Answer :
Sure, let's multiply the fractions [tex]\(\frac{3}{4}\)[/tex] and [tex]\(\frac{14}{15}\)[/tex] and simplify the result step-by-step.
Step 1: Multiply the numerators.
First, we take the numerators of the fractions and multiply them together:
[tex]\[ 3 \times 14 = 42 \][/tex]
Step 2: Multiply the denominators.
Next, we multiply the denominators of the fractions:
[tex]\[ 4 \times 15 = 60 \][/tex]
Step 3: Write the result as a fraction.
After multiplying, we have:
[tex]\[ \frac{42}{60} \][/tex]
Step 4: Simplify the fraction.
To simplify the fraction [tex]\(\frac{42}{60}\)[/tex], we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 42 and 60 is 6.
Now, we divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{42 \div 6}{60 \div 6} = \frac{7}{10} \][/tex]
So, the simplest form of the fraction is [tex]\(\frac{7}{10}\)[/tex].
Therefore, [tex]\(\frac{3}{4} \times \frac{14}{15} = \frac{7}{10}\)[/tex].
Step 1: Multiply the numerators.
First, we take the numerators of the fractions and multiply them together:
[tex]\[ 3 \times 14 = 42 \][/tex]
Step 2: Multiply the denominators.
Next, we multiply the denominators of the fractions:
[tex]\[ 4 \times 15 = 60 \][/tex]
Step 3: Write the result as a fraction.
After multiplying, we have:
[tex]\[ \frac{42}{60} \][/tex]
Step 4: Simplify the fraction.
To simplify the fraction [tex]\(\frac{42}{60}\)[/tex], we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 42 and 60 is 6.
Now, we divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{42 \div 6}{60 \div 6} = \frac{7}{10} \][/tex]
So, the simplest form of the fraction is [tex]\(\frac{7}{10}\)[/tex].
Therefore, [tex]\(\frac{3}{4} \times \frac{14}{15} = \frac{7}{10}\)[/tex].
