Basic Math Examples

$5 \frac{1}{4} \cdot 1 \frac{7}{9} + 3$

Step 1

Convert $5 \frac{1}{4}$ to an improper fraction.

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Step 1.1

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

$(5 + \frac{1}{4}) \cdot 1 \frac{7}{9} + 3$

Step 1.2

Add $5$ and $\frac{1}{4}$ .

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Step 1.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(5 \cdot \frac{4}{4} + \frac{1}{4}) \cdot 1 \frac{7}{9} + 3$

Step 1.2.2

Combine $5$ and $\frac{4}{4}$ .

$(\frac{5 \cdot 4}{4} + \frac{1}{4}) \cdot 1 \frac{7}{9} + 3$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{5 \cdot 4 + 1}{4} \cdot 1 \frac{7}{9} + 3$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $5$ by $4$ .

$\frac{20 + 1}{4} \cdot 1 \frac{7}{9} + 3$

Step 1.2.4.2

Add $20$ and $1$ .

$\frac{21}{4} \cdot 1 \frac{7}{9} + 3$

Step 2

Convert $1 \frac{7}{9}$ to an improper fraction.

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Step 2.1

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

$\frac{21}{4} \cdot (1 + \frac{7}{9}) + 3$

Step 2.2

Add $1$ and $\frac{7}{9}$ .

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Step 2.2.1

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

$\frac{21}{4} \cdot (\frac{9}{9} + \frac{7}{9}) + 3$

Step 2.2.2

Combine the numerators over the common denominator.

$\frac{21}{4} \cdot \frac{9 + 7}{9} + 3$

Step 2.2.3

Add $9$ and $7$ .

$\frac{21}{4} \cdot \frac{16}{9} + 3$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Factor $3$ out of $21$ .

$\frac{3 (7)}{4} \cdot \frac{16}{9} + 3$

Step 3.1.2

Factor $3$ out of $9$ .

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

Step 3.1.3

Cancel the common factor.

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

Step 3.1.4

Rewrite the expression.

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

Step 3.2

Cancel the common factor of $4$ .

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Step 3.2.1

Factor $4$ out of $16$ .

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

Step 3.2.2

Cancel the common factor.

$\frac{7}{4} \cdot \frac{4 \cdot 4}{3} + 3$

Step 3.2.3

Rewrite the expression.

$7 \cdot \frac{4}{3} + 3$

Step 3.3

Combine $7$ and $\frac{4}{3}$ .

$\frac{7 \cdot 4}{3} + 3$

Step 3.4

Multiply $7$ by $4$ .

$\frac{28}{3} + 3$

Step 4

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

$\frac{28}{3} + 3 \cdot \frac{3}{3}$

Step 5

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

$\frac{28}{3} + \frac{3 \cdot 3}{3}$

Step 6

Combine the numerators over the common denominator.

$\frac{28 + 3 \cdot 3}{3}$

Step 7

Simplify the numerator.

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Step 7.1

Multiply $3$ by $3$ .

$\frac{28 + 9}{3}$

Step 7.2

Add $28$ and $9$ .

$\frac{37}{3}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{37}{3}$

Decimal Form:

$12.\overline{3}$

Mixed Number Form:

$12 \frac{1}{3}$