Solve the Proportion 6/x = 18/24 (Answer: x = 8)

Exact Answer

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Problem: Solve the Proportion 6/x = 18/24
Formula / Expression: 6/x = 18/24 → 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:
6 / x = 18 / 24
Working: 6/x = 18/24

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: (6) × (24) = (x) × (18).
Working: (6) × (24) = (x) × (18)

Step 3: Isolate the Unknown Variable x
Combine known numbers to obtain a simple one-step linear equation:
18 × x = 144.
Working: 18x = 144

Step 4: Divide to Solve for x
Divide both sides of the equation by 18:
x = 144 ÷ 18 = 8.
Working: x = 144 / 18 = 8

Step 5: Verify Proportion and Scale Multiplier
Check your work: Substituting x = 8 gives both fractions a ratio of 3x. Both fractions evaluate to the exact same value, confirming the solution is 100% correct.
Working: Check: (6 ÷ 8) = (18 ÷ 24)

Key Values:
- Solved Value (x): x = 8
- Equation: 6/x = 18/24
- Cross Product: 144
- Scale Multiplier: 3x

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Solved with FractionsCalc:
https://fractionscalc.com/solve-proportion-6-x-equals-18-24/
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6x = 1824 → x = 8

Solved Value (x)

x = 8

Equation

6/x = 18/24

Cross Product

144

Scale Multiplier

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Step-by-Step Solution: 6/x = 18/24 → x = 8

Step 1

Set Up the Proportion Equation

Write the proportion equating the two ratios:
6 / x = 18 / 24

6/x = 18/24

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: (6) × (24) = (x) × (18).

(6) × (24) = (x) × (18)

Step 3

Isolate the Unknown Variable x

Combine known numbers to obtain a simple one-step linear equation:
18 × x = 144.

18x = 144

Step 4

Divide to Solve for x

Divide both sides of the equation by 18:
x = 144 ÷ 18 = 8.

x = 144 / 18 = 8

Step 5

Verify Proportion and Scale Multiplier

Check your work: Substituting x = 8 gives both fractions a ratio of 3x. Both fractions evaluate to the exact same value, confirming the solution is 100% correct.

Check: (6 ÷ 8) = (18 ÷ 24)

Visual Representation

The diagram below illustrates Solve proportion 6/x = 18/24 visually:

Summary & Alternative Representations

Property / Format	Value
Solved Value (x)	`x = 8`
Equation	`6/x = 18/24`
Cross Product	`144`
Scale Multiplier	`3x`

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Frequently Asked Questions

How do you solve for x in the proportion 6/x = 18/24?

Cross-multiply diagonally: multiply the known diagonal pair (6 × 24 = 144) and then divide by the coefficient paired with x (18), 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.