Comprehensive Calculator Guide
A proportion sets two ratios equal: a/b = c/x. Cross-multiply to find the unknown: x = b × c ÷ a. If a recipe needs 3 eggs for every 2 cups of flour, 8 cups need 3 × 8 ÷ 2 = 12 eggs. Enter the three known values and the unknown appears instantly.
Cross-multiplication
In a/b = c/x the product of the outer terms equals the product of the inner ones: a × x = b × c, so x = b × c ÷ a. Keep matching quantities in matching positions: if a and c are cups of flour, b and x must be eggs. None of the three inputs can be zero.
This is a direct proportion: both quantities grow together. In an inverse proportion one falls as the other rises, and the product stays fixed: if 4 workers take 12 days, 6 workers take 4 × 12 ÷ 6 = 8 days. Work those by hand with x = a × b ÷ c.
Everyday uses
Scaling recipes, reading map scales, estimating fuel for a longer trip, and percentages, which are proportions out of 100: 15% of 200 solves 15/100 = x/200, so x = 30.
How to Use
- 01Write the problem as a/b = c/x and enter a, b and c.
- 02Put the two same-kind quantities in a and c, the matching known value in b.
- 03Read x; for inverse proportions compute a × b ÷ c by hand.
Formula Used
a/b = c/x → x = b × c ÷ aPractical Examples
Example 1: scaling a recipe
2 cups of flour to 3 eggs; for 8 cups: x = 3 × 8 ÷ 2 = 12 eggs.
Example 2: map scale
1 cm = 50 km; 7.5 cm on the map is 375 km in a straight line.
Example 3: fuel for a trip
40 litres for 500 km; for 1,200 km: 40 × 1,200 ÷ 500 = 96 litres.
Important Tips
- Write units next to each value to catch swapped positions.
- Sanity-check: in a direct proportion, a bigger input must give a bigger answer.
Common Mistakes to Avoid
- Swapping matching quantities between positions.
- Solving an inverse problem, like workers and days, as a direct one.
Frequently Asked Questions
- How do I solve a proportion?
- Cross-multiply and divide: in 2/3 = 8/x, 2x = 24, so x = 12.
- What is the difference between direct and inverse proportion?
- In direct proportion the ratio stays fixed; in inverse proportion the product stays fixed.
- Can I use it for percentages?
- Yes: 15% of 200 is 15/100 = x/200, so x = 30.
- Why are zeros rejected?
- A ratio with a zero denominator is undefined, and a zero term does not determine a single answer.