Basic Math Examples

$3 \frac{1}{2} + 5 \frac{1}{3} + 1 \frac{3}{4}$

Step 1

Convert $3 \frac{1}{2}$ to an improper fraction.

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Step 1.1

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

$3 + \frac{1}{2} + 5 \frac{1}{3} + 1 \frac{3}{4}$

Step 1.2

Add $3$ and $\frac{1}{2}$ .

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Step 1.2.1

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$3 \cdot \frac{2}{2} + \frac{1}{2} + 5 \frac{1}{3} + 1 \frac{3}{4}$

Step 1.2.2

Combine $3$ and $\frac{2}{2}$ .

$\frac{3 \cdot 2}{2} + \frac{1}{2} + 5 \frac{1}{3} + 1 \frac{3}{4}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{3 \cdot 2 + 1}{2} + 5 \frac{1}{3} + 1 \frac{3}{4}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $3$ by $2$ .

$\frac{6 + 1}{2} + 5 \frac{1}{3} + 1 \frac{3}{4}$

Step 1.2.4.2

Add $6$ and $1$ .

$\frac{7}{2} + 5 \frac{1}{3} + 1 \frac{3}{4}$

Step 2

Convert $5 \frac{1}{3}$ to an improper fraction.

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Step 2.1

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

$\frac{7}{2} + 5 + \frac{1}{3} + 1 \frac{3}{4}$

Step 2.2

Add $5$ and $\frac{1}{3}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{7}{2} + 5 \cdot \frac{3}{3} + \frac{1}{3} + 1 \frac{3}{4}$

Step 2.2.2

Combine $5$ and $\frac{3}{3}$ .

$\frac{7}{2} + \frac{5 \cdot 3}{3} + \frac{1}{3} + 1 \frac{3}{4}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{7}{2} + \frac{5 \cdot 3 + 1}{3} + 1 \frac{3}{4}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $3$ .

$\frac{7}{2} + \frac{15 + 1}{3} + 1 \frac{3}{4}$

Step 2.2.4.2

Add $15$ and $1$ .

$\frac{7}{2} + \frac{16}{3} + 1 \frac{3}{4}$

Step 3

Convert $1 \frac{3}{4}$ to an improper fraction.

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Step 3.1

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

$\frac{7}{2} + \frac{16}{3} + 1 + \frac{3}{4}$

Step 3.2

Add $1$ and $\frac{3}{4}$ .

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Step 3.2.1

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

$\frac{7}{2} + \frac{16}{3} + \frac{4}{4} + \frac{3}{4}$

Step 3.2.2

Combine the numerators over the common denominator.

$\frac{7}{2} + \frac{16}{3} + \frac{4 + 3}{4}$

Step 3.2.3

Add $4$ and $3$ .

$\frac{7}{2} + \frac{16}{3} + \frac{7}{4}$

Step 4

Find the common denominator.

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Step 4.1

Multiply $\frac{7}{2}$ by $\frac{6}{6}$ .

$\frac{7}{2} \cdot \frac{6}{6} + \frac{16}{3} + \frac{7}{4}$

Step 4.2

Multiply $\frac{7}{2}$ by $\frac{6}{6}$ .

$\frac{7 \cdot 6}{2 \cdot 6} + \frac{16}{3} + \frac{7}{4}$

Step 4.3

Multiply $\frac{16}{3}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 6}{2 \cdot 6} + \frac{16}{3} \cdot \frac{4}{4} + \frac{7}{4}$

Step 4.4

Multiply $\frac{16}{3}$ by $\frac{4}{4}$ .

$\frac{7 \cdot 6}{2 \cdot 6} + \frac{16 \cdot 4}{3 \cdot 4} + \frac{7}{4}$

Step 4.5

Multiply $\frac{7}{4}$ by $\frac{3}{3}$ .

$\frac{7 \cdot 6}{2 \cdot 6} + \frac{16 \cdot 4}{3 \cdot 4} + \frac{7}{4} \cdot \frac{3}{3}$

Step 4.6

Multiply $\frac{7}{4}$ by $\frac{3}{3}$ .

$\frac{7 \cdot 6}{2 \cdot 6} + \frac{16 \cdot 4}{3 \cdot 4} + \frac{7 \cdot 3}{4 \cdot 3}$

Step 4.7

Multiply $2$ by $6$ .

$\frac{7 \cdot 6}{12} + \frac{16 \cdot 4}{3 \cdot 4} + \frac{7 \cdot 3}{4 \cdot 3}$

Step 4.8

Multiply $3$ by $4$ .

$\frac{7 \cdot 6}{12} + \frac{16 \cdot 4}{12} + \frac{7 \cdot 3}{4 \cdot 3}$

Step 4.9

Reorder the factors of $4 \cdot 3$ .

$\frac{7 \cdot 6}{12} + \frac{16 \cdot 4}{12} + \frac{7 \cdot 3}{3 \cdot 4}$

Step 4.10

Multiply $3$ by $4$ .

$\frac{7 \cdot 6}{12} + \frac{16 \cdot 4}{12} + \frac{7 \cdot 3}{12}$

Step 5

Combine the numerators over the common denominator.

$\frac{7 \cdot 6 + 16 \cdot 4 + 7 \cdot 3}{12}$

Step 6

Simplify each term.

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Step 6.1

Multiply $7$ by $6$ .

$\frac{42 + 16 \cdot 4 + 7 \cdot 3}{12}$

Step 6.2

Multiply $16$ by $4$ .

$\frac{42 + 64 + 7 \cdot 3}{12}$

Step 6.3

Multiply $7$ by $3$ .

$\frac{42 + 64 + 21}{12}$

Step 7

Simplify by adding numbers.

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Step 7.1

Add $42$ and $64$ .

$\frac{106 + 21}{12}$

Step 7.2

Add $106$ and $21$ .

$\frac{127}{12}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{127}{12}$

Decimal Form:

$10.58\overline{3}$

Mixed Number Form:

$10 \frac{7}{12}$