Solved Value
d = 8
Cross Product
24
Ratio
3:4
Leave one field blank and the calculator will solve for it using cross multiplication.
Solved for d
8
a × d
24
b × c
24
3:4
Cross multiplication: a × d = b × c
3 × d = 4 × 6
3 × d = 24
d = 24 / 3
d = 8
a × d = b × cIn a proportion a/b = c/d, the cross products are always equal. Use this to solve for any one unknown when the other three values are known.
Where:
a= Numerator of the first ratiob= Denominator of the first ratioc= Numerator of the second ratiod= Denominator of the second ratiox = (b × c) / aWhen solving a/b = c/x, rearrange the cross multiplication equation to isolate the unknown variable.
Where:
x= The unknown value to solve fora, b, c= The three known values in the proportionInputs
Result
Cross multiply: 3 × d = 4 × 6, so 3d = 24, d = 24/3 = 8. Verify: 3/4 = 0.75 and 6/8 = 0.75.
Inputs
Result
Cross multiply: 5 × 20 = x × 10, so 100 = 10x, x = 10. Both sides equal 0.5.
Inputs
Result
Cross multiply: 2 × 15 = 3 × x, so 30 = 3x, x = 10. Verify: 2/3 ≈ 0.667 and 10/15 ≈ 0.667.
A proportion is an equation stating two ratios are equal: a/b = c/d. Solve by cross multiplication: multiply diagonally (a × d = b × c) then isolate the unknown variable by dividing both sides.
| Proportion | Cross Multiply | Solution |
|---|---|---|
| 3/4 = 6/d | 3d = 24 | d = 8 |
| 5/x = 10/20 | 100 = 10x | x = 10 |
| x/7 = 12/21 | 21x = 84 | x = 4 |
| 8/12 = 2/x | 8x = 24 | x = 3 |
Proportions are used in cooking (scaling recipes), map reading (scale factors), photography (aspect ratios), construction (mixing ratios), and unit conversion. Any time two quantities maintain a constant ratio, proportions apply.
| Application | Example Proportion | Result |
|---|---|---|
| Recipe scaling | 2/4 = x/8 cups flour | x = 4 cups |
| Map distance | 1/50 = 3.5/x miles | x = 175 miles |
| Photo resize | 16/9 = 1920/x pixels | x = 1080 px |
| Mixing ratio | 1/3 = x/12 bags sand | x = 4 bags |
A ratio compares two quantities (a:b or a/b). A proportion states that two ratios are equal (a/b = c/d). Every proportion contains two ratios, but a single ratio by itself is not a proportion.
| Concept | Example | Key Feature |
|---|---|---|
| Ratio | 3:4 | Compares two quantities |
| Proportion | 3/4 = 6/8 | Two equal ratios |
| Rate | 60 miles/1 hour | Ratio with different units |
| Scale factor | 1:100 | Ratio used for sizing |
Cross multiply both sides: if a/b = c/d, then a × d must equal b × c. If the cross products are equal, the proportion is valid. For example, 3/4 = 6/8: 3 × 8 = 24 and 4 × 6 = 24, so it is correct.
| Proportion | Cross Products | Valid? |
|---|---|---|
| 2/3 = 4/6 | 12 = 12 | Yes |
| 3/5 = 7/10 | 30 ≠ 35 | No |
| 5/8 = 15/24 | 120 = 120 | Yes |
| 7/9 = 21/27 | 189 = 189 | Yes |
Yes, proportions work with any real numbers including negatives and decimals. Cross multiplication applies the same way. For example, 1.5/3 = 2.5/d gives d = 5. With negatives: -2/4 = x/6 gives x = -3.
| Proportion | Cross Multiply | Solution |
|---|---|---|
| 1.5/3 = 2.5/x | 1.5x = 7.5 | x = 5 |
| -2/4 = x/6 | -12 = 4x | x = -3 |
| 0.25/0.5 = x/10 | 2.5 = 0.5x | x = 5 |
A proportion is a mathematical statement that two ratios are equal, written as a/b = c/d.
Cross multiplication is the key technique: multiply diagonally to solve for an unknown value.
Proportions are foundational in scaling recipes, reading maps, resizing images, and many everyday tasks.
Last Updated: Mar 9, 2026
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