Evaluate $-\frac{2}{5}-x+\left(-\frac{9}{10}\right)$ where $x=\frac{4}{5}$ .

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Grade 6

Inequalities with decimal multiplication

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Q. Evaluate

-\frac{2}{5}-x+\left(-\frac{9}{10}\right)

where

x=\frac{4}{5}

Substitute x value: Substitute the value of $x$ into the expression. $\newline$ We are given $x = \frac{4}{5}$ , so we will replace $x$ in the expression with $\frac{4}{5}$ . $\newline$ Expression: $-\frac{2}{5} - \frac{4}{5} + \left(-\frac{9}{10}\right)$
Combine fractions: Combine the fractions with a common denominator. $\newline$ The fractions $-\frac{2}{5}$ and $-\frac{4}{5}$ already have a common denominator of $5$ , so we can combine them directly. The fraction $-\frac{9}{10}$ has a different denominator, so we will need to find a common denominator for all fractions. $\newline$ Common denominator for $5$ and $10$ is $10$ .
Convert to common denominator: Convert the fractions to have the common denominator. $\newline$ $-\frac{2}{5}$ becomes $-\frac{4}{10}$ when we multiply both the numerator and the denominator by $2$ . $\newline$ $-\frac{4}{5}$ becomes $-\frac{8}{10}$ when we multiply both the numerator and the denominator by $2$ . $\newline$ Now we have: $-\frac{4}{10}$ - $\frac{8}{10}$ + $-\frac{9}{10}$
Add fractions: Add the fractions together. $\newline$ Now that all fractions have the same denominator, we can add their numerators. $\newline$ $-\frac{4}{10} - \frac{8}{10} - \frac{9}{10} = -\frac{4 + 8 + 9}{10}$ $\newline$ Calculate the sum of the numerators: $4 + 8 + 9 = 21$ $\newline$ So, we have: $-\frac{21}{10}$
Simplify expression: Simplify the expression. $\newline$ The negative sign in front of the fraction means we are taking the negative of the entire fraction. $\newline$ Therefore, the simplified expression is: $-\frac{21}{10}$