Basic Math Examples

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

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:

$92 \frac{47}{68}$