$-1.75-\frac{22}{20}=$ $\newline$ Enter the answer as an exact decimal or simplified fraction.

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Algebra 1

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-1.75-\frac{22}{20}=

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Enter the answer as an exact decimal or simplified fraction.

Convert to Improper Fraction: Convert the mixed number to an improper fraction. $\newline$ $-1.75$ can be written as $-1 \frac{75}{100}$ , which simplifies to $-1 \frac{3}{4}$ because $\frac{75}{100}$ reduces to $\frac{3}{4}$ . $\newline$ Now, convert $-1 \frac{3}{4}$ to an improper fraction by multiplying the whole number part by the denominator of the fraction part and then adding the numerator of the fraction part. $\newline$ $-1 \times 4 = -4$ $\newline$ $-4 + 3 = -7$ $\newline$ So, $-1 \frac{3}{4}$ as an improper fraction is $-\frac{7}{4}$ .
Simplify Second Term: Simplify the second term. $\newline$ The fraction $\frac{22}{20}$ can be simplified by dividing both the numerator and the denominator by their greatest common divisor, which is $2$ . $\newline$ $22 \div 2 = 11$ $\newline$ $20 \div 2 = 10$ $\newline$ So, $\frac{22}{20}$ simplifies to $\frac{11}{10}$ .
Perform Subtraction: Perform the subtraction. $\newline$ Now we have $-\frac{7}{4} - \frac{11}{10}$ . To subtract these fractions, we need a common denominator. The least common multiple of $4$ and $10$ is $20$ . $\newline$ We convert $-\frac{7}{4}$ to a fraction with a denominator of $20$ by multiplying both the numerator and the denominator by $5$ . $\newline$ $-7 \times 5 = -35$ $\newline$ $4 \times 5 = 20$ $\newline$ So, $-\frac{7}{4}$ is equivalent to $4$ $0$ . $\newline$ We convert $4$ $1$ to a fraction with a denominator of $20$ by multiplying both the numerator and the denominator by $4$ $3$ . $\newline$ $4$ $4$ $\newline$ $4$ $5$ $\newline$ So, $4$ $1$ is equivalent to $4$ $7$ . $\newline$ Now we can subtract: $4$ $8$ .
Complete Subtraction: Complete the subtraction. $\newline$ $-\frac{35}{20} - \frac{22}{20} = \frac{(-35 - 22)}{20}$ $\newline$ $= -\frac{57}{20}$ $\newline$ This is the final answer as a simplified fraction.