Pre-Algebra Examples

$49 : 35 = 77 : 55$

Step 1

Convert the ratio to a fraction by making the left side of the ratio the numerator and the right side the denominator.

$\frac{49}{35} = 77 : 55$

Step 2

Cancel the common factor of $49$ and $35$ .

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Step 2.1

Factor $7$ out of $49$ .

$\frac{7 (7)}{35} = 77 : 55$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $7$ out of $35$ .

$\frac{7 \cdot 7}{7 \cdot 5} = 77 : 55$

Step 2.2.2

Cancel the common factor.

$\frac{7 \cdot 7}{7 \cdot 5} = 77 : 55$

Step 2.2.3

Rewrite the expression.

$\frac{7}{5} = 77 : 55$

Step 3

Convert the ratio to a fraction by making the left side of the ratio the numerator and the right side the denominator.

$\frac{7}{5} = \frac{77}{55}$

Step 4

Cancel the common factor of $77$ and $55$ .

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Step 4.1

Factor $11$ out of $77$ .

$\frac{7}{5} = \frac{11 (7)}{55}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $11$ out of $55$ .

$\frac{7}{5} = \frac{11 \cdot 7}{11 \cdot 5}$

Step 4.2.2

Cancel the common factor.

$\frac{7}{5} = \frac{11 \cdot 7}{11 \cdot 5}$

Step 4.2.3

Rewrite the expression.

$\frac{7}{5} = \frac{7}{5}$

Step 5

Since $\frac{7}{5} = \frac{7}{5}$ , the equation will always be true.

Always true

Step 6

Since the fractional versions of the ratios are equal, the ratios are equivalent.

$49 : 35 = 77 : 55$