Solving Linear Equations with Fractions and Decimals

April 12, 2026

Problem

Solve (2/3)x − 1/4 = 5/6. Show how to clear fractions by multiplying both sides by the LCD, then solve the resulting integer equation.

Explanation

When an equation has fractions, the fastest strategy is to clear all fractions by multiplying every term by the least common denominator (LCD).

For $(2/3)x - 1/4 = 5/6$ : LCD of 3, 4, 6 is 12.

Multiply everything by 12: $12 \cdot (2/3)x - 12 \cdot (1/4) = 12 \cdot (5/6)$ $8x - 3 = 10$ $8x = 13$ $x = 13/8 = 1.625$

Check: $(2/3)(13/8) - 1/4 = 26/24 - 6/24 = 20/24 = 5/6$ ✓

Try it in the visualization

Adjust the fraction numerators and denominators. Watch the LCD calculation, then see each term get multiplied and simplified. The fraction bars show the visual multiplication.

Interactive Visualization

Parameters

Numerator of coefficient2.00

Denominator of coefficient3.00

Numerator of constant1.00

Denominator of constant4.00

Right side numerator5.00

Right side denominator6.00

Show solution steps

Show LCD calculation

Show verification

Show fraction bar visualization

Show solution on number line

Show decimal equivalent

Your turn

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