Math / Numbers & Operations

QuestionSimplify the expression: $-\frac{1}{2}+\frac{2}{5}+\left(-\frac{3}{10}\right)-\frac{3}{4}$

Studdy Solution

STEP 1

1. We are simplifying a numerical expression involving fractions.
2. The expression includes both positive and negative fractions.
3. We need to find a common denominator to combine the fractions.

STEP 2

1. Identify the least common denominator (LCD).
2. Rewrite each fraction with the LCD.
3. Combine the fractions.
4. Simplify the resulting expression.

STEP 3

Identify the least common denominator (LCD) for the fractions $-\frac{1}{2}$ , $\frac{2}{5}$ , $-\frac{3}{10}$ , and $-\frac{3}{4}$ .
- The denominators are $2$ , $5$ , $10$ , and $4$ . - The least common multiple of $2$ , $5$ , $10$ , and $4$ is $20$ .

STEP 4

Rewrite each fraction with the LCD of $20$ .
- $-\frac{1}{2} = -\frac{10}{20}$ - $\frac{2}{5} = \frac{8}{20}$ - $-\frac{3}{10} = -\frac{6}{20}$ - $-\frac{3}{4} = -\frac{15}{20}$

STEP 5

Combine the fractions using the common denominator.
$-\frac{10}{20} + \frac{8}{20} - \frac{6}{20} - \frac{15}{20} = \frac{-10 + 8 - 6 - 15}{20}$

STEP 6

Calculate the numerator:
$-10 + 8 - 6 - 15 = -23$
So the expression becomes:
$\frac{-23}{20}$

STEP 7

Simplify the resulting expression.
The fraction $\frac{-23}{20}$ is already in its simplest form.
The simplified expression is:
$\boxed{-\frac{23}{20}}$

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QuestionSimplify the expression: $-\frac{1}{2}+\frac{2}{5}+\left(-\frac{3}{10}\right)-\frac{3}{4}$

Studdy Solution

STEP 1

1. We are simplifying a numerical expression involving fractions.
2. The expression includes both positive and negative fractions.
3. We need to find a common denominator to combine the fractions.

STEP 2

1. Identify the least common denominator (LCD).
2. Rewrite each fraction with the LCD.
3. Combine the fractions.
4. Simplify the resulting expression.

STEP 3

Identify the least common denominator (LCD) for the fractions $-\frac{1}{2}$ , $\frac{2}{5}$ , $-\frac{3}{10}$ , and $-\frac{3}{4}$ .
- The denominators are $2$ , $5$ , $10$ , and $4$ . - The least common multiple of $2$ , $5$ , $10$ , and $4$ is $20$ .

STEP 4

Rewrite each fraction with the LCD of $20$ .
- $-\frac{1}{2} = -\frac{10}{20}$ - $\frac{2}{5} = \frac{8}{20}$ - $-\frac{3}{10} = -\frac{6}{20}$ - $-\frac{3}{4} = -\frac{15}{20}$

STEP 5

Combine the fractions using the common denominator.
$-\frac{10}{20} + \frac{8}{20} - \frac{6}{20} - \frac{15}{20} = \frac{-10 + 8 - 6 - 15}{20}$

STEP 6

Calculate the numerator:
$-10 + 8 - 6 - 15 = -23$
So the expression becomes:
$\frac{-23}{20}$

STEP 7

Simplify the resulting expression.
The fraction $\frac{-23}{20}$ is already in its simplest form.
The simplified expression is:
$\boxed{-\frac{23}{20}}$

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QuestionSimplify the expression: −12+25+(−310)−34-\frac{1}{2}+\frac{2}{5}+\left(-\frac{3}{10}\right)-\frac{3}{4}−21​+52​+(−103​)−43​

Studdy Solution

STEP 1

1. We are simplifying a numerical expression involving fractions.2. The expression includes both positive and negative fractions.3. We need to find a common denominator to combine the fractions.

STEP 2

1. Identify the least common denominator (LCD).2. Rewrite each fraction with the LCD.3. Combine the fractions.4. Simplify the resulting expression.

STEP 3

Identify the least common denominator (LCD) for the fractions −12-\frac{1}{2}−21​, 25\frac{2}{5}52​, −310-\frac{3}{10}−103​, and −34-\frac{3}{4}−43​.- The denominators are 222, 555, 101010, and 444. - The least common multiple of 222, 555, 101010, and 444 is 202020.

STEP 4

Rewrite each fraction with the LCD of 202020.- −12=−1020-\frac{1}{2} = -\frac{10}{20}−21​=−2010​ - 25=820\frac{2}{5} = \frac{8}{20}52​=208​ - −310=−620-\frac{3}{10} = -\frac{6}{20}−103​=−206​ - −34=−1520-\frac{3}{4} = -\frac{15}{20}−43​=−2015​

STEP 5

Combine the fractions using the common denominator.−1020+820−620−1520=−10+8−6−1520-\frac{10}{20} + \frac{8}{20} - \frac{6}{20} - \frac{15}{20} = \frac{-10 + 8 - 6 - 15}{20}−2010​+208​−206​−2015​=20−10+8−6−15​

STEP 6

Calculate the numerator:−10+8−6−15=−23-10 + 8 - 6 - 15 = -23−10+8−6−15=−23So the expression becomes:−2320\frac{-23}{20}20−23​

STEP 7

Simplify the resulting expression.The fraction −2320\frac{-23}{20}20−23​ is already in its simplest form. The simplified expression is:−2320\boxed{-\frac{23}{20}}−2023​​

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QuestionSimplify the expression: $-\frac{1}{2}+\frac{2}{5}+\left(-\frac{3}{10}\right)-\frac{3}{4}$

1. We are simplifying a numerical expression involving fractions.
2. The expression includes both positive and negative fractions.
3. We need to find a common denominator to combine the fractions.

1. Identify the least common denominator (LCD).
2. Rewrite each fraction with the LCD.
3. Combine the fractions.
4. Simplify the resulting expression.

Identify the least common denominator (LCD) for the fractions $-\frac{1}{2}$ , $\frac{2}{5}$ , $-\frac{3}{10}$ , and $-\frac{3}{4}$ .
- The denominators are $2$ , $5$ , $10$ , and $4$ . - The least common multiple of $2$ , $5$ , $10$ , and $4$ is $20$ .

Rewrite each fraction with the LCD of $20$ .
- $-\frac{1}{2} = -\frac{10}{20}$ - $\frac{2}{5} = \frac{8}{20}$ - $-\frac{3}{10} = -\frac{6}{20}$ - $-\frac{3}{4} = -\frac{15}{20}$

Combine the fractions using the common denominator.
$-\frac{10}{20} + \frac{8}{20} - \frac{6}{20} - \frac{15}{20} = \frac{-10 + 8 - 6 - 15}{20}$

Calculate the numerator:
$-10 + 8 - 6 - 15 = -23$
So the expression becomes:
$\frac{-23}{20}$

Simplify the resulting expression.
The fraction $\frac{-23}{20}$ is already in its simplest form.
The simplified expression is:
$\boxed{-\frac{23}{20}}$