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Arrange the following fractions in ascending order: 2/5, 6/10, 7/20, 1/2, 3/4. Compare the following fractions using >, <, or =: 5/2 and 4 1/2, and 4/5 and 9/5.

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2 parts
a

720,25,12,610,34\frac{7}{20}, \frac{2}{5}, \frac{1}{2}, \frac{6}{10}, \frac{3}{4}

b

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Step-by-step solution

8 steps

Here are the solutions to the problems from the image:

Part a· 5 steps

Arrange in ascending order.

  1. List the given fractions

    25,610,720,12,34\frac{2}{5}, \frac{6}{10}, \frac{7}{20}, \frac{1}{2}, \frac{3}{4}.

  2. Find the least common denominator (LCD) for all fractions.

    The denominators are 5, 10, 20, 2, 4. The LCD is 20.

  3. Convert each fraction to an equivalent fraction with a denominator of 20.

    25=2×45×4=820\frac{2}{5} = \frac{2 \times 4}{5 \times 4} = \frac{8}{20} 610=6×210×2=1220\frac{6}{10} = \frac{6 \times 2}{10 \times 2} = \frac{12}{20} 720=720\frac{7}{20} = \frac{7}{20} 12=1×102×10=1020\frac{1}{2} = \frac{1 \times 10}{2 \times 10} = \frac{10}{20} 34=3×54×5=1520\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}

  4. Arrange the fractions in ascending order by comparing their numerators

    7, 8, 10, 12, 15.

    720,820,1020,1220,1520\frac{7}{20}, \frac{8}{20}, \frac{10}{20}, \frac{12}{20}, \frac{15}{20}

  5. Write the original fractions in ascending order.

    720,25,12,610,34\boxed{\frac{7}{20}, \frac{2}{5}, \frac{1}{2}, \frac{6}{10}, \frac{3}{4}}

Part b

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Say if > < or =

b.1 52□412\frac{5}{2} \square 4\frac{1}{2}

  1. Convert both numbers to decimals or improper fractions.

    52=2.5\frac{5}{2} = 2.5 412=4.54\frac{1}{2} = 4.5

  2. Compare the decimal values.

    2.5<4.52.5 < 4.5

    The symbol is <\boxed{<}.

    b.2 45□95\frac{4}{5} \square \frac{9}{5}

  3. Compare the numerators since the denominators are the same.

    4<94 < 9

    The symbol is <\boxed{<}.

    b.3 $2\frac{7}{10} \square

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