Basic Math Examples

24 \frac{34}{51} + 23 \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}

$24 \frac{34}{51} + 23 \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 1

Convert

$24 \frac{34}{51}$ to an improper fraction.

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Step 1.1

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

$24 + \frac{34}{51} + 23 \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 1.2

Add

$24$ and

$\frac{34}{51}$ .

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Step 1.2.1

To write

$24$ as a fraction with a common denominator, multiply by

$\frac{51}{51}$ .

$24 \cdot \frac{51}{51} + \frac{34}{51} + 23 \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 1.2.2

Combine

$24$ and

$\frac{51}{51}$ .

$\frac{24 \cdot 51}{51} + \frac{34}{51} + 23 \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{24 \cdot 51 + 34}{51} + 23 \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply

$24$ by

$51$ .

$\frac{1224 + 34}{51} + 23 \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 1.2.4.2

Add

$1224$ and

$34$ .

$\frac{1258}{51} + 23 \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 2

Convert

$23 \frac{3}{4}$ to an improper fraction.

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Step 2.1

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

$\frac{1258}{51} + 23 + \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 2.2

Add

$23$ and

$\frac{3}{4}$ .

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Step 2.2.1

To write

$23$ as a fraction with a common denominator, multiply by

$\frac{4}{4}$ .

$\frac{1258}{51} + 23 \cdot \frac{4}{4} + \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 2.2.2

Combine

$23$ and

$\frac{4}{4}$ .

$\frac{1258}{51} + \frac{23 \cdot 4}{4} + \frac{3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{1258}{51} + \frac{23 \cdot 4 + 3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply

$23$ by

$4$ .

$\frac{1258}{51} + \frac{92 + 3}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 2.2.4.2

Add

$92$ and

$3$ .

$\frac{1258}{51} + \frac{95}{4} + 21 \frac{1}{3} + 22 \frac{16}{17}$

Step 3

Convert

$21 \frac{1}{3}$ to an improper fraction.

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Step 3.1

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

$\frac{1258}{51} + \frac{95}{4} + 21 + \frac{1}{3} + 22 \frac{16}{17}$

Step 3.2

Add

$21$ and

$\frac{1}{3}$ .

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Step 3.2.1

To write

$21$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$\frac{1258}{51} + \frac{95}{4} + 21 \cdot \frac{3}{3} + \frac{1}{3} + 22 \frac{16}{17}$

Step 3.2.2

Combine

$21$ and

$\frac{3}{3}$ .

$\frac{1258}{51} + \frac{95}{4} + \frac{21 \cdot 3}{3} + \frac{1}{3} + 22 \frac{16}{17}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{1258}{51} + \frac{95}{4} + \frac{21 \cdot 3 + 1}{3} + 22 \frac{16}{17}$

Step 3.2.4

Simplify the numerator.

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Step 3.2.4.1

Multiply

$21$ by

$3$ .

$\frac{1258}{51} + \frac{95}{4} + \frac{63 + 1}{3} + 22 \frac{16}{17}$

Step 3.2.4.2

Add

$63$ and

$1$ .

$\frac{1258}{51} + \frac{95}{4} + \frac{64}{3} + 22 \frac{16}{17}$

Step 4

Convert

$22 \frac{16}{17}$ to an improper fraction.

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Step 4.1

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

$\frac{1258}{51} + \frac{95}{4} + \frac{64}{3} + 22 + \frac{16}{17}$

Step 4.2

Add

$22$ and

$\frac{16}{17}$ .

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Step 4.2.1

To write

$22$ as a fraction with a common denominator, multiply by

$\frac{17}{17}$ .

$\frac{1258}{51} + \frac{95}{4} + \frac{64}{3} + 22 \cdot \frac{17}{17} + \frac{16}{17}$

Step 4.2.2

Combine

$22$ and

$\frac{17}{17}$ .

$\frac{1258}{51} + \frac{95}{4} + \frac{64}{3} + \frac{22 \cdot 17}{17} + \frac{16}{17}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{1258}{51} + \frac{95}{4} + \frac{64}{3} + \frac{22 \cdot 17 + 16}{17}$

Step 4.2.4

Simplify the numerator.

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Step 4.2.4.1

Multiply

$22$ by

$17$ .

$\frac{1258}{51} + \frac{95}{4} + \frac{64}{3} + \frac{374 + 16}{17}$

Step 4.2.4.2

Add

$374$ and

$16$ .

$\frac{1258}{51} + \frac{95}{4} + \frac{64}{3} + \frac{390}{17}$

Step 5

Find the common denominator.

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Step 5.1

Multiply

$\frac{1258}{51}$ by

$\frac{4}{4}$ .

$\frac{1258}{51} \cdot \frac{4}{4} + \frac{95}{4} + \frac{64}{3} + \frac{390}{17}$

Step 5.2

Multiply

$\frac{1258}{51}$ by

$\frac{4}{4}$ .

$\frac{1258 \cdot 4}{51 \cdot 4} + \frac{95}{4} + \frac{64}{3} + \frac{390}{17}$

Step 5.3

Multiply

$\frac{95}{4}$ by

$\frac{51}{51}$ .

$\frac{1258 \cdot 4}{51 \cdot 4} + \frac{95}{4} \cdot \frac{51}{51} + \frac{64}{3} + \frac{390}{17}$

Step 5.4

Multiply

$\frac{95}{4}$ by

$\frac{51}{51}$ .

$\frac{1258 \cdot 4}{51 \cdot 4} + \frac{95 \cdot 51}{4 \cdot 51} + \frac{64}{3} + \frac{390}{17}$

Step 5.5

Multiply

$\frac{64}{3}$ by

$\frac{68}{68}$ .

$\frac{1258 \cdot 4}{51 \cdot 4} + \frac{95 \cdot 51}{4 \cdot 51} + \frac{64}{3} \cdot \frac{68}{68} + \frac{390}{17}$

Step 5.6

Multiply

$\frac{64}{3}$ by

$\frac{68}{68}$ .

$\frac{1258 \cdot 4}{51 \cdot 4} + \frac{95 \cdot 51}{4 \cdot 51} + \frac{64 \cdot 68}{3 \cdot 68} + \frac{390}{17}$

Step 5.7

Multiply

$\frac{390}{17}$ by

$\frac{12}{12}$ .

$\frac{1258 \cdot 4}{51 \cdot 4} + \frac{95 \cdot 51}{4 \cdot 51} + \frac{64 \cdot 68}{3 \cdot 68} + \frac{390}{17} \cdot \frac{12}{12}$

Step 5.8

Multiply

$\frac{390}{17}$ by

$\frac{12}{12}$ .

$\frac{1258 \cdot 4}{51 \cdot 4} + \frac{95 \cdot 51}{4 \cdot 51} + \frac{64 \cdot 68}{3 \cdot 68} + \frac{390 \cdot 12}{17 \cdot 12}$

Step 5.9

Reorder the factors of

$51 \cdot 4$ .

$\frac{1258 \cdot 4}{4 \cdot 51} + \frac{95 \cdot 51}{4 \cdot 51} + \frac{64 \cdot 68}{3 \cdot 68} + \frac{390 \cdot 12}{17 \cdot 12}$

Step 5.10

Multiply

$4$ by

$51$ .

$\frac{1258 \cdot 4}{204} + \frac{95 \cdot 51}{4 \cdot 51} + \frac{64 \cdot 68}{3 \cdot 68} + \frac{390 \cdot 12}{17 \cdot 12}$

Step 5.11

Multiply

$4$ by

$51$ .

$\frac{1258 \cdot 4}{204} + \frac{95 \cdot 51}{204} + \frac{64 \cdot 68}{3 \cdot 68} + \frac{390 \cdot 12}{17 \cdot 12}$

Step 5.12

Multiply

$3$ by

$68$ .

$\frac{1258 \cdot 4}{204} + \frac{95 \cdot 51}{204} + \frac{64 \cdot 68}{204} + \frac{390 \cdot 12}{17 \cdot 12}$

Step 5.13

Reorder the factors of

$17 \cdot 12$ .

$\frac{1258 \cdot 4}{204} + \frac{95 \cdot 51}{204} + \frac{64 \cdot 68}{204} + \frac{390 \cdot 12}{12 \cdot 17}$

Step 5.14

Multiply

$12$ by

$17$ .

$\frac{1258 \cdot 4}{204} + \frac{95 \cdot 51}{204} + \frac{64 \cdot 68}{204} + \frac{390 \cdot 12}{204}$

Step 6

Combine the numerators over the common denominator.

$\frac{1258 \cdot 4 + 95 \cdot 51 + 64 \cdot 68 + 390 \cdot 12}{204}$

Step 7

Simplify each term.

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Step 7.1

Multiply

$1258$ by

$4$ .

$\frac{5032 + 95 \cdot 51 + 64 \cdot 68 + 390 \cdot 12}{204}$

Step 7.2

Multiply

$95$ by

$51$ .

$\frac{5032 + 4845 + 64 \cdot 68 + 390 \cdot 12}{204}$

Step 7.3

Multiply

$64$ by

$68$ .

$\frac{5032 + 4845 + 4352 + 390 \cdot 12}{204}$

Step 7.4

Multiply

$390$ by

$12$ .

$\frac{5032 + 4845 + 4352 + 4680}{204}$

Step 8

Reduce the expression by cancelling the common factors.

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Step 8.1

Add

$5032$ and

$4845$ .

$\frac{9877 + 4352 + 4680}{204}$

Step 8.2

Simplify by adding numbers.

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Step 8.2.1

Add

$9877$ and

$4352$ .

$\frac{14229 + 4680}{204}$

Step 8.2.2

Add

$14229$ and

$4680$ .

$\frac{18909}{204}$

Step 8.3

Cancel the common factor of

$18909$ and

$204$ .

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Step 8.3.1

Factor

$3$ out of

$18909$ .

$\frac{3 (6303)}{204}$

Step 8.3.2

Cancel the common factors.

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Step 8.3.2.1

Factor

$3$ out of

$204$ .

$\frac{3 \cdot 6303}{3 \cdot 68}$

Step 8.3.2.2

Cancel the common factor.

$\frac{3 \cdot 6303}{3 \cdot 68}$

Step 8.3.2.3

Rewrite the expression.

$\frac{6303}{68}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$\frac{6303}{68}$

Decimal Form:

$92.69117647 \dots$

Mixed Number Form:

$92 \frac{47}{68}$