Multiply and simplify

Explanation

• Multiply the numerators.  Multiply the denominators
  • \(\frac58 \cdot \frac45 = \frac{5 \cdot 4}{8 \cdot 5}\)
• To prepare to simplify, write 4 and 8 in prime-factored form
  • \(\frac{5 \cdot 2 \cdot 2}{2 \cdot 2 \cdot 2 \cdot 5}\)
• To simplify, remove the common factors of 2 and 5 from the numerator and denominator
  • \( \require{cancel} \frac{\cancel{5}^1 \cdot \cancel{2}^1 \cdot \cancel{2}^1}{\cancel{2}_1 \cdot \cancel{2}_1 \cdot 2 \cdot \cancel{5}_1}\)
• Multiply the remaining factors in the numerator: 1 • 1 • 1 = 1.  Multiply the reamining factors in the denominator: 1 • 1 • 2 • 1 = 2
  • \(\frac12\)