High School

Find the products in simplest form.

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

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

Answer :

To solve the problem, we need to multiply and simplify two fractions.

1. For the first fraction multiplication:

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

- Multiply the numerators: [tex]\(8 \times 5 = 40\)[/tex].
- Multiply the denominators: [tex]\(21 \times 16 = 336\)[/tex].
- You have the product: [tex]\(\frac{40}{336}\)[/tex].

Now, simplify [tex]\(\frac{40}{336}\)[/tex]. We find the greatest common divisor (GCD) of 40 and 336, which is 8.

- Divide the numerator and the denominator by 8:

[tex]\(\frac{40 \div 8}{336 \div 8} = \frac{5}{42}\)[/tex].

So, the simplified form of the product for the first fraction is [tex]\(\frac{5}{42}\)[/tex].

2. For the second fraction multiplication:

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

- Multiply the numerators: [tex]\(12 \times 15 = 180\)[/tex].
- Multiply the denominators: [tex]\(25 \times 16 = 400\)[/tex].
- You have the product: [tex]\(\frac{180}{400}\)[/tex].

Now, simplify [tex]\(\frac{180}{400}\)[/tex]. We find the greatest common divisor (GCD) of 180 and 400, which is 20.

- Divide the numerator and the denominator by 20:

[tex]\(\frac{180 \div 20}{400 \div 20} = \frac{9}{20}\)[/tex].

So, the simplified form of the product for the second fraction is [tex]\(\frac{9}{20}\)[/tex].

In conclusion, the products in their simplest forms are:

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