Simplify. Express your answer as a single fraction in simplest form. $\newline$ $\frac{5}{4} - 5d$

Full solution

Q. Simplify. Express your answer as a single fraction in simplest form.

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\frac{5}{4} - 5d

Identify Terms: Identify the terms in the expression that need to be combined into a single fraction. The expression given is $\frac{5}{4} - 5d$ . We need to combine these terms into a single fraction.
Find Common Denominator: Find a common denominator for the terms. $\newline$ Since $\frac{5}{4}$ is already a fraction and $5d$ is not, we can write $5d$ as a fraction with a denominator of $1$ to find a common denominator. The common denominator between $4$ and $1$ is $4$ .
Rewrite with Common Denominator: Rewrite $5d$ with the common denominator. $\newline$ We can express $5d$ as $(5d \times 4)/4$ to have the same denominator as $\frac{5}{4}$ .
Combine Fractions: Combine the fractions. $\newline$ Now we have $\frac{5}{4} - \left(\frac{5d \times 4}{4}\right)$ . Since the denominators are the same, we can combine the numerators. $\newline$ $\left(\frac{5 - (5d \times 4)}{4}\right)$
Simplify Numerator: Simplify the numerator. $\newline$ Multiply $5d$ by $4$ in the numerator to get $20d$ . $\newline$ $\frac{5 - 20d}{4}$
Check for Simplification: Check for any further simplification. $\newline$ The fraction $(5 - 20d)/4$ is already in simplest form because the numerator and denominator do not have any common factors other than $1$ .