Question
Mathematics
$\frac{3\cdot \frac{10}{13}}{13}-\frac{4}{7}=$(3*(10)/(13))/(13)-(4)/(7)=
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The answer is $\frac{98}{219}$(98)/(219).
Solution:
First, we evaluate the expression within the parentheses:
$\frac{3\cdot 10}{13}=\frac{30}{13}$(3*10)/(13)=(30)/(13)
Next, we can simplify the expression by finding a common denominator:
$\frac{30}{13\cdot 1}-\frac{4\cdot 13}{7\cdot 13}=\frac{30}{13}-\frac{52}{91}$(30)/(13*1)-(4*13)/(7*13)=(30)/(13)-(52)/(91)
To find a common denominator for these two fractions, we need to find the least common multiple (LCM) of 13 and 91, which is 1001.
$\frac{30\cdot 77}{13\cdot 77}-\frac{52\cdot 13}{91\cdot 13}=\frac{2310}{1001}-\frac{676}{1001}$(30*77)/(13*77)-(52*13)/(91*13)=(2310)/(1001)-(676)/(1001)
Now we can combine the fractions:
$\frac{2310-676}{1001}=\frac{1634}{1001}$(2310-676)/(1001)=(1634)/(1001)
We can simplify this fraction further by dividing both the numerator and denominator by their greatest common factor, which is 1.
So, $\frac{3\cdot \frac{10}{13}}{13}-\frac{4}{7}=\frac{98}{219}$(3*(10)/(13))/(13)-(4)/(7)=(98)/(219).
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