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Using Number Lines to Divide Fractions
What is the quotient of 7/3 ÷ 2/3 Write the answer as a mixed number, or a number that has a whole-number part and a fraction part.

1/3 __/3 3/3

7 thirds divided by 2 thirds equals ___ whole groups and 1 fractional part.

What fraction of a group is left over?

I have_____of a group left over.

7/3 ÷ 2 /3 = ___1/2

1 answer

To solve the division of fractions \( \frac{7}{3} \div \frac{2}{3} \), we can rewrite it as \( \frac{7}{3} \times \frac{3}{2} \).

  1. First, we multiply: \[ \frac{7}{3} \times \frac{3}{2} = \frac{7 \times 3}{3 \times 2} = \frac{21}{6} \]

  2. Now, we simplify \( \frac{21}{6} \):

    • Divide both the numerator and denominator by 3: \[ \frac{21 \div 3}{6 \div 3} = \frac{7}{2} \]

  3. Now, convert \( \frac{7}{2} \) to a mixed number:

    • \( \frac{7}{2} \) can be expressed as \( 3 \frac{1}{2} \) (since 2 goes into 7 three times with a remainder of 1).

Now let's fill in the blanks:

  1. The number line can be represented from \( \frac{1}{3} \) to \( \frac{3}{3} \) to \( \frac{7}{3} \) as follows:

    1/3    __/3    3/3

  2. We have determined above that \( 7 \) thirds divided by \( 2 \) thirds equals \( 3 \) whole groups and \( 1 \) fractional part.

  3. What fraction of a group is left over:

    • The remainder is \( \frac{1}{2} \).

  4. Therefore, filling everything in:

    • \( 7/3 \div 2/3 = 3 \frac{1}{2} \)

Final Answer:

  • So, the completed sentences are as follows:

    1. 1/3 __/3 3/3
    2. 7 thirds divided by 2 thirds equals 3 whole groups and 1 fractional part.
    3. I have 1/2 of a group left over.
    4. \( 7/3 \div 2/3 = 3 \frac{1}{2} \)