Basic Math Examples

12 \cdot (0.5 \cdot (- 1 \frac{5}{16})) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})

$12 \cdot (0.5 \cdot (- 1 \frac{5}{16})) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 1

Convert

1 \frac{5}{16}

$1 \frac{5}{16}$ to an improper fraction.

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Step 1.1

A mixed number is an addition of its whole and fractional parts.

12 \cdot (0.5 \cdot (- (1 + \frac{5}{16}))) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})

$12 \cdot (0.5 \cdot (- (1 + \frac{5}{16}))) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 1.2

Add

1

$1$ and

\frac{5}{16}

$\frac{5}{16}$ .

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Step 1.2.1

Write

1

$1$ as a fraction with a common denominator.

12 \cdot (0.5 \cdot (- (\frac{16}{16} + \frac{5}{16}))) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})

$12 \cdot (0.5 \cdot (- (\frac{16}{16} + \frac{5}{16}))) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 1.2.2

Combine the numerators over the common denominator.

12 \cdot (0.5 \cdot (- \frac{16 + 5}{16})) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})

$12 \cdot (0.5 \cdot (- \frac{16 + 5}{16})) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 1.2.3

Add

16

$16$ and

5

$5$ .

12 \cdot (0.5 \cdot (- \frac{21}{16})) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})

$12 \cdot (0.5 \cdot (- \frac{21}{16})) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

12 \cdot (0.5 \cdot (- \frac{21}{16})) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})

$12 \cdot (0.5 \cdot (- \frac{21}{16})) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

12 \cdot (0.5 \cdot (- \frac{21}{16})) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})

$12 \cdot (0.5 \cdot (- \frac{21}{16})) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 2

Cancel the common factor of

0.5

$0.5$ .

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Step 2.1

Move the leading negative in

- \frac{21}{16}

$- \frac{21}{16}$ into the numerator.

12 \cdot (0.5 \cdot \frac{- 21}{16}) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})

$12 \cdot (0.5 \cdot \frac{- 21}{16}) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 2.2

Factor

0.5

$0.5$ out of

16

$16$ .

12 \cdot (0.5 \cdot \frac{- 21}{0.5 (32)}) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})

$12 \cdot (0.5 \cdot \frac{- 21}{0.5 (32)}) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 2.3

Cancel the common factor.

$12 \cdot (0.5 \cdot \frac{- 21}{0.5 \cdot 32}) - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 2.4

Rewrite the expression.

$12 \cdot \frac{- 21}{32} - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 3

Cancel the common factor of

$4$ .

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Step 3.1

Factor

$4$ out of

$12$ .

$4 (3) \cdot \frac{- 21}{32} - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 3.2

Factor

$4$ out of

$32$ .

$4 \cdot 3 \cdot \frac{- 21}{4 \cdot 8} - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 3.3

Cancel the common factor.

$4 \cdot 3 \cdot \frac{- 21}{4 \cdot 8} - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 3.4

Rewrite the expression.

$3 \cdot \frac{- 21}{8} - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 4

Combine

$3$ and

$\frac{- 21}{8}$ .

$\frac{3 \cdot - 21}{8} - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 5

Multiply

$3$ by

$- 21$ .

$\frac{- 63}{8} - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 6

Move the negative in front of the fraction.

$- \frac{63}{8} - 35 \cdot (0.4 \cdot (- 1 \frac{5}{16}) + \frac{2}{7})$

Step 7

Simplify each term.

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Step 7.1

Convert

$1 \frac{5}{16}$ to an improper fraction.

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Step 7.1.1

A mixed number is an addition of its whole and fractional parts.

$- \frac{63}{8} - 35 \cdot (0.4 \cdot (- (1 + \frac{5}{16})) + \frac{2}{7})$

Step 7.1.2

Add

$1$ and

$\frac{5}{16}$ .

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Step 7.1.2.1

Write

$1$ as a fraction with a common denominator.

$- \frac{63}{8} - 35 \cdot (0.4 \cdot (- (\frac{16}{16} + \frac{5}{16})) + \frac{2}{7})$

Step 7.1.2.2

Combine the numerators over the common denominator.

$- \frac{63}{8} - 35 \cdot (0.4 \cdot (- \frac{16 + 5}{16}) + \frac{2}{7})$

Step 7.1.2.3

Add

$16$ and

$5$ .

$- \frac{63}{8} - 35 \cdot (0.4 \cdot (- \frac{21}{16}) + \frac{2}{7})$

Step 7.2

Cancel the common factor of

$0.4$ .

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Step 7.2.1

Move the leading negative in

$- \frac{21}{16}$ into the numerator.

$- \frac{63}{8} - 35 \cdot (0.4 \cdot \frac{- 21}{16} + \frac{2}{7})$

Step 7.2.2

Factor

$0.4$ out of

$16$ .

$- \frac{63}{8} - 35 \cdot (0.4 \cdot \frac{- 21}{0.4 (40)} + \frac{2}{7})$

Step 7.2.3

Cancel the common factor.

$- \frac{63}{8} - 35 \cdot (0.4 \cdot \frac{- 21}{0.4 \cdot 40} + \frac{2}{7})$

Step 7.2.4

Rewrite the expression.

$- \frac{63}{8} - 35 \cdot (\frac{- 21}{40} + \frac{2}{7})$

Step 7.3

Move the negative in front of the fraction.

$- \frac{63}{8} - 35 \cdot (- \frac{21}{40} + \frac{2}{7})$

Step 8

To write

$- \frac{21}{40}$ as a fraction with a common denominator, multiply by

$\frac{7}{7}$ .

$- \frac{63}{8} - 35 \cdot (- \frac{21}{40} \cdot \frac{7}{7} + \frac{2}{7})$

Step 9

To write

$\frac{2}{7}$ as a fraction with a common denominator, multiply by

$\frac{40}{40}$ .

$- \frac{63}{8} - 35 \cdot (- \frac{21}{40} \cdot \frac{7}{7} + \frac{2}{7} \cdot \frac{40}{40})$

Step 10

Write each expression with a common denominator of

$280$ , by multiplying each by an appropriate factor of

$1$ .

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Step 10.1

Multiply

$\frac{21}{40}$ by

$\frac{7}{7}$ .

$- \frac{63}{8} - 35 \cdot (- \frac{21 \cdot 7}{40 \cdot 7} + \frac{2}{7} \cdot \frac{40}{40})$

Step 10.2

Multiply

$40$ by

$7$ .

$- \frac{63}{8} - 35 \cdot (- \frac{21 \cdot 7}{280} + \frac{2}{7} \cdot \frac{40}{40})$

Step 10.3

Multiply

$\frac{2}{7}$ by

$\frac{40}{40}$ .

$- \frac{63}{8} - 35 \cdot (- \frac{21 \cdot 7}{280} + \frac{2 \cdot 40}{7 \cdot 40})$

Step 10.4

Multiply

$7$ by

$40$ .

$- \frac{63}{8} - 35 \cdot (- \frac{21 \cdot 7}{280} + \frac{2 \cdot 40}{280})$

Step 11

Combine the numerators over the common denominator.

$- \frac{63}{8} - 35 \cdot \frac{- 21 \cdot 7 + 2 \cdot 40}{280}$

Step 12

Simplify the numerator.

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Step 12.1

Multiply

$- 21$ by

$7$ .

$- \frac{63}{8} - 35 \cdot \frac{- 147 + 2 \cdot 40}{280}$

Step 12.2

Multiply

$2$ by

$40$ .

$- \frac{63}{8} - 35 \cdot \frac{- 147 + 80}{280}$

Step 12.3

Add

$- 147$ and

$80$ .

$- \frac{63}{8} - 35 \cdot \frac{- 67}{280}$

Step 13

Cancel the common factor of

$35$ .

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Step 13.1

Factor

$35$ out of

$- 35$ .

$- \frac{63}{8} + 35 (- 1) \cdot \frac{- 67}{280}$

Step 13.2

Factor

$35$ out of

$280$ .

$- \frac{63}{8} + 35 \cdot - 1 \cdot \frac{- 67}{35 \cdot 8}$

Step 13.3

Cancel the common factor.

$- \frac{63}{8} + 35 \cdot - 1 \cdot \frac{- 67}{35 \cdot 8}$

Step 13.4

Rewrite the expression.

$- \frac{63}{8} - 1 \cdot \frac{- 67}{8}$

Step 14

Move the negative in front of the fraction.

$- \frac{63}{8} - 1 (- \frac{67}{8})$

Step 15

Multiply

$- 1 (- \frac{67}{8})$ .

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Step 15.1

Multiply

$- 1$ by

$- 1$ .

$- \frac{63}{8} + 1 (\frac{67}{8})$

Step 15.2

Multiply

$\frac{67}{8}$ by

$1$ .

$- \frac{63}{8} + \frac{67}{8}$

Step 16

Combine the numerators over the common denominator.

$\frac{- 63 + 67}{8}$

Step 17

Add

$- 63$ and

$67$ .

$\frac{4}{8}$

Step 18

Cancel the common factor of

$4$ and

$8$ .

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Step 18.1

Factor

$4$ out of

$4$ .

$\frac{4 (1)}{8}$

Step 18.2

Cancel the common factors.

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Step 18.2.1

Factor

$4$ out of

$8$ .

$\frac{4 \cdot 1}{4 \cdot 2}$

Step 18.2.2

Cancel the common factor.

$\frac{4 \cdot 1}{4 \cdot 2}$

Step 18.2.3

Rewrite the expression.

$\frac{1}{2}$