Solve for c c÷1 11/16=4/9

$c \div 1 \frac{11}{16} = \frac{4}{9}$

Step 1

Simplify the left side.

Simplify $c \div 1 \frac{11}{16}$ .

Convert $1 \frac{11}{16}$ to an improper fraction.

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

$c \div (1 + \frac{11}{16}) = \frac{4}{9}$

Add $1$ and $\frac{11}{16}$ .

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

$c \div (\frac{16}{16} + \frac{11}{16}) = \frac{4}{9}$

Combine the numerators over the common denominator.

$c \div \frac{16 + 11}{16} = \frac{4}{9}$

Add $16$ and $11$ .

$c \div \frac{27}{16} = \frac{4}{9}$

To divide by a fraction, multiply by its reciprocal.

$c \frac{16}{27} = \frac{4}{9}$

Combine $c$ and $\frac{16}{27}$ .

$\frac{c \cdot 16}{27} = \frac{4}{9}$

Move $16$ to the left of $c$ .

$\frac{16 c}{27} = \frac{4}{9}$

Step 2

Multiply both sides of the equation by $\frac{27}{16}$ .

$\frac{27}{16} \cdot \frac{16 c}{27} = \frac{27}{16} \cdot \frac{4}{9}$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{27}{16} \cdot \frac{16 c}{27}$ .

Cancel the common factor of $27$ .

Cancel the common factor.

$\frac{27}{16} \cdot \frac{16 c}{27} = \frac{27}{16} \cdot \frac{4}{9}$

Rewrite the expression.

$\frac{1}{16} (16 c) = \frac{27}{16} \cdot \frac{4}{9}$

Cancel the common factor of $16$ .

Factor $16$ out of $16 c$ .

$\frac{1}{16} (16 (c)) = \frac{27}{16} \cdot \frac{4}{9}$

Cancel the common factor.

$\frac{1}{16} (16 c) = \frac{27}{16} \cdot \frac{4}{9}$

Rewrite the expression.

$c = \frac{27}{16} \cdot \frac{4}{9}$

Simplify the right side.

Simplify $\frac{27}{16} \cdot \frac{4}{9}$ .

Cancel the common factor of $9$ .

Factor $9$ out of $27$ .

$c = \frac{9 (3)}{16} \cdot \frac{4}{9}$

Cancel the common factor.

$c = \frac{9 \cdot 3}{16} \cdot \frac{4}{9}$

Rewrite the expression.

$c = \frac{3}{16} \cdot 4$

Cancel the common factor of $4$ .

Factor $4$ out of $16$ .

$c = \frac{3}{4 (4)} \cdot 4$

Cancel the common factor.

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

Rewrite the expression.

$c = \frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$c = \frac{3}{4}$

Decimal Form:

$c = 0.75$

Solve for c c÷1 11/16=4/9

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