Solve the Proportion 2/3 = x/12 (Answer: x = 8)

Exact Answer

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Problem: Solve the Proportion 2/3 = x/12
Formula / Expression: 2/3 = x/12 → x = 8
Final Answer: x = 8
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Step-by-Step Solution:

Step 1: Set Up the Proportion Equation
Write the proportion equating the two ratios:
2 / 3 = x / 12
Working: 2/3 = x/12

Step 2: Apply the Cross-Multiplication Property
In any true proportion A/B = C/D, the cross products are always equal: A × D = B × C.
Multiplying diagonally: (2) × (12) = (3) × (x).
Working: (2) × (12) = (3) × (x)

Step 3: Isolate the Unknown Variable x
Combine known numbers to obtain a simple one-step linear equation:
3 × x = 24.
Working: 3x = 24

Step 4: Divide to Solve for x
Divide both sides of the equation by 3:
x = 24 ÷ 3 = 8.
Working: x = 24 / 3 = 8

Step 5: Verify Proportion and Scale Multiplier
Check your work: Substituting x = 8 gives both fractions a ratio of 4x. Both fractions evaluate to the exact same value, confirming the solution is 100% correct.
Working: Check: (2 ÷ 3) = (8 ÷ 12)

Key Values:
- Solved Value (x): x = 8
- Equation: 2/3 = x/12
- Cross Product: 24
- Scale Multiplier: 4x

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Solved with FractionsCalc:
https://fractionscalc.com/solve-proportion-2-3-equals-x-12/
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23 = x12 → x = 8

Solved Value (x)

x = 8

Equation

2/3 = x/12

Cross Product

Scale Multiplier

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Step-by-Step Solution: 2/3 = x/12 → x = 8

Step 1

Set Up the Proportion Equation

Write the proportion equating the two ratios:
2 / 3 = x / 12

2/3 = x/12

Step 2

Apply the Cross-Multiplication Property

In any true proportion A/B = C/D, the cross products are always equal: A × D = B × C.
Multiplying diagonally: (2) × (12) = (3) × (x).

(2) × (12) = (3) × (x)

Step 3

Isolate the Unknown Variable x

Combine known numbers to obtain a simple one-step linear equation:
3 × x = 24.

3x = 24

Step 4

Divide to Solve for x

Divide both sides of the equation by 3:
x = 24 ÷ 3 = 8.

x = 24 / 3 = 8

Step 5

Verify Proportion and Scale Multiplier

Check your work: Substituting x = 8 gives both fractions a ratio of 4x. Both fractions evaluate to the exact same value, confirming the solution is 100% correct.

Check: (2 ÷ 3) = (8 ÷ 12)

Visual Representation

The diagram below illustrates Solve proportion 2/3 = x/12 visually:

Summary & Alternative Representations

Property / Format	Value
Solved Value (x)	`x = 8`
Equation	`2/3 = x/12`
Cross Product	`24`
Scale Multiplier	`4x`

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Frequently Asked Questions

How do you solve for x in the proportion 2/3 = x/12?

Cross-multiply diagonally: multiply the known diagonal pair (2 × 12 = 24) and then divide by the coefficient paired with x (3), resulting in x = 8.

What is the cross multiplication rule for proportions?

For any proportion A/B = C/D, the product of the extremes (A × D) is always equal to the product of the means (B × C).

Can a proportion have decimal answers?

Yes! If the cross-product is not evenly divisible by the coefficient, the result can be written as an exact decimal or as a simplified fraction / mixed number.