High School

Find the products in simplest form.

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

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

Answer :

Sure! Let's simplify the products of the fractions step-by-step.

### First Fraction Product:
We have:
[tex]\[
\frac{8}{21} \times \frac{5}{16}
\][/tex]

Step 1: Multiply the numerators.
Multiply the top numbers (numerators) together:
[tex]\[
8 \times 5 = 40
\][/tex]

Step 2: Multiply the denominators.
Multiply the bottom numbers (denominators) together:
[tex]\[
21 \times 16 = 336
\][/tex]

Step 3: Simplify the resulting fraction.
We have [tex]\(\frac{40}{336}\)[/tex].
To simplify, find the greatest common divisor (GCD) of 40 and 336, which is 8.

Step 4: Divide both the numerator and the denominator by their GCD.
[tex]\[
\frac{40 \div 8}{336 \div 8} = \frac{5}{42}
\][/tex]

So, the product of the first pair of fractions in simplest form is [tex]\(\frac{5}{42}\)[/tex].

### Second Fraction Product:
We have:
[tex]\[
\frac{12}{25} \times \frac{15}{16}
\][/tex]

Step 1: Multiply the numerators.
Multiply the top numbers (numerators) together:
[tex]\[
12 \times 15 = 180
\][/tex]

Step 2: Multiply the denominators.
Multiply the bottom numbers (denominators) together:
[tex]\[
25 \times 16 = 400
\][/tex]

Step 3: Simplify the resulting fraction.
We have [tex]\(\frac{180}{400}\)[/tex].
To simplify, find the greatest common divisor (GCD) of 180 and 400, which is 20.

Step 4: Divide both the numerator and the denominator by their GCD.
[tex]\[
\frac{180 \div 20}{400 \div 20} = \frac{9}{20}
\][/tex]

So, the product of the second pair of fractions in simplest form is [tex]\(\frac{9}{20}\)[/tex].

### Final Answer:
- [tex]\(\frac{8}{21} \times \frac{5}{16} = \frac{5}{42}\)[/tex]
- [tex]\(\frac{12}{25} \times \frac{15}{16} = \frac{9}{20}\)[/tex]