To find fractions equivalent to \(-\frac{48}{72}\), we can reduce the fraction and also find equivalent fractions through multiplication by the same number.
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Reduce \(-\frac{48}{72}\):
- Find the greatest common divisor (GCD) of 48 and 72. The GCD is 24.
- Divide the numerator and the denominator by 24:
\[ -\frac{48 \div 24}{72 \div 24} = -\frac{2}{3} \]
So, \(-\frac{48}{72}\) simplifies to \(-\frac{2}{3}\).
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Find equivalent fractions:
- Multiply both the numerator and denominator of \(-\frac{2}{3}\) by the same integer. Here are some examples:
- Multiply by 2: \[-\frac{2 \times 2}{3 \times 2} = -\frac{4}{6}\]
- Multiply by 3: \[-\frac{2 \times 3}{3 \times 3} = -\frac{6}{9}\]
- Multiply by 4: \[-\frac{2 \times 4}{3 \times 4} = -\frac{8}{12}\]
- Multiply by -1 (to get a positive fraction): \[\frac{2}{3}\]
- Multiply both the numerator and denominator of \(-\frac{2}{3}\) by the same integer. Here are some examples:
Here are some equivalent fractions to \(-\frac{48}{72}\):
- \(-\frac{2}{3}\)
- \(-\frac{4}{6}\)
- \(-\frac{6}{9}\)
- \(-\frac{8}{12}\)
- \(-\frac{10}{15}\) (by multiplying by 5)
- \(-\frac{20}{30}\) (by multiplying by 10)
In general, any fraction of the form \(-\frac{2k}{3k}\) for any integer \(k \neq 0\) will be equivalent to \(-\frac{48}{72}\).