Todd Brewer
09/09/2024 · High School
SSESSMENL Lect all the fractions that have the same decimal \( 1 \frac{1}{3} \) \( \frac{12}{9} \) \( \frac{3}{9} \) \( 1 \frac{2}{3} \) \( \frac{4}{3} \)
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Tutor-Verified Answer
Step-by-step Solution
To find all the fractions that have the same decimal representation, we first need to convert the mixed number and the fractions into decimal form.
1. **Convert \( 1 \frac{1}{3} \)**:
\[
1 \frac{1}{3} = 1 + \frac{1}{3} = 1 + 0.3333... = 1.3333...
\]
2. **Convert \( \frac{12}{9} \)**:
\[
\frac{12}{9} = \frac{4}{3} = 1.3333...
\]
3. **Convert \( \frac{3}{9} \)**:
\[
\frac{3}{9} = \frac{1}{3} = 0.3333...
\]
4. **Convert \( 1 \frac{2}{3} \)**:
\[
1 \frac{2}{3} = 1 + \frac{2}{3} = 1 + 0.6666... = 1.6666...
\]
5. **Convert \( \frac{4}{3} \)**:
\[
\frac{4}{3} = 1.3333...
\]
Now, let's summarize the decimal representations:
- \( 1 \frac{1}{3} = 1.3333... \)
- \( \frac{12}{9} = 1.3333... \)
- \( \frac{3}{9} = 0.3333... \)
- \( 1 \frac{2}{3} = 1.6666... \)
- \( \frac{4}{3} = 1.3333... \)
The fractions that have the same decimal representation \( 1.3333... \) are:
- \( 1 \frac{1}{3} \)
- \( \frac{12}{9} \)
- \( \frac{4}{3} \)
So, the fractions that have the same decimal representation are:
- \( 1 \frac{1}{3} \)
- \( \frac{12}{9} \)
- \( \frac{4}{3} \)
Quick Answer
The fractions with the same decimal representation are \( 1 \frac{1}{3} \), \( \frac{12}{9} \), and \( \frac{4}{3} \).
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