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Math  /  Algebra

QuestionSubtract. Write your answer in simplified form x5−14\frac{x}{5}-\frac{1}{4}

Studdy Solution

STEP 1

1. The problem involves the subtraction of two fractions with different denominators.
2. To subtract these fractions, we need to find a common denominator.
3. The final expression should be in simplified form.

STEP 2

1. Identify and find the least common denominator (LCD) of the fractions.
2. Rewrite each fraction with the common denominator.
3. Perform the subtraction.
4. Simplify the resulting fraction if necessary.

STEP 3

Identify the least common denominator (LCD) of the fractions x5\frac{x}{5} and 14\frac{1}{4}. The denominators are 5 and 4. The LCD is the least common multiple (LCM) of 5 and 4, which is 20. LCD=20 \text{LCD} = 20

STEP 4

Rewrite each fraction with the common denominator 20. For x5\frac{x}{5}, multiply both the numerator and the denominator by 4: x5=x⋅45⋅4=4x20 \frac{x}{5} = \frac{x \cdot 4}{5 \cdot 4} = \frac{4x}{20} For 14\frac{1}{4}, multiply both the numerator and the denominator by 5: 14=1⋅54⋅5=520 \frac{1}{4} = \frac{1 \cdot 5}{4 \cdot 5} = \frac{5}{20}

STEP 5

Perform the subtraction of the two fractions with the common denominator: 4x20−520 \frac{4x}{20} - \frac{5}{20} Since the denominators are the same, subtract the numerators: 4x−520 \frac{4x - 5}{20}

STEP 6

Simplify the resulting fraction if possible. In this case, the fraction 4x−520\frac{4x - 5}{20} is already in its simplest form.
The simplified form of the expression is: 4x−520 \frac{4x - 5}{20}

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