Answer :
To solve the problem of finding the products in simplest form, let's go through each multiplication step by step:
1. Calculate [tex]\(\frac{8}{21} \cdot \frac{5}{16}\)[/tex]:
- First, multiply the numerators together: [tex]\(8 \times 5 = 40\)[/tex].
- Then, multiply the denominators together: [tex]\(21 \times 16 = 336\)[/tex].
So, we have [tex]\(\frac{40}{336}\)[/tex].
To simplify [tex]\(\frac{40}{336}\)[/tex], 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]
2. Calculate [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].
So, we have [tex]\(\frac{180}{400}\)[/tex].
To simplify [tex]\(\frac{180}{400}\)[/tex], find the 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]
In conclusion, the simplified form of [tex]\(\frac{8}{21} \cdot \frac{5}{16}\)[/tex] is [tex]\(\frac{5}{42}\)[/tex], and the simplified form of [tex]\(\frac{12}{25} \cdot \frac{15}{16}\)[/tex] is [tex]\(\frac{9}{20}\)[/tex].
1. Calculate [tex]\(\frac{8}{21} \cdot \frac{5}{16}\)[/tex]:
- First, multiply the numerators together: [tex]\(8 \times 5 = 40\)[/tex].
- Then, multiply the denominators together: [tex]\(21 \times 16 = 336\)[/tex].
So, we have [tex]\(\frac{40}{336}\)[/tex].
To simplify [tex]\(\frac{40}{336}\)[/tex], 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]
2. Calculate [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].
So, we have [tex]\(\frac{180}{400}\)[/tex].
To simplify [tex]\(\frac{180}{400}\)[/tex], find the 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]
In conclusion, the simplified form of [tex]\(\frac{8}{21} \cdot \frac{5}{16}\)[/tex] is [tex]\(\frac{5}{42}\)[/tex], and the simplified form of [tex]\(\frac{12}{25} \cdot \frac{15}{16}\)[/tex] is [tex]\(\frac{9}{20}\)[/tex].