Ratio, Proportion and Percent

A ratio of $3:5$ has $3+5=8$ parts. To share 40 learners in the ratio $3:5$, one part is $40\div8=5$, so the groups are $15$ and $25$. Simplify ratios like fractions: $18:24=3:4$ (divide both by 6), and keep the order.

If 5 kg of rice costs ₱275, the unit price is $275\div5=₱55$ per kg, so 8 kg costs $8\times55=₱440$. Written as a proportion: $\frac{275}{5}=\frac{x}{8}$. Cross-multiply to solve: $5x=2200$, $x=440$. Proportions never work by adding the same number to top and bottom.

• Percent of a quantity: $25\%$ of 80 is $0.25\times80=20$.
• What percent: $12$ out of $48$ is $\frac{12}{48}=0.25=25\%$.
• Discount: ₱1,200 at $15\%$ off is $0.85\times1200=₱1{,}020$.
• VAT: ₱500 plus $12\%$ VAT is $1.12\times500=₱560$.

Galunggong rose from ₱50 to ₱60 a kilo. The increase is ₱10, and the percent increase is $\frac{10}{50}=20\%$. Dividing by the new price (₱60) is the most common mistake. Successive changes multiply: a $20\%$ discount then $10\%$ off leaves $0.8\times0.9=72\%$ of the price, a total discount of $28\%$, not $30\%$.

A ₱15,000 salary is cut by $10\%$ ($0.9\times15000=13500$) and later raised by $10\%$ ($1.1\times13500=14850$). The worker ends up with ₱14,850, less than before, because the raise was computed on a smaller base.

• Treating $3:5$ as $\frac{3}{5}$ of the whole instead of 3 parts out of 8.
• Adding ₱15 instead of taking $15\%$.
• Reporting the discount (₱180) when the question asks for the price paid.
• Dividing by the new amount in a percent change.
• Adding successive percents instead of multiplying the remaining fractions.