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Write the missing numbers on each line. Draw lines between matching decimals and fractions.

Mathematics

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Step-by-step solution

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Here are the solutions to the problems:

1. Write the missing numbers on each line (0 to 1).

  1. Determine the value of each increment on the number line.

    The number line from 0 to 1 is divided into 10 equal parts.
    Each part represents 110\frac{1}{10} or 0.1.

  2. Fill in the missing numbers.

    • The first missing number is 2 increments from 0: 0+2×0.1=0.20 + 2 \times 0.1 = 0.2.
    • The second missing number is 1 increment from 0.5: 0.5+1×0.1=0.60.5 + 1 \times 0.1 = 0.6.
    • The third missing number is 2 increments from 0.5: 0.5+2×0.1=0.70.5 + 2 \times 0.1 = 0.7.

    The missing numbers are 0.2\boxed{0.2}, 0.6\boxed{0.6}, and 0.7\boxed{0.7}.

    2. Write the missing numbers on each line (3 to 4).

  3. Determine the value of each increment on the number line.

    The number line from 3 to 4 is divided into 10 equal parts.
    Each part represents 110\frac{1}{10} or 0.1.

  4. Fill in the missing numbers.

    • The first missing number is 1 increment from 3: 3+1×0.1=3.13 + 1 \times 0.1 = 3.1.
    • The second missing number is 2 increments from 3: 3+2×0.1=3.23 + 2 \times 0.1 = 3.2.
    • The third missing number is 1 increment from 3.5: 3.5+1×0.1=3.63.5 + 1 \times 0.1 = 3.6.
    • The fourth missing number is 2 increments from 3.5: 3.5+2×0.1=3.73.5 + 2 \times 0.1 = 3.7.
    • The fifth missing number is 3 increments from 3.5: 3.5+3×0.1=3.83.5 + 3 \times 0.1 = 3.8.

    The missing numbers are 3.1\boxed{3.1}, 3.2\boxed{3.2}, 3.6\boxed{3.6}, 3.7\boxed{3.7}, and 3.8\boxed{3.8}.

    3. Draw lines between matching decimals and fractions.

  5. Convert all fractions to decimals for easier comparison.

    • Top row:
      • 110=0.1\frac{1}{10} = 0.1
      • 5.5
      • 710=0.7\frac{7}{10} = 0.7
      • 0.3
      • 12=0.5\frac{1}{2} = 0.5
      • 0.1
      • 2.4
    • Bottom row:
      • 0.7
      • 2410=2+410=2+0.4=2.42\frac{4}{10} = 2 + \frac{4}{10} = 2 + 0.4 = 2.4
      • 2
      • 0.5
      • 310=0.3\frac{3}{10} = 0.3
      • 512=5+12=5+0.5=5.55\frac{1}{2} = 5 + \frac{1}{2} = 5 + 0.5 = 5.5
  6. Identify the matching pairs between the top and bottom rows.

    • 5.5 (top row) matches 5125\frac{1}{2} (bottom row).
    • 710\frac{7}{10} (top row) matches 0.7 (bottom row).
    • 0.3 (top row) matches 310\frac{3}{10} (bottom row).
    • 12\frac{1}{2} (top row) matches 0.5 (bottom row).
    • 2.4 (top row) matches 24102\frac{4}{10} (bottom row).

    The matching pairs are:

    • 5.5↔512\boxed{5.5 \leftrightarrow 5\frac{1}{2}}
    • 710↔0.7\boxed{\frac{7}{10} \leftrightarrow 0.7}
    • 0.3↔310\boxed{0.3 \leftrightarrow \frac{3}{10}}
    • 12↔0.5\boxed{\frac{1}{2} \leftrightarrow 0.5}
    • 2.4↔2410\boxed{2.4 \leftrightarrow 2\frac{4}{10}}
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