Fractions \(\tfrac{15}{39}\) and \(\tfrac{45}{117}\) are equivalent fractions.
We will simplify each fraction to its simplest form and compare.
Step 1: Simplify \(\tfrac{15}{39}\)
Both 15 and 39 are divisible by 3.
\(15 \div 3 = 5\)
\(39 \div 3 = 13\)
So, \(\tfrac{15}{39} = \tfrac{5}{13}\).
Step 2: Simplify \(\tfrac{45}{117}\)
Both 45 and 117 are divisible by 3.
\(45 \div 3 = 15\)
\(117 \div 3 = 39\)
So, \(\tfrac{45}{117} = \tfrac{15}{39}\).
We can simplify \(\tfrac{15}{39}\) again by 3.
\(15 \div 3 = 5\)
\(39 \div 3 = 13\)
So, \(\tfrac{45}{117} = \tfrac{5}{13}\).
Step 3: Compare
Both fractions become \(\tfrac{5}{13}\). Therefore, they are equivalent.
Optional quick check (cross-multiplication):
\(15 \times 117 = 1755\)
\(39 \times 45 = 1755\)
The cross-products are equal, so the fractions are equivalent.