Question
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write down 3 e equivalent Fraction each for the following. \( \begin{array}{lll}\text { - } \frac{3}{2} & \text { (2) } \frac{7}{5} \frac{1}{4} & \text { (3) }\end{array} \)

Ask by Peterson Ayala. in Ghana
Jan 19,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

Here are three equivalent fractions for each of the given numbers: 1. **For \( -\frac{3}{2} \):** - \( -\frac{6}{4} \) - \( -\frac{9}{6} \) - \( -\frac{12}{8} \) 2. **For \( \frac{7}{5} \):** - \( \frac{14}{10} \) - \( \frac{21}{15} \) - \( \frac{28}{20} \) 3. **For \( \frac{1}{4} \):** - \( \frac{2}{8} \) - \( \frac{3}{12} \) - \( \frac{4}{16} \) Each set of fractions is equivalent to the original number, meaning they represent the same value expressed differently.

Solution

Sure! Here are three equivalent fractions for each of the following: ### (1) \( -\frac{3}{2} \) To find equivalent fractions, multiply both the numerator and the denominator by the same non-zero integer. 1. **Multiply by 2**: \[ -\frac{3 \times 2}{2 \times 2} = -\frac{6}{4} \] 2. **Multiply by 3**: \[ -\frac{3 \times 3}{2 \times 3} = -\frac{9}{6} \] 3. **Multiply by 4**: \[ -\frac{3 \times 4}{2 \times 4} = -\frac{12}{8} \] ### (2) \( \frac{7}{5} \) 1. **Multiply by 2**: \[ \frac{7 \times 2}{5 \times 2} = \frac{14}{10} \] 2. **Multiply by 3**: \[ \frac{7 \times 3}{5 \times 3} = \frac{21}{15} \] 3. **Multiply by 4**: \[ \frac{7 \times 4}{5 \times 4} = \frac{28}{20} \] ### (3) \( \frac{1}{4} \) 1. **Multiply by 2**: \[ \frac{1 \times 2}{4 \times 2} = \frac{2}{8} \] 2. **Multiply by 3**: \[ \frac{1 \times 3}{4 \times 3} = \frac{3}{12} \] 3. **Multiply by 4**: \[ \frac{1 \times 4}{4 \times 4} = \frac{4}{16} \] Each of these fractions is equivalent to the original fraction because they represent the same value, just expressed with different numerators and denominators.

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Bonus Knowledge

To find equivalent fractions for \( \frac{3}{2} \), you can multiply the numerator and the denominator by the same number. For example, if you multiply by 2, you get \( \frac{6}{4} \). If you multiply by 3, you get \( \frac{9}{6} \). Lastly, multiplying by 4 gives you \( \frac{12}{8} \). So, the three equivalent fractions are \( \frac{6}{4}, \frac{9}{6}, \frac{12}{8} \). For \( \frac{7}{5} \), you can also multiply by the same numbers. Multiplying by 2 gives \( \frac{14}{10} \). Multiplying by 3 results in \( \frac{21}{15} \), and multiplying by 4 gives \( \frac{28}{20} \). Therefore, the three equivalent fractions for \( \frac{7}{5} \) are \( \frac{14}{10}, \frac{21}{15}, \frac{28}{20} \). For \( \frac{1}{4} \), you can multiply by 2 to get \( \frac{2}{8} \), by 3 for \( \frac{3}{12} \), and by 5 for \( \frac{5}{20} \). Thus, the three equivalent fractions for \( \frac{1}{4} \) are \( \frac{2}{8}, \frac{3}{12}, \frac{5}{20} \).

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