Answer :
Sure, let's multiply the fractions [tex]\(\frac{3}{7} \cdot \frac{10}{13} \cdot \frac{14}{15}\)[/tex] together and simplify the result to its lowest terms.
Step 1: Multiply the numerators together.
[tex]\[ 3 \times 10 \times 14 = 420 \][/tex]
Step 2: Multiply the denominators together.
[tex]\[ 7 \times 13 \times 15 = 1365 \][/tex]
So, the product of the fractions is:
[tex]\[ \frac{420}{1365} \][/tex]
Step 3: Simplify the fraction to its lowest terms.
To simplify, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 420 and 1365 is 105.
Divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{420 \div 105}{1365 \div 105} = \frac{4}{13} \][/tex]
So, [tex]\(\frac{3}{7} \cdot \frac{10}{13} \cdot \frac{14}{15}\)[/tex] simplifies to [tex]\(\frac{4}{13}\)[/tex] in its lowest terms.
Step 1: Multiply the numerators together.
[tex]\[ 3 \times 10 \times 14 = 420 \][/tex]
Step 2: Multiply the denominators together.
[tex]\[ 7 \times 13 \times 15 = 1365 \][/tex]
So, the product of the fractions is:
[tex]\[ \frac{420}{1365} \][/tex]
Step 3: Simplify the fraction to its lowest terms.
To simplify, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 420 and 1365 is 105.
Divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{420 \div 105}{1365 \div 105} = \frac{4}{13} \][/tex]
So, [tex]\(\frac{3}{7} \cdot \frac{10}{13} \cdot \frac{14}{15}\)[/tex] simplifies to [tex]\(\frac{4}{13}\)[/tex] in its lowest terms.
