What is 1 3/4-2+(-4 3/4) ?

The solution to 1 3/4-2+(-4 3/4) is -5

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1 3/4-2+(-4 3/4)

1 \frac{3}{4} - 2 + (- 4 \frac{3}{4})

- 5

Solution steps

1 \frac{3}{4} - 2 + (- 4 \frac{3}{4})

Convert mixed numbers to improper fractions:

1 \frac{3}{4} = \frac{7}{4}

1 \frac{3}{4}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

1 \frac{3}{4} = \frac{1 \cdot 4 + 3}{4}

= \frac{7}{4}

= \frac{7}{4} - 2 + (- 4 \frac{3}{4})

Convert mixed numbers to improper fractions:

4 \frac{3}{4} = \frac{19}{4}

4 \frac{3}{4}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

4 \frac{3}{4} = \frac{4 \cdot 4 + 3}{4}

= \frac{19}{4}

= \frac{7}{4} - 2 + (- \frac{19}{4})

Follow the PEMDAS order of operations

Add and subtract (left to right)

\frac{7}{4} - 2 + (- \frac{19}{4}) : - 5

\frac{7}{4} - 2 + (- \frac{19}{4})

\frac{7}{4} - 2 = - \frac{1}{4}

\frac{7}{4} - 2

Convert element to fraction:

2 = \frac{2 \cdot 4}{4}

= - \frac{2 \cdot 4}{4} + \frac{7}{4}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 2 \cdot 4 + 7}{4}

- 2 \cdot 4 + 7 = - 1

- 2 \cdot 4 + 7

Multiply the numbers:

2 \cdot 4 = 8

= - 8 + 7

Add/Subtract the numbers:

- 8 + 7 = - 1

= - 1

= \frac{- 1}{4}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{1}{4}

= - \frac{1}{4} + (- \frac{19}{4})

Apply rule

+ (- a) = - a

+ (- \frac{19}{4}) = - \frac{19}{4}

= - \frac{1}{4} - \frac{19}{4}

- \frac{1}{4} - \frac{19}{4} = - 5

- \frac{1}{4} - \frac{19}{4}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{- 1 - 19}{4}

Subtract the numbers:

- 1 - 19 = - 20

= \frac{- 20}{4}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{20}{4}

Divide the numbers:

\frac{20}{4} = 5

= - 5

= - 5

= - 5

8 - (- (- 9 - 8) + (- 2 + 7)) - (- 3 + 8)

- (- 3)^{2} - 6 (- 3) + 1

3 (- 1)^{2} - 2 (- 1) + 1

16 + (2 \cdot 256)

- 180 (1 - \frac{10}{50})