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3 answers
To compare \( \frac{3}{5} \) and \( 0.6 \), we can convert \( \frac{3}{5} \) to a decimal.
Calculating \( \frac{3}{5} \):
\[ \frac{3}{5} = 0.6 \]
Now we can compare them:
\[ \frac{3}{5} = 0.6 \]
Thus, \( \frac{3}{5} \) is equal to \( 0.6 \).
So the correct symbol to use is \( = \):
\[ \frac{3}{5} , = , 0.6 \]
To compare the mixed numbers \(-40 \frac{16}{571}\) and \(-40 \frac{75}{584}\), we can first convert them to improper fractions.
\[ -40 \frac{16}{571} = -\left(40 \cdot 571 + 16\right) / 571 = -\frac{22840 + 16}{571} = -\frac{22856}{571} \]
\[ -40 \frac{75}{584} = -\left(40 \cdot 584 + 75\right) / 584 = -\frac{23360 + 75}{584} = -\frac{23335}{584} \]
Now we can compare the two improper fractions \(-\frac{22856}{571}\) and \(-\frac{23335}{584}\).
To compare the fractions, it is often easier to find a common denominator:
The least common multiple (LCM) of \(571\) and \(584\) is \(571 \times 584\). We can convert both fractions to have this common denominator:
\[ -\frac{22856}{571} \text{ becomes } -\frac{22856 \times 584}{571 \times 584} = -\frac{13362584}{333964} \]
\[ -\frac{23335}{584} \text{ becomes } -\frac{23335 \times 571}{584 \times 571} = -\frac{13352585}{333964} \]
Now we have the fractions:
Now, since both fractions are negative, we can compare their absolute values:
Thus:
\[ -\frac{13362584}{333964} < -\frac{13352585}{333964} \]
In conclusion:
\[ -40 \frac{16}{571} < -40 \frac{75}{584} \]
So, \(-40 \frac{16}{571} , < , -40 \frac{75}{584}\).
