High School

1. Compare the fractions:

a. (i) \(\frac{3}{5}, \frac{9}{10}\)

b. (i) \(\frac{6}{7}, \frac{9}{10}\)

(ii) \(\frac{3}{8}, \frac{9}{16}\)

(iii) \(8, \frac{14}{3}\)

(iv) \(\frac{21}{25}, \frac{18}{20}\)

(v) \(4\frac{2}{4}, 9\frac{3}{5}\)

2.

a. Arrange the fractions \(\frac{5}{6}, \frac{7}{16}, \frac{3}{8}, \frac{6}{12}\) in ascending order.

b. Arrange the following fractions in descending order:

(i) \(\frac{1}{5}, \frac{3}{7}, \frac{7}{10}\)

(ii) \(\frac{2}{9}, \frac{5}{6}, \frac{7}{12}\)

Answer :

To compare fractions, we first convert them to have a common denominator or convert them to decimal form. Let's tackle each pair step-by-step:

  1. (a)

    (i) Compare [tex]\frac{3}{5}[/tex] and [tex]\frac{9}{10}[/tex]:

    Convert both fractions to decimal by dividing the numerator by the denominator:

    [tex]\frac{3}{5} = 0.6[/tex] and [tex]\frac{9}{10} = 0.9[/tex].

    Since 0.6 < 0.9, [tex]\frac{3}{5} < \frac{9}{10}[/tex].

    (b)

    (i) Compare [tex]\frac{6}{7}[/tex] and [tex]\frac{9}{10}[/tex]:

    Convert both to decimal:

    [tex]\frac{6}{7} \approx 0.857[/tex] and [tex]\frac{9}{10} = 0.9[/tex].

    Since 0.857 < 0.9, [tex]\frac{6}{7} < \frac{9}{10}[/tex].

    (ii) Compare [tex]\frac{3}{8}[/tex] and [tex]\frac{9}{16}[/tex]:

    Convert to decimals:

    [tex]\frac{3}{8} = 0.375[/tex] and [tex]\frac{9}{16} = 0.5625[/tex].

    So, [tex]\frac{3}{8} < \frac{9}{16}[/tex].

    (iii) Compare [tex]8[/tex] and [tex]\frac{14}{3}[/tex]:

    First convert [tex]\frac{14}{3}[/tex] to a mixed number: [tex]4\frac{2}{3}[/tex] which is approximately 4.67 in decimal.

    Since 8 > 4.67, 8 > [tex]\frac{14}{3}[/tex].

    (iii) Compare [tex]\frac{21}{25}[/tex] and [tex]\frac{18}{20}[/tex]:

    Convert to decimals:

    [tex]\frac{21}{25} = 0.84[/tex] and [tex]\frac{18}{20} = 0.9[/tex].

    Therefore, [tex]\frac{21}{25} < \frac{18}{20}[/tex].

    (iii) Compare [tex]4\frac{2}{4}[/tex] and [tex]9\frac{3}{5}[/tex]:

    Convert to improper fractions:

    [tex]4\frac{2}{4} = 4.5[/tex] and [tex]9\frac{3}{5} = 9.6[/tex].

    Clearly, 4.5 < 9.6.

  2. (a) Arrange [tex]\frac{5}{6}[/tex], [tex]\frac{7}{16}[/tex], [tex]\frac{3}{8}[/tex], and [tex]\frac{6}{12}[/tex] in ascending order:

    Convert each to decimal:

    • [tex]\frac{5}{6} \approx 0.833[/tex]
    • [tex]\frac{7}{16} = 0.4375[/tex]
    • [tex]\frac{3}{8} = 0.375[/tex]
    • [tex]\frac{6}{12} = 0.5[/tex]

    Ordering them: [tex]\frac{3}{8} < \frac{7}{16} < \frac{6}{12} < \frac{5}{6}[/tex].

(b) Arrange the fractions in descending order:

(i) [tex]\frac{1}{5}[/tex], [tex]\frac{3}{7}[/tex], [tex]\frac{7}{10}[/tex] in descending order:

Convert to decimals:

  • [tex]\frac{1}{5} = 0.2[/tex]
  • [tex]\frac{3}{7} \approx 0.429[/tex]
  • [tex]\frac{7}{10} = 0.7[/tex]

Ordering them: [tex]\frac{7}{10} > \frac{3}{7} > \frac{1}{5}[/tex].

(ii) [tex]\frac{2}{9}[/tex], [tex]\frac{5}{6}[/tex], [tex]\frac{7}{12}[/tex] in descending order:

Convert to decimals:

  • [tex]\frac{2}{9} \approx 0.222[/tex]
  • [tex]\frac{5}{6} \approx 0.833[/tex]
  • [tex]\frac{7}{12} \approx 0.583[/tex]

Ordering them: [tex]\frac{5}{6} > \frac{7}{12} > \frac{2}{9}[/tex].

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