Basic Math Examples

$(\frac{3}{7} - \frac{16}{21}) \cdot 2 \frac{1}{7} + \frac{\frac{11}{15} + 0.3}{12 \frac{2}{5}}$

Step 1

Convert $2 \frac{1}{7}$ to an improper fraction.

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Step 1.1

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

$(\frac{3}{7} - \frac{16}{21}) \cdot (2 + \frac{1}{7}) + \frac{\frac{11}{15} + 0.3}{12 \frac{2}{5}}$

Step 1.2

Add $2$ and $\frac{1}{7}$ .

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Step 1.2.1

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

$(\frac{3}{7} - \frac{16}{21}) \cdot (2 \cdot \frac{7}{7} + \frac{1}{7}) + \frac{\frac{11}{15} + 0.3}{12 \frac{2}{5}}$

Step 1.2.2

Combine $2$ and $\frac{7}{7}$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot (\frac{2 \cdot 7}{7} + \frac{1}{7}) + \frac{\frac{11}{15} + 0.3}{12 \frac{2}{5}}$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{2 \cdot 7 + 1}{7} + \frac{\frac{11}{15} + 0.3}{12 \frac{2}{5}}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $2$ by $7$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{14 + 1}{7} + \frac{\frac{11}{15} + 0.3}{12 \frac{2}{5}}$

Step 1.2.4.2

Add $14$ and $1$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11}{15} + 0.3}{12 \frac{2}{5}}$

Step 2

Convert $12 \frac{2}{5}$ to an improper fraction.

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Step 2.1

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

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11}{15} + 0.3}{12 + \frac{2}{5}}$

Step 2.2

Add $12$ and $\frac{2}{5}$ .

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Step 2.2.1

To write $12$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11}{15} + 0.3}{12 \cdot \frac{5}{5} + \frac{2}{5}}$

Step 2.2.2

Combine $12$ and $\frac{5}{5}$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11}{15} + 0.3}{\frac{12 \cdot 5}{5} + \frac{2}{5}}$

Step 2.2.3

Combine the numerators over the common denominator.

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11}{15} + 0.3}{\frac{12 \cdot 5 + 2}{5}}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $12$ by $5$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11}{15} + 0.3}{\frac{60 + 2}{5}}$

Step 2.2.4.2

Add $60$ and $2$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11}{15} + 0.3}{\frac{62}{5}}$

Step 3

To write $0.3$ as a fraction with a common denominator, multiply by $\frac{15}{15}$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11}{15} + 0.3 \cdot \frac{15}{15}}{\frac{62}{5}}$

Step 4

Combine fractions.

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Step 4.1

Combine $0.3$ and $\frac{15}{15}$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11}{15} + \frac{0.3 \cdot 15}{15}}{\frac{62}{5}}$

Step 4.2

Simplify the expression.

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Step 4.2.1

Combine the numerators over the common denominator.

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11 + 0.3 \cdot 15}{15}}{\frac{62}{5}}$

Step 4.2.2

Multiply $0.3$ by $15$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{11 + 4.5}{15}}{\frac{62}{5}}$

Step 4.2.3

Add $11$ and $4.5$ .

$(\frac{3}{7} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5

Simplify each term.

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Step 5.1

To write $\frac{3}{7}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{3}{7} \cdot \frac{3}{3} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.2

Write each expression with a common denominator of $21$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.2.1

Multiply $\frac{3}{7}$ by $\frac{3}{3}$ .

$(\frac{3 \cdot 3}{7 \cdot 3} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.2.2

Multiply $7$ by $3$ .

$(\frac{3 \cdot 3}{21} - \frac{16}{21}) \cdot \frac{15}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 - 16}{21} \cdot \frac{15}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.4

Simplify the numerator.

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Step 5.4.1

Multiply $3$ by $3$ .

$\frac{9 - 16}{21} \cdot \frac{15}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.4.2

Subtract $16$ from $9$ .

$\frac{- 7}{21} \cdot \frac{15}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.5

Cancel the common factor of $7$ .

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Step 5.5.1

Factor $7$ out of $- 7$ .

$\frac{7 (- 1)}{21} \cdot \frac{15}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.5.2

Cancel the common factor.

$\frac{7 \cdot - 1}{21} \cdot \frac{15}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.5.3

Rewrite the expression.

$\frac{- 1}{21} \cdot 15 + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.6

Cancel the common factor of $3$ .

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Step 5.6.1

Factor $3$ out of $21$ .

$\frac{- 1}{3 (7)} \cdot 15 + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.6.2

Factor $3$ out of $15$ .

$\frac{- 1}{3 \cdot 7} \cdot (3 \cdot 5) + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.6.3

Cancel the common factor.

$\frac{- 1}{3 \cdot 7} \cdot (3 \cdot 5) + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.6.4

Rewrite the expression.

$\frac{- 1}{7} \cdot 5 + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.7

Combine $\frac{- 1}{7}$ and $5$ .

$\frac{- 1 \cdot 5}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.8

Multiply $- 1$ by $5$ .

$\frac{- 5}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.9

Move the negative in front of the fraction.

$- \frac{5}{7} + \frac{\frac{15.5}{15}}{\frac{62}{5}}$

Step 5.10

Multiply the numerator by the reciprocal of the denominator.

$- \frac{5}{7} + \frac{15.5}{15} \cdot \frac{5}{62}$

Step 5.11

Cancel the common factor of $15.5$ .

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Step 5.11.1

Factor $15.5$ out of $62$ .

$- \frac{5}{7} + \frac{15.5}{15} \cdot \frac{5}{15.5 (4)}$

Step 5.11.2

Cancel the common factor.

$- \frac{5}{7} + \frac{15.5}{15} \cdot \frac{5}{15.5 \cdot 4}$

Step 5.11.3

Rewrite the expression.

$- \frac{5}{7} + \frac{1}{15} \cdot \frac{5}{4}$

Step 5.12

Cancel the common factor of $5$ .

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Step 5.12.1

Factor $5$ out of $15$ .

$- \frac{5}{7} + \frac{1}{5 (3)} \cdot \frac{5}{4}$

Step 5.12.2

Cancel the common factor.

$- \frac{5}{7} + \frac{1}{5 \cdot 3} \cdot \frac{5}{4}$

Step 5.12.3

Rewrite the expression.

$- \frac{5}{7} + \frac{1}{3} \cdot \frac{1}{4}$

Step 5.13

Multiply $\frac{1}{3}$ by $\frac{1}{4}$ .

$- \frac{5}{7} + \frac{1}{3 \cdot 4}$

Step 5.14

Multiply $3$ by $4$ .

$- \frac{5}{7} + \frac{1}{12}$

Step 6

To write $- \frac{5}{7}$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$- \frac{5}{7} \cdot \frac{12}{12} + \frac{1}{12}$

Step 7

To write $\frac{1}{12}$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$- \frac{5}{7} \cdot \frac{12}{12} + \frac{1}{12} \cdot \frac{7}{7}$

Step 8

Write each expression with a common denominator of $84$ , by multiplying each by an appropriate factor of $1$ .

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Step 8.1

Multiply $\frac{5}{7}$ by $\frac{12}{12}$ .

$- \frac{5 \cdot 12}{7 \cdot 12} + \frac{1}{12} \cdot \frac{7}{7}$

Step 8.2

Multiply $7$ by $12$ .

$- \frac{5 \cdot 12}{84} + \frac{1}{12} \cdot \frac{7}{7}$

Step 8.3

Multiply $\frac{1}{12}$ by $\frac{7}{7}$ .

$- \frac{5 \cdot 12}{84} + \frac{7}{12 \cdot 7}$

Step 8.4

Multiply $12$ by $7$ .

$- \frac{5 \cdot 12}{84} + \frac{7}{84}$

Step 9

Combine the numerators over the common denominator.

$\frac{- 5 \cdot 12 + 7}{84}$

Step 10

Simplify the numerator.

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Step 10.1

Multiply $- 5$ by $12$ .

$\frac{- 60 + 7}{84}$

Step 10.2

Add $- 60$ and $7$ .

$\frac{- 53}{84}$

Step 11

Move the negative in front of the fraction.

$- \frac{53}{84}$

Step 12

The result can be shown in multiple forms.

Exact Form:

$- \frac{53}{84}$

Decimal Form:

$- 0.63095238 \dots$