(ii) A bag of apples consists of 3 red apples and 4 green apples. of the whole bag of apples are red apples.

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1 Chapter 0 0. Fractions A. Proper Fractions, Improper Fractions and Mixed Fractions Consider the following situations. (i) A pizza is cut into equal pieces. (ii) A bag of apples consists of red apples and green apples. Each piece is of the whole pizza. of the whole bag of apples are red apples. Both the numbers and are fractions where and are called numerators while and are called denominators. Fractions are used to represent the relationship between parts and a whole. denominator numerator fraction bar There are three different types of fractions as shown below. Proper fraction The numerator of a proper fraction is less than the denominator. e.g., 6, Improper fraction The numerator of an improper fraction is greater than or equal to the denominator. e.g., 6,, Mixed fraction In a mixed fraction, a natural number is written on the left of a proper fraction. The value of the mixed fraction is the sum of the natural number and the proper fraction. e.g.,, A mixed fraction is also known as a mixed number. + If the numerator of an improper fraction is greater than the denominator, the improper fraction can be converted to a mixed fraction. On the other hand, a mixed fraction can be converted to an improper fraction. numerator denominator proper fraction improper fraction mixed fraction 0.

2 Section 0. Level Example 0. Convert into an improper fraction. Convert into a mixed fraction. Solution # g Practice 0. Convert 6 into an improper fraction. Exercise 0.: Convert into a mixed fraction. B. Expanding a Fraction / Reducing a Fraction Let us go through the table below. Expanding a fraction When multiplying both the numerator and the denominator of a fraction by a number which is greater than, the fraction is expanded but its value remains unchanged. e.g. Expanding the fraction : Reducing a fraction When dividing both the numerator and the denominator of a fraction by a common factor which is greater than, the fraction is reduced but its value remains unchanged. e.g. Reducing the fraction : # # ' ' and are equal in value. Also, and are equal in value. When a fraction cannot be further reduced, the fraction is called fraction in simplest form. Therefore, the simplest form of is and the simplest form of is. Note that, unless otherwise stated, always write fractions in simplest form. fraction in simplest form 0.

3 Chapter 0 Level Example 0.6 Solution Reduce 0 to its simplest form. 0 0 ' ' 0 ' ' The H.C.F. of and is. Practice 0.6 Reduce to its simplest form. Exercise 0.: C. Comparing Fractions Consider two fractions with the same denominator. The larger the numerator, the larger is the fraction, e.g... Consider two fractions with different denominators. In order to compare their values, we can expand or reduce the fractions such that they have the same denominator. The symbol. means is greater than, while the symbol, means is less than. Level Example 0. In each of the following, compare the values of the fractions.,, Solution Strategy The L.C.M. of and is. Therefore, we can first expand the fractions and into fractions with as their denominators respectively. Then compare the values of their numerators of the fractions obtained. # # # # 0 a, `, 0 0.

4 Section 0. # # # # a. The L.C.M. of and is. `. Practice 0. In each of the following, compare the values of the fractions.,, 0 6 Exercise 0.: Class Exercise 0.. Convert into an improper fraction.. Convert into a mixed fraction.. Reduce to its simplest form. 0. Compare the values of 6 and. Which one is greater? Exercise 0. Level. Convert each of the following improper fractions into a mixed fraction. 6 6 Example 0. 0.

5 Open-ended Open-ended Chapter 0. Convert each of the following mixed fractions into an improper fraction. 6. Reduce each of the following fractions to the simplest form. 0 6 Example 0.6. Compare the values of 0 and. Which one is greater? Level. Convert each of the following improper fractions into a mixed fraction In each of the following, expand the two fractions with the same denominator.,,. Reduce each of the following fractions to the simplest form. 0. Compare the values of and. Example 0.. Compare the values of and. 0. Write down three fractions between and.. Write down three fractions between and. 0.6