Simplify ratios, solve proportions, scale ratios, and compare equivalent ratios. Calculate ratio to fraction, decimal, and percentage with step-by-step solutions.
Simplified Ratio
2 : 3
Original
12 : 18
Simplified
2 : 3
Decimal
0.6667
Percentage
66.6667%
Fraction
2/3
Parts Total
5
Golden Ratio
1:1.618
Design, Art
Screen 16:9
16:9
HD Video
Screen 4:3
4:3
Classic TV
Photo 3:2
3:2
35mm Film
Square
1:1
1/3 Rule
1:2
Design
Cement:Sand
1:3
Mortar
Coffee:Water
1:15
Pour Over
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Simplified Ratio
2 : 3
A ratio compares two or more quantities. To simplify a ratio, divide all parts by their GCF. For example, 12:8 simplifies to 3:2 (divide by 4). To solve a proportion (a:b = c:x), use cross-multiplication: a*x = b*c, so x = (b*c)/a. Equivalent ratios have the same relationship (2:3 = 4:6 = 6:9).
A ratio is a comparison between two or more numbers that shows their relative sizes. Written as a:b or a/b, ratios express the relationship between quantities without specifying actual values. Ratios are used in cooking, construction, finance, map scales, aspect ratios, and anywhere relative proportions matter.
A ratio compares two or more quantities. To simplify a ratio, divide all parts by their GCF. For example, 12:8 simplifies to 3:2 (divide by 4). To solve a proportion (a:b = c:x), use cross-multiplication: a*x = b*c, so x = (b*c)/a. Equivalent ratios have the same relationship (2:3 = 4:6 = 6:9).
A ratio compares two or more quantities. It shows the relative size of two values. For example, a ratio of 2:3 means for every 2 units of the first quantity, there are 3 units of the second. Ratios can be written as 2:3, 2/3, or "2 to 3".
To simplify a ratio, divide both numbers by their greatest common factor (GCF). For example, 12:18 has a GCF of 6, so dividing both by 6 gives 2:3. The simplified ratio has the same relationship but uses smaller numbers.
A proportion is an equation stating that two ratios are equal. For example, 1:2 = 3:6 is a proportion. Cross multiplication can be used to verify: if a:b = c:d, then a×d = b×c. Proportions are used to solve for unknown values.
Use cross multiplication. For a:b = c:x, cross multiply to get a×x = b×c, then solve for x = (b×c)/a. For a:b = x:d, you get b×x = a×d, so x = (a×d)/b.
Equivalent ratios have the same value when simplified or converted to decimals. Examples: 1:2, 2:4, 3:6, and 50:100 are all equivalent (they all equal 0.5). Multiply or divide both parts by the same number to find equivalent ratios.
Ratios appear everywhere: recipes (2:1 flour to sugar), maps (1:50000 scale), finance (P/E ratio), mixing (3:1 paint dilution), aspect ratios (16:9 screens), and probability (1:6 odds). They're essential for scaling, comparing, and proportioning.
Last updated: 2025-01-15
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Simplified Ratio
2 : 3