Chapter Analysis
Beginner26 pages • EnglishQuick Summary
This chapter on 'Working with Fractions' explains the fundamental operations on fractions including multiplication and division. It introduces various methods for solving problems involving fractions, such as using reciprocals in division. The chapter utilizes Brahmagupta’s ancient formulas to teach these concepts and presents real-life examples to illustrate them effectively. Additionally, the chapter provides practice problems to reinforce understanding of the relationships between fractions, products, and quotients.
Key Topics
- •Multiplication of Fractions
- •Division of Fractions
- •Reciprocal of Fractions
- •Brahmagupta's Formulas
- •Real-life Fraction Problems
- •Understanding Quotients and Products
- •Simplification Techniques
Learning Objectives
- ✓Understand and perform multiplication of fractions
- ✓Use reciprocals to divide fractions effectively
- ✓Apply Brahmagupta’s formulas to solve complex fraction problems
- ✓Simplify the result of fractional multiplications and divisions
- ✓Recognize and solve real-life problems involving fractions
Questions in Chapter
Find the area of a rectangle of sides 3 3/4 ft and 9 3/5 ft.
Page 183
If 1/4 kg of flour is used to make 12 rotis, how much flour is used to make 6 rotis?
Page 196
What fraction of the whole square is shaded?
Page 197
Mira is reading a novel that has 400 pages. She read 1/5 of the pages yesterday and 3/10 of the pages today. How many more pages does she need to read to finish the novel?
Page 196
A colony of ants set out in search of food. As they search, they keep splitting equally at each point and reach two food sources, one near a mango tree and another near a sugarcane field. What fraction of the original group reached each food source?
Page 197
Additional Practice Questions
Calculate the product of 3/4 and 5/6. Simplify your answer.
easyAnswer: The product of 3/4 and 5/6 is (3 * 5) / (4 * 6) = 15/24 = 5/8 after simplification.
If a cake recipe requires 2/5 cup of oil, how much oil is needed to make 1.5 times the recipe?
mediumAnswer: 1.5 times the recipe requires 2/5 * 3/2 = 6/10 = 3/5 cup of oil.
Divide 7/8 by 1/4 and find the result. Next, explain why the quotient is greater than 7/8.
mediumAnswer: Dividing 7/8 by 1/4 is the same as multiplying 7/8 by 4/1, which equals 28/8 or 7/2. The quotient is greater than 7/8 because the divisor is a fraction less than 1.
What is the result of subtracting 1/5 from 3/10?
easyAnswer: Converting 1/5 to a common denominator with 3/10, we get 2/10. So, 3/10 - 2/10 = 1/10.
Determine the area of a triangle with a base of 3/5 units and a height of 4/5 units.
hardAnswer: The area of the triangle is 1/2 * base * height = 1/2 * 3/5 * 4/5 = 6/25 square units.