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Determine if the following statements are true or false, showing your work: a) 1/2 = 2/4 = 3/6 = 4/8 = 5/10 = 6/12 b) 500 mm = 50 cm c) 500 mm = 1 m d) 1/2 km = 500 m

Mathematics

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Answers

5 parts
a

True\text{True}

b

True\text{True}

c

False\text{False}

d

True\text{True}

e

False\text{False}

Step-by-step solution

11 steps

Here are the answers for the true or false statements:

Part a· 2 steps

  1. Simplify each fraction to its lowest terms.

    12=12\frac{1}{2} = \frac{1}{2} 24=12\frac{2}{4} = \frac{1}{2} 36=12\frac{3}{6} = \frac{1}{2} 48=12\frac{4}{8} = \frac{1}{2} 510=12\frac{5}{10} = \frac{1}{2} 612=12\frac{6}{12} = \frac{1}{2}

  2. Compare the simplified fractions.

    All fractions are equal to 12\frac{1}{2}.
    The statement is True\boxed{\text{True}}.

Part b

True\text{True}

  1. Convert millimeters (mm) to centimeters (cm).

    There are 10 mm10 \text{ mm} in 1 cm1 \text{ cm}.

    500 mm=50010 cm=50 cm500 \text{ mm} = \frac{500}{10} \text{ cm} = 50 \text{ cm}

  2. Compare the converted value with the given value.

    50 cm=50 cm50 \text{ cm} = 50 \text{ cm}

    The statement is True\boxed{\text{True}}.

Part c

False\text{False}

  1. Convert millimeters (mm) to meters (m).

    There are 1000 mm1000 \text{ mm} in 1 m1 \text{ m}.

    500 mm=5001000 m=0.5 m500 \text{ mm} = \frac{500}{1000} \text{ m} = 0.5 \text{ m}

  2. Compare the converted value with the given value.

    0.5 m≠1 m0.5 \text{ m} \neq 1 \text{ m}

    The statement is False\boxed{\text{False}}.

Part d

True\text{True}

  1. Simplify the fractions.

    As shown in part (a), all fractions 12,24,36,48,510,612\frac{1}{2}, \frac{2}{4}, \frac{3}{6}, \frac{4}{8}, \frac{5}{10}, \frac{6}{12} are equivalent to 12\frac{1}{2}.

  2. Convert 12 km\frac{1}{2} \text{ km} to meters (m).

    There are 1000 m1000 \text{ m} in 1 km1 \text{ km}.

    12 km=12×1000 m=500 m\frac{1}{2} \text{ km} = \frac{1}{2} \times 1000 \text{ m} = 500 \text{ m}

  3. Compare the converted value with the given value.

    500 m=500 m500 \text{ m} = 500 \text{ m}

    The statement is True\boxed{\text{True}}.

Part e

False\text{False}

  1. Simplify both fractions.

    612=12\frac{6}{12} = \frac{1}{2} 24=12\frac{2}{4} = \frac{1}{2}

  2. Compare the simplified fractions.

    12 is not bigger than 12 (they are equal)\frac{1}{2} \text{ is not bigger than } \frac{1}{2} \text{ (they are equal)}

    The statement is False\boxed{\text{False}}.

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