Algebra Examples

$(6 \frac{5}{6} - 5 \frac{3}{8}) \div \frac{7}{48}$

Step 1

Convert $6 \frac{5}{6}$ to an improper fraction.

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Step 1.1

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

$(6 + \frac{5}{6} - 5 \frac{3}{8}) \div \frac{7}{48}$

Step 1.2

Add $6$ and $\frac{5}{6}$ .

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Step 1.2.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$(6 \cdot \frac{6}{6} + \frac{5}{6} - 5 \frac{3}{8}) \div \frac{7}{48}$

Step 1.2.2

Combine $6$ and $\frac{6}{6}$ .

$(\frac{6 \cdot 6}{6} + \frac{5}{6} - 5 \frac{3}{8}) \div \frac{7}{48}$

Step 1.2.3

Combine the numerators over the common denominator.

$(\frac{6 \cdot 6 + 5}{6} - 5 \frac{3}{8}) \div \frac{7}{48}$

Step 1.2.4

Simplify the numerator.

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Step 1.2.4.1

Multiply $6$ by $6$ .

$(\frac{36 + 5}{6} - 5 \frac{3}{8}) \div \frac{7}{48}$

Step 1.2.4.2

Add $36$ and $5$ .

$(\frac{41}{6} - 5 \frac{3}{8}) \div \frac{7}{48}$

Step 2

Convert $5 \frac{3}{8}$ to an improper fraction.

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Step 2.1

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

$(\frac{41}{6} - (5 + \frac{3}{8})) \div \frac{7}{48}$

Step 2.2

Add $5$ and $\frac{3}{8}$ .

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Step 2.2.1

To write $5$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$(\frac{41}{6} - (5 \cdot \frac{8}{8} + \frac{3}{8})) \div \frac{7}{48}$

Step 2.2.2

Combine $5$ and $\frac{8}{8}$ .

$(\frac{41}{6} - (\frac{5 \cdot 8}{8} + \frac{3}{8})) \div \frac{7}{48}$

Step 2.2.3

Combine the numerators over the common denominator.

$(\frac{41}{6} - \frac{5 \cdot 8 + 3}{8}) \div \frac{7}{48}$

Step 2.2.4

Simplify the numerator.

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Step 2.2.4.1

Multiply $5$ by $8$ .

$(\frac{41}{6} - \frac{40 + 3}{8}) \div \frac{7}{48}$

Step 2.2.4.2

Add $40$ and $3$ .

$(\frac{41}{6} - \frac{43}{8}) \div \frac{7}{48}$

Step 3

To divide by a fraction, multiply by its reciprocal.

$(\frac{41}{6} - \frac{43}{8}) \frac{48}{7}$

Step 4

To write $\frac{41}{6}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$(\frac{41}{6} \cdot \frac{4}{4} - \frac{43}{8}) \frac{48}{7}$

Step 5

To write $- \frac{43}{8}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$(\frac{41}{6} \cdot \frac{4}{4} - \frac{43}{8} \cdot \frac{3}{3}) \frac{48}{7}$

Step 6

Write each expression with a common denominator of $24$ , by multiplying each by an appropriate factor of $1$ .

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Step 6.1

Multiply $\frac{41}{6}$ by $\frac{4}{4}$ .

$(\frac{41 \cdot 4}{6 \cdot 4} - \frac{43}{8} \cdot \frac{3}{3}) \frac{48}{7}$

Step 6.2

Multiply $6$ by $4$ .

$(\frac{41 \cdot 4}{24} - \frac{43}{8} \cdot \frac{3}{3}) \frac{48}{7}$

Step 6.3

Multiply $\frac{43}{8}$ by $\frac{3}{3}$ .

$(\frac{41 \cdot 4}{24} - \frac{43 \cdot 3}{8 \cdot 3}) \frac{48}{7}$

Step 6.4

Multiply $8$ by $3$ .

$(\frac{41 \cdot 4}{24} - \frac{43 \cdot 3}{24}) \frac{48}{7}$

Step 7

Combine the numerators over the common denominator.

$\frac{41 \cdot 4 - 43 \cdot 3}{24} \cdot \frac{48}{7}$

Step 8

Simplify the numerator.

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Step 8.1

Multiply $41$ by $4$ .

$\frac{164 - 43 \cdot 3}{24} \cdot \frac{48}{7}$

Step 8.2

Multiply $- 43$ by $3$ .

$\frac{164 - 129}{24} \cdot \frac{48}{7}$

Step 8.3

Subtract $129$ from $164$ .

$\frac{35}{24} \cdot \frac{48}{7}$

Step 9

Cancel the common factor of $7$ .

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Step 9.1

Factor $7$ out of $35$ .

$\frac{7 (5)}{24} \cdot \frac{48}{7}$

Step 9.2

Cancel the common factor.

$\frac{7 \cdot 5}{24} \cdot \frac{48}{7}$

Step 9.3

Rewrite the expression.

$\frac{5}{24} \cdot 48$

Step 10

Cancel the common factor of $24$ .

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Step 10.1

Factor $24$ out of $48$ .

$\frac{5}{24} \cdot (24 (2))$

Step 10.2

Cancel the common factor.

$\frac{5}{24} \cdot (24 \cdot 2)$

Step 10.3

Rewrite the expression.

$5 \cdot 2$

Step 11

Multiply $5$ by $2$ .

$10$