Pre-Algebra Examples

$- 7 \frac{1}{11} \cdot 5 \frac{1}{24}$

Step 1

Convert $7 \frac{1}{11}$ to an improper fraction.

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Step 1.1

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

$- (7 + \frac{1}{11}) \cdot 5 \frac{1}{24}$

Step 1.2

Add $7$ and $\frac{1}{11}$ .

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Step 1.2.1

To write $7$ as a fraction with a common denominator, multiply by $\frac{11}{11}$ .

$- (7 \cdot \frac{11}{11} + \frac{1}{11}) \cdot 5 \frac{1}{24}$

Step 1.2.2

Combine $7$ and $\frac{11}{11}$ .

$- (\frac{7 \cdot 11}{11} + \frac{1}{11}) \cdot 5 \frac{1}{24}$

Step 1.2.3

Combine the numerators over the common denominator.

$- \frac{7 \cdot 11 + 1}{11} \cdot 5 \frac{1}{24}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $7$ by $11$ .

$- \frac{77 + 1}{11} \cdot 5 \frac{1}{24}$

Step 1.2.4.2

Add $77$ and $1$ .

$- \frac{78}{11} \cdot 5 \frac{1}{24}$

Step 2

Convert $5 \frac{1}{24}$ to an improper fraction.

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Step 2.1

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

$- \frac{78}{11} \cdot (5 + \frac{1}{24})$

Step 2.2

Add $5$ and $\frac{1}{24}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{24}{24}$ .

$- \frac{78}{11} \cdot (5 \cdot \frac{24}{24} + \frac{1}{24})$

Step 2.2.2

Combine $5$ and $\frac{24}{24}$ .

$- \frac{78}{11} \cdot (\frac{5 \cdot 24}{24} + \frac{1}{24})$

Step 2.2.3

Combine the numerators over the common denominator.

$- \frac{78}{11} \cdot \frac{5 \cdot 24 + 1}{24}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $24$ .

$- \frac{78}{11} \cdot \frac{120 + 1}{24}$

Step 2.2.4.2

Add $120$ and $1$ .

$- \frac{78}{11} \cdot \frac{121}{24}$

Step 3

Cancel the common factor of $6$ .

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Step 3.1

Move the leading negative in $- \frac{78}{11}$ into the numerator.

$\frac{- 78}{11} \cdot \frac{121}{24}$

Step 3.2

Factor $6$ out of $- 78$ .

$\frac{6 (- 13)}{11} \cdot \frac{121}{24}$

Step 3.3

Factor $6$ out of $24$ .

$\frac{6 \cdot - 13}{11} \cdot \frac{121}{6 \cdot 4}$

Step 3.4

Cancel the common factor.

$\frac{6 \cdot - 13}{11} \cdot \frac{121}{6 \cdot 4}$

Step 3.5

Rewrite the expression.

$\frac{- 13}{11} \cdot \frac{121}{4}$

Step 4

Cancel the common factor of $11$ .

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Step 4.1

Factor $11$ out of $121$ .

$\frac{- 13}{11} \cdot \frac{11 (11)}{4}$

Step 4.2

Cancel the common factor.

$\frac{- 13}{11} \cdot \frac{11 \cdot 11}{4}$

Step 4.3

Rewrite the expression.

$- 13 \cdot \frac{11}{4}$

Step 5

Combine $- 13$ and $\frac{11}{4}$ .

$\frac{- 13 \cdot 11}{4}$

Step 6

Simplify the expression.

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Step 6.1

Multiply $- 13$ by $11$ .

$\frac{- 143}{4}$

Step 6.2

Move the negative in front of the fraction.

$- \frac{143}{4}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$- \frac{143}{4}$

Decimal Form:

$- 35.75$

Mixed Number Form:

$- 35 \frac{3}{4}$