College

Find the products in simplest form.

1. [tex]\frac{8}{21} \cdot \frac{5}{16} =[/tex]

2. [tex]\frac{12}{25} \cdot \frac{15}{16} =[/tex]

Answer :

Let's solve each of the given fraction multiplication problems step-by-step to find their products in simplest form.

1. For the first problem:
[tex]\[
\frac{8}{21} \times \frac{5}{16}
\][/tex]

To multiply these fractions, multiply the numerators together and the denominators together:

- Multiply the numerators: [tex]\(8 \times 5 = 40\)[/tex]
- Multiply the denominators: [tex]\(21 \times 16 = 336\)[/tex]

So, the product is:
[tex]\[
\frac{40}{336}
\][/tex]

Next, simplify the fraction by finding the greatest common divisor (GCD) of 40 and 336, which is 8.

Divide both the numerator and the denominator by 8:
[tex]\[
\frac{40 \div 8}{336 \div 8} = \frac{5}{42}
\][/tex]

So, the simplest form of the product [tex]\( \frac{8}{21} \times \frac{5}{16} \)[/tex] is:
[tex]\[
\frac{5}{42}
\][/tex]

2. For the second problem:
[tex]\[
\frac{12}{25} \times \frac{15}{16}
\][/tex]

Similarly, multiply the numerators and the denominators:

- Multiply the numerators: [tex]\(12 \times 15 = 180\)[/tex]
- Multiply the denominators: [tex]\(25 \times 16 = 400\)[/tex]

So, the product is:
[tex]\[
\frac{180}{400}
\][/tex]

Simplify the fraction by finding the GCD of 180 and 400, which is 20.

Divide both the numerator and the denominator by 20:
[tex]\[
\frac{180 \div 20}{400 \div 20} = \frac{9}{20}
\][/tex]

Thus, the simplest form of the product [tex]\( \frac{12}{25} \times \frac{15}{16} \)[/tex] is:
[tex]\[
\frac{9}{20}
\][/tex]

In conclusion, the products in simplest form are:

1. [tex]\( \frac{8}{21} \cdot \frac{5}{16} = \frac{5}{42} \)[/tex]
2. [tex]\( \frac{12}{25} \cdot \frac{15}{16} = \frac{9}{20} \)[/tex]