Pre-Algebra Examples

$2 \frac{5}{32} + 2 \frac{3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 1

Convert $2 \frac{5}{32}$ to an improper fraction.

Tap for more steps...

Step 1.1

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

$2 + \frac{5}{32} + 2 \frac{3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 1.2

Add $2$ and $\frac{5}{32}$ .

Tap for more steps...

Step 1.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{32}{32}$ .

$2 \cdot \frac{32}{32} + \frac{5}{32} + 2 \frac{3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 1.2.2

Combine $2$ and $\frac{32}{32}$ .

$\frac{2 \cdot 32}{32} + \frac{5}{32} + 2 \frac{3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 1.2.3

Combine the numerators over the common denominator.

$\frac{2 \cdot 32 + 5}{32} + 2 \frac{3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 1.2.4

Simplify the numerator.

Tap for more steps...

Step 1.2.4.1

Multiply $2$ by $32$ .

$\frac{64 + 5}{32} + 2 \frac{3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 1.2.4.2

Add $64$ and $5$ .

$\frac{69}{32} + 2 \frac{3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 2

Convert $2 \frac{3}{8}$ to an improper fraction.

Tap for more steps...

Step 2.1

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

$\frac{69}{32} + 2 + \frac{3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 2.2

Add $2$ and $\frac{3}{8}$ .

Tap for more steps...

Step 2.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$\frac{69}{32} + 2 \cdot \frac{8}{8} + \frac{3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 2.2.2

Combine $2$ and $\frac{8}{8}$ .

$\frac{69}{32} + \frac{2 \cdot 8}{8} + \frac{3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 2.2.3

Combine the numerators over the common denominator.

$\frac{69}{32} + \frac{2 \cdot 8 + 3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 2.2.4

Simplify the numerator.

Tap for more steps...

Step 2.2.4.1

Multiply $2$ by $8$ .

$\frac{69}{32} + \frac{16 + 3}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 2.2.4.2

Add $16$ and $3$ .

$\frac{69}{32} + \frac{19}{8} + 2 \frac{15}{16} + 2 \frac{5}{16}$

Step 3

Convert $2 \frac{15}{16}$ to an improper fraction.

Tap for more steps...

Step 3.1

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

$\frac{69}{32} + \frac{19}{8} + 2 + \frac{15}{16} + 2 \frac{5}{16}$

Step 3.2

Add $2$ and $\frac{15}{16}$ .

Tap for more steps...

Step 3.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{69}{32} + \frac{19}{8} + 2 \cdot \frac{16}{16} + \frac{15}{16} + 2 \frac{5}{16}$

Step 3.2.2

Combine $2$ and $\frac{16}{16}$ .

$\frac{69}{32} + \frac{19}{8} + \frac{2 \cdot 16}{16} + \frac{15}{16} + 2 \frac{5}{16}$

Step 3.2.3

Combine the numerators over the common denominator.

$\frac{69}{32} + \frac{19}{8} + \frac{2 \cdot 16 + 15}{16} + 2 \frac{5}{16}$

Step 3.2.4

Simplify the numerator.

Tap for more steps...

Step 3.2.4.1

Multiply $2$ by $16$ .

$\frac{69}{32} + \frac{19}{8} + \frac{32 + 15}{16} + 2 \frac{5}{16}$

Step 3.2.4.2

Add $32$ and $15$ .

$\frac{69}{32} + \frac{19}{8} + \frac{47}{16} + 2 \frac{5}{16}$

Step 4

Convert $2 \frac{5}{16}$ to an improper fraction.

Tap for more steps...

Step 4.1

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

$\frac{69}{32} + \frac{19}{8} + \frac{47}{16} + 2 + \frac{5}{16}$

Step 4.2

Add $2$ and $\frac{5}{16}$ .

Tap for more steps...

Step 4.2.1

To write $2$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{69}{32} + \frac{19}{8} + \frac{47}{16} + 2 \cdot \frac{16}{16} + \frac{5}{16}$

Step 4.2.2

Combine $2$ and $\frac{16}{16}$ .

$\frac{69}{32} + \frac{19}{8} + \frac{47}{16} + \frac{2 \cdot 16}{16} + \frac{5}{16}$

Step 4.2.3

Combine the numerators over the common denominator.

$\frac{69}{32} + \frac{19}{8} + \frac{47}{16} + \frac{2 \cdot 16 + 5}{16}$

Step 4.2.4

Simplify the numerator.

Tap for more steps...

Step 4.2.4.1

Multiply $2$ by $16$ .

$\frac{69}{32} + \frac{19}{8} + \frac{47}{16} + \frac{32 + 5}{16}$

Step 4.2.4.2

Add $32$ and $5$ .

$\frac{69}{32} + \frac{19}{8} + \frac{47}{16} + \frac{37}{16}$

Step 5

Combine the numerators over the common denominator.

$\frac{69}{32} + \frac{19}{8} + \frac{47 + 37}{16}$

Step 6

Add $47$ and $37$ .

$\frac{69}{32} + \frac{19}{8} + \frac{84}{16}$

Step 7

Find the common denominator.

Tap for more steps...

Step 7.1

Multiply $\frac{19}{8}$ by $\frac{4}{4}$ .

$\frac{69}{32} + \frac{19}{8} \cdot \frac{4}{4} + \frac{84}{16}$

Step 7.2

Multiply $\frac{19}{8}$ by $\frac{4}{4}$ .

$\frac{69}{32} + \frac{19 \cdot 4}{8 \cdot 4} + \frac{84}{16}$

Step 7.3

Multiply $\frac{84}{16}$ by $\frac{2}{2}$ .

$\frac{69}{32} + \frac{19 \cdot 4}{8 \cdot 4} + \frac{84}{16} \cdot \frac{2}{2}$

Step 7.4

Multiply $\frac{84}{16}$ by $\frac{2}{2}$ .

$\frac{69}{32} + \frac{19 \cdot 4}{8 \cdot 4} + \frac{84 \cdot 2}{16 \cdot 2}$

Step 7.5

Reorder the factors of $8 \cdot 4$ .

$\frac{69}{32} + \frac{19 \cdot 4}{4 \cdot 8} + \frac{84 \cdot 2}{16 \cdot 2}$

Step 7.6

Multiply $4$ by $8$ .

$\frac{69}{32} + \frac{19 \cdot 4}{32} + \frac{84 \cdot 2}{16 \cdot 2}$

Step 7.7

Reorder the factors of $16 \cdot 2$ .

$\frac{69}{32} + \frac{19 \cdot 4}{32} + \frac{84 \cdot 2}{2 \cdot 16}$

Step 7.8

Multiply $2$ by $16$ .

$\frac{69}{32} + \frac{19 \cdot 4}{32} + \frac{84 \cdot 2}{32}$

Step 8

Combine the numerators over the common denominator.

$\frac{69 + 19 \cdot 4 + 84 \cdot 2}{32}$

Step 9

Simplify each term.

Tap for more steps...

Step 9.1

Multiply $19$ by $4$ .

$\frac{69 + 76 + 84 \cdot 2}{32}$

Step 9.2

Multiply $84$ by $2$ .

$\frac{69 + 76 + 168}{32}$

Step 10

Simplify by adding numbers.

Tap for more steps...

Step 10.1

Add $69$ and $76$ .

$\frac{145 + 168}{32}$

Step 10.2

Add $145$ and $168$ .

$\frac{313}{32}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{313}{32}$

Decimal Form:

$9.78125$

Mixed Number Form:

$9 \frac{25}{32}$