To find the product of the fractions [tex]\(\frac{5}{4}\)[/tex] and [tex]\(\frac{1}{4}\)[/tex], we will follow these detailed steps:
1. Multiply the Numerators:
- The numerators (the top parts of the fractions) are 5 and 1.
- Multiply these two numbers: [tex]\(5 \times 1 = 5\)[/tex].
2. Multiply the Denominators:
- The denominators (the bottom parts of the fractions) are both 4.
- Multiply these two numbers: [tex]\(4 \times 4 = 16\)[/tex].
3. Form the New Fraction:
- The new fraction will have the product of the numerators as its numerator, and the product of the denominators as its denominator.
- This new fraction is [tex]\(\frac{5}{16}\)[/tex].
4. Simplify If Necessary:
- In this case, [tex]\(\frac{5}{16}\)[/tex] is already in its simplest form since 5 and 16 have no common factors other than 1.
5. Convert to a Decimal (Optional):
- To express the fraction [tex]\(\frac{5}{16}\)[/tex] as a decimal, perform the division [tex]\(5 \div 16 = 0.3125\)[/tex].
So, the product of [tex]\(\frac{5}{4} \times \frac{1}{4}\)[/tex] is [tex]\(\frac{5}{16}\)[/tex] or 0.3125 when expressed as a decimal.
