Answer :
To divide fractions, you multiply by the reciprocal of the divisor. Here’s a step-by-step explanation for solving
[tex]$$
\frac{13}{15} \div \frac{7}{10}:
$$[/tex]
1. First, change the division to multiplication by taking the reciprocal of [tex]$\frac{7}{10}$[/tex]:
[tex]$$
\frac{13}{15} \div \frac{7}{10} = \frac{13}{15} \times \frac{10}{7}.
$$[/tex]
2. Multiply the numerators and the denominators:
[tex]$$
\text{Numerator: } 13 \times 10 = 130,
$$[/tex]
[tex]$$
\text{Denominator: } 15 \times 7 = 105.
$$[/tex]
So the expression becomes:
[tex]$$
\frac{130}{105}.
$$[/tex]
3. Next, simplify the fraction. Find the greatest common divisor (GCD) of 130 and 105. In this case, the GCD is 5. Divide both the numerator and the denominator by 5:
[tex]$$
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}.
$$[/tex]
Thus, the simplest form of the expression is
[tex]$$
\frac{26}{21}.
$$[/tex]
[tex]$$
\frac{13}{15} \div \frac{7}{10}:
$$[/tex]
1. First, change the division to multiplication by taking the reciprocal of [tex]$\frac{7}{10}$[/tex]:
[tex]$$
\frac{13}{15} \div \frac{7}{10} = \frac{13}{15} \times \frac{10}{7}.
$$[/tex]
2. Multiply the numerators and the denominators:
[tex]$$
\text{Numerator: } 13 \times 10 = 130,
$$[/tex]
[tex]$$
\text{Denominator: } 15 \times 7 = 105.
$$[/tex]
So the expression becomes:
[tex]$$
\frac{130}{105}.
$$[/tex]
3. Next, simplify the fraction. Find the greatest common divisor (GCD) of 130 and 105. In this case, the GCD is 5. Divide both the numerator and the denominator by 5:
[tex]$$
\frac{130 \div 5}{105 \div 5} = \frac{26}{21}.
$$[/tex]
Thus, the simplest form of the expression is
[tex]$$
\frac{26}{21}.
$$[/tex]
