Answer :
Let's solve each multiplication of fractions step-by-step.
1. Multiply [tex]\(\frac{8}{21} \cdot \frac{5}{16}\)[/tex]:
- Step 1: Multiply the numerators: [tex]\(8 \times 5 = 40\)[/tex].
- Step 2: Multiply the denominators: [tex]\(21 \times 16 = 336\)[/tex].
- Step 3: Now, the product is [tex]\(\frac{40}{336}\)[/tex].
- Step 4: Simplify the fraction. Find the greatest common divisor (GCD) of 40 and 336, which is 8.
- Step 5: Divide the numerator and denominator by their GCD:
- Numerator: [tex]\(40 \div 8 = 5\)[/tex]
- Denominator: [tex]\(336 \div 8 = 42\)[/tex]
- Simplified product: [tex]\(\frac{5}{42}\)[/tex]
2. Multiply [tex]\(\frac{12}{25} \cdot \frac{15}{16}\)[/tex]:
- Step 1: Multiply the numerators: [tex]\(12 \times 15 = 180\)[/tex].
- Step 2: Multiply the denominators: [tex]\(25 \times 16 = 400\)[/tex].
- Step 3: Now, the product is [tex]\(\frac{180}{400}\)[/tex].
- Step 4: Simplify the fraction. Find the greatest common divisor (GCD) of 180 and 400, which is 20.
- Step 5: Divide the numerator and denominator by their GCD:
- Numerator: [tex]\(180 \div 20 = 9\)[/tex]
- Denominator: [tex]\(400 \div 20 = 20\)[/tex]
- Simplified product: [tex]\(\frac{9}{20}\)[/tex]
So, 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]
1. Multiply [tex]\(\frac{8}{21} \cdot \frac{5}{16}\)[/tex]:
- Step 1: Multiply the numerators: [tex]\(8 \times 5 = 40\)[/tex].
- Step 2: Multiply the denominators: [tex]\(21 \times 16 = 336\)[/tex].
- Step 3: Now, the product is [tex]\(\frac{40}{336}\)[/tex].
- Step 4: Simplify the fraction. Find the greatest common divisor (GCD) of 40 and 336, which is 8.
- Step 5: Divide the numerator and denominator by their GCD:
- Numerator: [tex]\(40 \div 8 = 5\)[/tex]
- Denominator: [tex]\(336 \div 8 = 42\)[/tex]
- Simplified product: [tex]\(\frac{5}{42}\)[/tex]
2. Multiply [tex]\(\frac{12}{25} \cdot \frac{15}{16}\)[/tex]:
- Step 1: Multiply the numerators: [tex]\(12 \times 15 = 180\)[/tex].
- Step 2: Multiply the denominators: [tex]\(25 \times 16 = 400\)[/tex].
- Step 3: Now, the product is [tex]\(\frac{180}{400}\)[/tex].
- Step 4: Simplify the fraction. Find the greatest common divisor (GCD) of 180 and 400, which is 20.
- Step 5: Divide the numerator and denominator by their GCD:
- Numerator: [tex]\(180 \div 20 = 9\)[/tex]
- Denominator: [tex]\(400 \div 20 = 20\)[/tex]
- Simplified product: [tex]\(\frac{9}{20}\)[/tex]
So, 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]