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 :

Sure! Let's find the products of the given fractions in their simplest form step by step.

1. First Pair of Fractions:

[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: Write the product as a fraction:

[tex]\(\frac{40}{336}\)[/tex]

Step 4: Simplify the fraction by finding the greatest common divisor (GCD) and dividing both the numerator and denominator by it. The GCD of 40 and 336 is 8.

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

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

2. Second Pair of Fractions:

[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: Write the product as a fraction:

[tex]\(\frac{180}{400}\)[/tex]

Step 4: Simplify the fraction by finding the greatest common divisor (GCD) and dividing both the numerator and denominator by it. The GCD of 180 and 400 is 20.

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

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

In conclusion, the products in simplest form 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]