Choose whether to simplify, compare, scale, or find a missing term. Enter each part in its own field to see the resulting ratio and why it is equivalent, or why it is not.
Result
The ratio simplifies to 3:4
18:24=3:4
Conditions
The first part is 18 and the second part is 24; their order is preserved.
The second part is nonzero, so the ratio can also be compared as a fraction.
Steps
Find a common factor The greatest common divisor of 18 and 24 is 6.gcd(18,24)=6
Divide both parts Apply the same nonzero divisor to the first and second part.18÷6=3,24÷6=4
Keep the original order The first-to-second comparison remains three to four.18:24=3:4
✓
Independent check
Cross-multiplication gives 18×4=72 and 24×3=72, independently checking that the two defined ratios are equivalent.
Scope
What this ratio calculation covers
A ratio a:b compares two quantities in a stated order. To simplify, divide both parts by the same nonzero factor. Two defined ratios a:b and c:d are equivalent when ad=bc. Scaling both parts by a nonzero factor preserves the comparison.
Simplify without reversing the parts
Reduce integer or rational entries by one common nonzero factor. The displayed order stays first part to second part; it is not converted to a mixed number.
Examples: 18:24 becomes 3:4, 1/2:3/4 becomes 2:3
Compare equivalent ratios
Test whether two defined ratios make the same comparison by checking cross-products, then name the result instead of relying on rounded decimals.
Examples: 2:3 and 8:12 are equivalent, 2:3 and 3:5 are not
Scale and build an equivalent-ratio row
Multiply both parts by the same nonzero rational factor. Repeat with another factor to extend an equivalent-ratio table.
Examples: 3:5, 6:10, 12:20, 4:7 scaled by 3
Solve one missing proportional part
In a:b=c:d, leave exactly one part unknown. Solve by cross-products only when both denominator positions are valid.
Examples: 3:4=x:20, 5:8=15:x
How to use it
Enter enough information for one clear task
1
Choose what you need
Simplify uses one pair. Compare uses two complete pairs. Scale uses one pair and a factor. Find a missing part uses a proportion with exactly one empty field.
2
Enter values in separate fields
The left field is the first part of a ratio. The right field is the second. Keep units consistent when the pair represents quantities of the same kind.
3
Read the equivalence check
For a proportion, compare cross-products; for scaling, check that both parts changed by the same factor. A missing or zero denominator is not silently ignored.
Worked inputs
Examples to try
Use these examples to recognize the method, compare equivalent forms, and check your own work.
Simplify whole-number parts
Divide both numbers by their greatest common divisor, 6.
18:24
Expected result
3:4
Clear fractional parts exactly
Multiply both parts by 4, then reduce 2:3 if necessary.
21:43
Expected result
2:3
Check whether two ratios match
Compare the cross-products 2×12 and 3×8.
2:3and8:12
Expected result
2⋅12=3⋅8=24
Make a short ratio table
Multiply both entries by each nonzero scale factor.
3:5scaled by1,2,4
Expected result
3:5=6:10=12:20
Find the first missing part
The second part was multiplied by 5, so multiply the first part by 5 too.
3:4=x:20
Expected result
x=15
Find the second missing part
Cross-multiply: 5x=8×15.
5:8=15:x
Expected result
x=24
Keep a zero first part
A zero numerator is allowed when the second part is nonzero.
0:9
Expected result
0:1
Complete example
Scale a recipe ratio to a new batch
The original and new pairs must use the same order and units. Let f be the flour amount in the larger batch.
Flour : oats=3:5,oats=20 cups
1
Set matching parts beside each other
Flour stays first, oats stays second; only the new flour part is missing.
3:5=f:20
2
Find the scale factor
The oats amount changes from 5 cups to 20 cups, a factor of 4.
20÷5=4
3
Apply it to the other part
The flour amount must be multiplied by the same factor.
f=3⋅4=12
Flour=12 cups
Verification: The original fraction is 3/5 and the new fraction is 12/20; cross-products are both 60.
Avoidable errors
Common mistakes and how to fix them
Reversing one ratio
Problem: Compare flour:oats with oats:flour as though they were in the same order.
Why it matters: Reversing only one pair changes the comparison, so the cross-products no longer represent the intended proportion.
Better approach: Label the quantities once and keep the order consistent in every pair.
Changing only one part
Problem: Turn 3:5 into 3:20 by multiplying only the second part.
Why it matters: The ratio changes because the parts no longer have the same common multiplier.
Better approach: Multiply or divide both parts by the same nonzero value.
Dividing by a zero second part
Problem: Treat 4:0 as the fraction 4/0 or solve a proportion with a zero denominator.
Why it matters: Division by zero is undefined; ordinary fraction-based proportion rules do not apply.
Better approach: Correct the second part or express a different mathematical comparison with explicit assumptions.
Rounding too early
Problem: Round 1/3 to 0.33 before testing equivalence.
Why it matters: A rounded decimal can make equal ratios look unequal, or unequal ratios look close enough.
Better approach: Keep exact rational values through the cross-product check.
Trust the result for the right reasons
Checks, assumptions, and limits
How results are checked
For defined ratios, cross-products are compared using exact rational arithmetic.
Simplification is checked by reconstructing the original comparison from the reduced pair.
A missing proportional term is substituted back into the original equality.
Scaling confirms that the same nonzero factor was applied to both parts.
When to stop and revise the input
Inputs are finite integers, finite decimals, or simple fractions; decimals are interpreted as exact written rational values.
A second part of zero cannot be used as the denominator of an ordinary ratio or proportion.
A proportion with more than one missing part does not determine a unique answer.
Negative values can be compared algebraically, but a real-world part-to-part interpretation may require nonnegative quantities and compatible units.
Common questions
Calculate ratios without guessing the next step FAQ
How do I simplify a ratio?
Divide both parts by a common nonzero factor. For 18:24, dividing both by 6 gives 3:4. Keep the same first-to-second order.
How can I tell whether two ratios are equivalent?
For defined ratios a:b and c:d with nonzero second parts, compare a×d with b×c. Equality means the fractions a/b and c/d have the same value.
What does a ratio table show?
Each row is made by multiplying both parts of a starting ratio by one nonzero factor. Starting from 3:5, factors 1, 2, and 4 give 3:5, 6:10, and 12:20.
Can a ratio have a zero part?
A zero first part and nonzero second part is valid, such as 0:9=0:1. A zero second part cannot be treated as a fraction denominator; 0:0 has no defined proportional comparison.
Is a ratio the same as a rate?
Both compare quantities through division, but a rate usually compares quantities with different units, such as miles per hour. Include units and their order when interpreting a rate.
Sources and curriculum alignment
This page follows standard introductory mathematics notation and learning sequences. Use these references to continue with a complete course treatment.
