Basic Math Examples

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

Step 1

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

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Step 1.1

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

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

Step 1.2

Add $1$ and $\frac{5}{16}$ .

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Step 1.2.1

Write $1$ as a fraction with a common denominator.

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

Step 1.2.2

Combine the numerators over the common denominator.

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

Step 1.2.3

Add $16$ and $5$ .

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

Step 2

Cancel the common factor of $0.5$ .

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Step 2.1

Move the leading negative in $- \frac{21}{16}$ into the numerator.

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

Step 2.2

Factor $0.5$ out of $16$ .

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

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.

$\frac{1}{2}$