How a two-part ratio divides a total and scales a known amount
A two-part ratio compares relative sizes. Reducing the whole-number pair preserves the comparison; the same proportion can allocate a combined total or solve the matching right amount when the left amount is known.
A ratio 2:3 contains five total parts. A total of 100 splits into 40 and 60. If the left side of an equivalent ratio is 10, the matching right side is 10×3/2 = 15. Simplifying the ratio uses the greatest common divisor and does not change either relationship.
The simplified pair, total split and equivalent-pair result appear together. Proportional share blocks show how a two-part ratio divides one whole while the matching-right fact answers a separate scaling question.
How ratio parts, the total and a known left amount are used
The two ratio parts are shared by two separate answers: a split of the total and a matching amount for a known left side. All four boxes must be filled, even when you need only one answer.
- First and second ratio parts
- Two positive whole numbers up to one billion that state the proportion, left then right. Decimal parts such as 1.5:2 are rejected, so multiply both sides by the same number first; 1.5:2 becomes 3:4. Swapping the order swaps every result, because the first part always drives the left share and the left side of the scaling question.
- Total to split
- The combined amount shared between the two sides, zero or more. With 3:5 and a total of 250, the whole holds eight parts, giving 93.75 and 156.25. The box is required even when you want only the matching-amount answer, so enter 0 if there is nothing to split; both shares then show 0.
- Known left amount
- A quantity already fixed on the left side, scaled by right ÷ left to find its partner. For 3:5 and a known left of 12, the matching right is 20. It is independent of the total and also required, so enter 0 when unused; to start from a known right amount, enter the ratio reversed, as 5:3, and type that amount here.
- Two-decimal shares
- Shares, the matching amount and the left percentage are rounded to at most two decimals for display. A 1:2 split of 100 prints 33.33 and 66.67, which happen to add to 100, but two independently rounded figures can occasionally miss the total by 0.01. When every cent must be assigned, give any leftover cent to one side by your own rule.
Steps
- Enter two positive whole-number ratio parts.
- Enter a nonnegative combined total and a known left amount for an equivalent ratio.
- Read the simplified pair, two shares of the total and the right amount matching the known left.
Reading tip: Read the simplified pair first. The total-split result and equivalent-pair result answer different questions; enter the full combined total separately from a known left amount.
Splitting and scaling tasks a two-part ratio handles
Split a budget
Allocate one total between two positive parts in a chosen proportion.
Scale a recipe
Find the second ingredient quantity when the first amount is known.
Check an allocation
Verify that two precise shares add to the entered combined total.
Explain proportions
See each side's percentage of all ratio parts instead of treating a:b as percent values.
How the calculation works
- a / b
- Positive whole-number first and second parts of the comparison.
- g
- Greatest common divisor that reduces both sides without altering the proportion.
- total
- Nonnegative combined amount that is allocated between the two sides.
- a+b
- Number of combined ratio parts forming one whole for allocation.
Shares are calculated before rounding. The ratio itself does not carry units; the entered total determines their units.
What every part means
- a / b
- Positive whole-number first and second parts of the comparison.
- g
- Greatest common divisor that reduces both sides without altering the proportion.
- total
- Nonnegative combined amount that is allocated between the two sides.
- a+b
- Number of combined ratio parts forming one whole for allocation.
Calculate it step by step
Divide both positive whole-number sides by their common integer factor.
The two exact shares add back to the entered total.
Scale both sides by the same factor when the equivalent left side is supplied.
The ratio reduction uses integers. Split amounts use Decimal arithmetic before display rounding, which avoids changing the underlying proportion.
See how Calculation Guide tests examples and handles calculation limits.
See it in practice
- First ratio part
- 2
- Second ratio part
- 3
- Total to split
- 100 units
- Known left amount for equivalent ratio
- 10 units
For 2:3 and total 100, five parts make the whole: first share = 100×2/5 = 40 and second = 60. A known left of 10 matches a right of 10×3/2 = 15.
- Left share40
- Right share60
Interpretation & limitations
How to read your result
A 2:3 split means 40% versus 60%, not 2% versus 3%. With a known left amount of 10, its equivalent right side is 15; this does not mean the combined total is 100.
Where this estimate stops
Both ratio parts must be positive whole numbers. This model handles two-part ratios and a known left side only; it does not solve a three-way ratio or a known right side.
Frequently asked questions
01Why divide by the sum of the parts?
For 2:3, the combined whole contains five parts: 2/5 goes left and 3/5 goes right.
02Does 4:6 mean the same as 2:3?
Yes. Dividing both sides by their common divisor 2 preserves the proportion.
03What if the ratio cannot be reduced?
Its greatest common divisor is 1, so the same pair is displayed.
04Can the total be zero?
Yes. Both allocated amounts are then zero while the ratio remains defined.
05Can shares contain decimals?
Yes. The exact split may be fractional even though the ratio parts are whole numbers.
06Why might rounded shares miss a cent?
Each share is rounded independently for display. The underlying Decimal shares still sum to the entered total.