Answer :
Sure, let's solve the problem step-by-step:
To divide fractions, you need to multiply by the reciprocal. This means flipping the numerator and denominator of the fraction you're dividing by. So we'll solve the problem [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] by changing it to a multiplication:
[tex]\[
\frac{13}{15} \times \frac{10}{7}
\][/tex]
Step 1: Multiply the numerators and the denominators
Multiply the numerators (top numbers) together:
[tex]\[ 13 \times 10 = 130 \][/tex]
Multiply the denominators (bottom numbers) together:
[tex]\[ 15 \times 7 = 105 \][/tex]
So, the fractional multiplication results in:
[tex]\[
\frac{130}{105}
\][/tex]
Step 2: Simplify the fraction
To simplify the fraction, find the greatest common divisor (GCD) of the numerator and the denominator, which is the largest number that divides both numbers evenly.
The GCD of 130 and 105 is 5.
Now, divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}
\][/tex]
So, the simplest form of [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] is:
[tex]\[
\frac{26}{21}
\][/tex]
Therefore, the answer is [tex]\(\frac{26}{21}\)[/tex].
To divide fractions, you need to multiply by the reciprocal. This means flipping the numerator and denominator of the fraction you're dividing by. So we'll solve the problem [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] by changing it to a multiplication:
[tex]\[
\frac{13}{15} \times \frac{10}{7}
\][/tex]
Step 1: Multiply the numerators and the denominators
Multiply the numerators (top numbers) together:
[tex]\[ 13 \times 10 = 130 \][/tex]
Multiply the denominators (bottom numbers) together:
[tex]\[ 15 \times 7 = 105 \][/tex]
So, the fractional multiplication results in:
[tex]\[
\frac{130}{105}
\][/tex]
Step 2: Simplify the fraction
To simplify the fraction, find the greatest common divisor (GCD) of the numerator and the denominator, which is the largest number that divides both numbers evenly.
The GCD of 130 and 105 is 5.
Now, divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}
\][/tex]
So, the simplest form of [tex]\(\frac{13}{15} \div \frac{7}{10}\)[/tex] is:
[tex]\[
\frac{26}{21}
\][/tex]
Therefore, the answer is [tex]\(\frac{26}{21}\)[/tex].
