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Arrange the given fractions in the ascen...

Arrange the given fractions in the ascending order :
(i) `7/8, 15/6, 5/6" (ii) "3/4, 15/22, 26/33`.

Text Solution

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The correct Answer is:
To arrange the given fractions in ascending order, we will follow these steps: ### Part (i): Arrange `7/8`, `15/6`, `5/6` 1. **Identify the fractions**: The fractions we need to arrange are \( \frac{7}{8}, \frac{15}{6}, \frac{5}{6} \). 2. **Find the LCM of the denominators**: The denominators are 8 and 6. The LCM of 8 and 6 is 24. 3. **Convert each fraction to have a common denominator**: - For \( \frac{7}{8} \): \[ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \] - For \( \frac{15}{6} \): \[ \frac{15}{6} = \frac{15 \times 4}{6 \times 4} = \frac{60}{24} \] - For \( \frac{5}{6} \): \[ \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \] 4. **Compare the numerators**: Now we have the fractions \( \frac{21}{24}, \frac{60}{24}, \frac{20}{24} \). The numerators are 21, 60, and 20. - The smallest numerator is 20, so \( \frac{5}{6} \) is the smallest fraction. - Next is 21, so \( \frac{7}{8} \) is the second. - Lastly, 60 corresponds to \( \frac{15}{6} \). 5. **Arrange in ascending order**: Thus, the fractions in ascending order are: \[ \frac{5}{6}, \frac{7}{8}, \frac{15}{6} \] ### Part (ii): Arrange `3/4`, `15/22`, `26/33` 1. **Identify the fractions**: The fractions we need to arrange are \( \frac{3}{4}, \frac{15}{22}, \frac{26}{33} \). 2. **Find the LCM of the denominators**: The denominators are 4, 22, and 33. The LCM of 4, 22, and 33 is 132. 3. **Convert each fraction to have a common denominator**: - For \( \frac{3}{4} \): \[ \frac{3}{4} = \frac{3 \times 33}{4 \times 33} = \frac{99}{132} \] - For \( \frac{15}{22} \): \[ \frac{15}{22} = \frac{15 \times 6}{22 \times 6} = \frac{90}{132} \] - For \( \frac{26}{33} \): \[ \frac{26}{33} = \frac{26 \times 4}{33 \times 4} = \frac{104}{132} \] 4. **Compare the numerators**: Now we have the fractions \( \frac{99}{132}, \frac{90}{132}, \frac{104}{132} \). The numerators are 99, 90, and 104. - The smallest numerator is 90, so \( \frac{15}{22} \) is the smallest fraction. - Next is 99, so \( \frac{3}{4} \) is the second. - Lastly, 104 corresponds to \( \frac{26}{33} \). 5. **Arrange in ascending order**: Thus, the fractions in ascending order are: \[ \frac{15}{22}, \frac{3}{4}, \frac{26}{33} \] ### Final Answer: - For part (i): \( \frac{5}{6}, \frac{7}{8}, \frac{15}{6} \) - For part (ii): \( \frac{15}{22}, \frac{3}{4}, \frac{26}{33} \)
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