Questions: Write each mixed number as a common fraction. 1 3/8 = Rewrite both fractions so the denominators are the same. 2/6 = 1/2 = 9/6 =

Write each mixed number as a common fraction. 1 3/8 = Rewrite both fractions so the denominators are the same. 2/6 = 1/2 = 9/6 =
Transcript text: Write each mixed number as a common fraction. \[ \left.1 \frac{3}{8} \right\rvert\,= \] Rewrite both fractions so the denominators are the same. $\frac{2}{6}=\frac{1}{2}=\square$ $\frac{9}{6}=$ $\square$
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Solution

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Solution Steps

To convert a mixed number to a common fraction, multiply the whole number by the denominator of the fractional part and add the numerator. For rewriting fractions with a common denominator, find the least common multiple (LCM) of the denominators and adjust the numerators accordingly.

Step 1: Convert Mixed Number to Common Fraction

To convert the mixed number \(1 \frac{3}{8}\) to a common fraction, we use the formula: \[ \text{Fraction} = \text{Whole} \times \text{Denominator} + \text{Numerator} \] Substituting the values, we have: \[ \text{Fraction} = 1 \times 8 + 3 = 8 + 3 = 11 \] Thus, the mixed number \(1 \frac{3}{8}\) can be expressed as: \[ \frac{11}{8} \]

Step 2: Rewrite Fractions with a Common Denominator

We need to rewrite the fractions \(\frac{2}{6}\) and \(\frac{1}{2}\) with a common denominator. The denominators are \(6\) and \(2\). The least common multiple (LCM) of \(6\) and \(2\) is \(6\).

Now, we rewrite \(\frac{1}{2}\) to have a denominator of \(6\): \[ \frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6} \] Thus, the fractions with a common denominator are: \[ \frac{2}{6} \quad \text{and} \quad \frac{3}{6} \]

Final Answer

The mixed number \(1 \frac{3}{8}\) as a common fraction is: \[ \boxed{\frac{11}{8}} \] The fractions rewritten with a common denominator are: \[ \boxed{\left(\frac{2}{6}, \frac{3}{6}\right)} \]

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