Solve for b 5/6b=1 7/8

$\frac{5}{6} b = 1 \frac{7}{8}$

Simplify the left side.

Combine $\frac{5}{6}$ and $b$ .

$\frac{5 b}{6} = 1 \frac{7}{8}$

Simplify the right side.

Convert $1 \frac{7}{8}$ to an improper fraction.

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

$\frac{5 b}{6} = 1 + \frac{7}{8}$

Add $1$ and $\frac{7}{8}$ .

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

$\frac{5 b}{6} = \frac{8}{8} + \frac{7}{8}$

Combine the numerators over the common denominator.

$\frac{5 b}{6} = \frac{8 + 7}{8}$

Add $8$ and $7$ .

$\frac{5 b}{6} = \frac{15}{8}$

Multiply both sides of the equation by $\frac{6}{5}$ .

$\frac{6}{5} \cdot \frac{5 b}{6} = \frac{6}{5} \cdot \frac{15}{8}$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{6}{5} \cdot \frac{5 b}{6}$ .

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6}{5} \cdot \frac{5 b}{6} = \frac{6}{5} \cdot \frac{15}{8}$

Rewrite the expression.

$\frac{1}{5} (5 b) = \frac{6}{5} \cdot \frac{15}{8}$

Cancel the common factor of $5$ .

Factor $5$ out of $5 b$ .

$\frac{1}{5} (5 (b)) = \frac{6}{5} \cdot \frac{15}{8}$

Cancel the common factor.

$\frac{1}{5} (5 b) = \frac{6}{5} \cdot \frac{15}{8}$

Rewrite the expression.

$b = \frac{6}{5} \cdot \frac{15}{8}$

Simplify the right side.

Simplify $\frac{6}{5} \cdot \frac{15}{8}$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$b = \frac{2 (3)}{5} \cdot \frac{15}{8}$

Factor $2$ out of $8$ .

$b = \frac{2 \cdot 3}{5} \cdot \frac{15}{2 \cdot 4}$

Cancel the common factor.

$b = \frac{2 \cdot 3}{5} \cdot \frac{15}{2 \cdot 4}$

Rewrite the expression.

$b = \frac{3}{5} \cdot \frac{15}{4}$

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$b = \frac{3}{5} \cdot \frac{5 (3)}{4}$

Cancel the common factor.

$b = \frac{3}{5} \cdot \frac{5 \cdot 3}{4}$

Rewrite the expression.

$b = 3 (\frac{3}{4})$

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

$b = \frac{3 \cdot 3}{4}$

Multiply $3$ by $3$ .

$b = \frac{9}{4}$

The result can be shown in multiple forms.

Exact Form:

$b = \frac{9}{4}$

Decimal Form:

$b = 2.25$

Mixed Number Form:

$b = 2 \frac{1}{4}$

Solve for b 5/6b=1 7/8

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