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Chapter Analysis
Beginner35 pages • EnglishQuick Summary
Chapter 7 on Fractions introduces students to the fundamental concept of fractions as parts of a whole. It covers basic terminology such as numerators and denominators, and explains how to identify and create equivalent fractions. The chapter also explores fractions that are greater than one, known as mixed fractions, and illustrates how to add and subtract fractions using common denominators. Students are engaged through practical exercises and historical insights, reinforcing the idea that fractions are an essential part of mathematical literacy.
Key Topics
- •Understanding fractions as parts of a whole
- •Numerators and denominators
- •Equivalent fractions
- •Mixed fractions
- •Addition and subtraction of fractions
- •Representation of fractions on a number line
- •Historical aspects of fractions
Learning Objectives
- ✓Recognize and write fractions as parts of a whole
- ✓Identify and create equivalent fractions
- ✓Convert improper fractions to mixed fractions
- ✓Add and subtract fractions with like denominators
- ✓Interpret fractions larger than one
- ✓Apply fractions to real-life situations
Questions in Chapter
Can all fractions greater than 1 be written as mixed numbers?
Answer: No. For example: 8/4 = 2 cannot be written as a mixed number.
Page 162
Write the following fractions as mixed fractions: a. 9/2 b. 9/5 c. 21/19 d. 47/9 e. 12/11 f. 19/6
Answer: a. 9/2 = 4 1/2 b. 9/5 = 1 4/5 c. 21/19 = 1 2/19 d. 47/9 = 5 2/9 e. 12/11 = 1 1/11 f. 19/6 = 3 1/6
Page 163
Are the lengths 1/2 and 3/6 equal?
Answer: Yes.
Page 164
Are 2/3 and 4/6 equivalent fractions? Why?
Answer: Yes, since they are of equal length which can be seen in fractional wall also.
Page 164
Additional Practice Questions
What is a fraction and how is it expressed?
easyAnswer: A fraction represents a part of a whole or, more generally, any number of equal parts. It is written as a/b, where a is the numerator, and b is the denominator.
How do you convert an improper fraction to a mixed number?
mediumAnswer: To convert an improper fraction to a mixed number, divide the numerator by the denominator. The quotient becomes the whole number, and the remainder forms the new numerator over the original denominator.
What are equivalent fractions and how do you find them?
easyAnswer: Equivalent fractions are different fractions that represent the same part of a whole. They can be found by multiplying or dividing the numerator and denominator by the same number.
Explain Brahmagupta's method for adding fractions.
mediumAnswer: Brahmagupta's method involves representing both fractions with a common denominator before adding their numerators. Simplify the resultant fraction, if needed.
Describe a real-world example where fractions are used.
easyAnswer: Fractions are used in cooking for measuring ingredients, such as 1/2 cup of flour or 3/4 teaspoon of salt, to ensure correct proportions in recipes.