Pre-Algebra Examples

$y = 1.791 (x) + 32.64$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Change $1.791$ into a fraction.

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Step 2.1

Multiply by $\frac{1000}{1000}$ to remove the decimal.

$y = \frac{1000 \cdot 1.791}{1000} x + 32.64$

Step 2.2

Multiply $1000$ by $1.791$ .

$y = \frac{1791}{1000} x + 32.64$

Step 2.3

Cancel the common factor of $1791$ and $1000$ .

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Step 2.3.1

Rewrite $1791$ as $1 (1791)$ .

$y = \frac{1 (1791)}{1000} x + 32.64$

Step 2.3.2

Cancel the common factors.

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Step 2.3.2.1

Rewrite $1000$ as $1 (1000)$ .

$y = \frac{1 \cdot 1791}{1 \cdot 1000} x + 32.64$

Step 2.3.2.2

Cancel the common factor.

$y = \frac{1 \cdot 1791}{1 \cdot 1000} x + 32.64$

Step 2.3.2.3

Rewrite the expression.

$y = \frac{1791}{1000} x + 32.64$

Step 3

Change $32.64$ into a fraction.

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Step 3.1

Multiply by $\frac{100}{100}$ to remove the decimal.

$y = \frac{1791}{1000} x + \frac{100 \cdot 32.64}{100}$

Step 3.2

Multiply $100$ by $32.64$ .

$y = \frac{1791}{1000} x + \frac{3264}{100}$

Step 3.3

Cancel the common factor of $3264$ and $100$ .

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Step 3.3.1

Factor $4$ out of $3264$ .

$y = \frac{1791}{1000} x + \frac{4 (816)}{100}$

Step 3.3.2

Cancel the common factors.

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Step 3.3.2.1

Factor $4$ out of $100$ .

$y = \frac{1791}{1000} x + \frac{4 \cdot 816}{4 \cdot 25}$

Step 3.3.2.2

Cancel the common factor.

$y = \frac{1791}{1000} x + \frac{4 \cdot 816}{4 \cdot 25}$

Step 3.3.2.3

Rewrite the expression.

$y = \frac{1791}{1000} x + \frac{816}{25}$

Step 4

Find the LCD of $\frac{1791}{1000}$ and $\frac{816}{25}$ .

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Step 4.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$1000, 25$

Step 4.2

Since $1000, 25$ contains both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part $1000, 25$ then find LCM for the variable part .

Step 4.3

The LCM is the smallest positive number that all of the numbers divide into evenly.

1. List the prime factors of each number.

2. Multiply each factor the greatest number of times it occurs in either number.

Step 4.4

The prime factors for $1000$ are $2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5$ .

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Step 4.4.1

$1000$ has factors of $2$ and $500$ .

$2 \cdot 500$

Step 4.4.2

$500$ has factors of $2$ and $250$ .

$2 \cdot 2 \cdot 250$

Step 4.4.3

$250$ has factors of $2$ and $125$ .

$2 \cdot 2 \cdot 2 \cdot 125$

Step 4.4.4

$125$ has factors of $5$ and $25$ .

$2 \cdot 2 \cdot 2 \cdot 5 \cdot 25$

Step 4.4.5

$25$ has factors of $5$ and $5$ .

$2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5$

Step 4.5

$25$ has factors of $5$ and $5$ .

$5 \cdot 5$

Step 4.6

The LCM of $1000, 25$ is the result of multiplying all prime factors the greatest number of times they occur in either number.

$2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5$

Step 4.7

Multiply $2 \cdot 2 \cdot 2 \cdot 5 \cdot 5 \cdot 5$ .

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Step 4.7.1

Multiply $2$ by $2$ .

$4 \cdot 2 \cdot 5 \cdot 5 \cdot 5$

Step 4.7.2

Multiply $4$ by $2$ .

$8 \cdot 5 \cdot 5 \cdot 5$

Step 4.7.3

Multiply $8$ by $5$ .

$40 \cdot 5 \cdot 5$

Step 4.7.4

Multiply $40$ by $5$ .

$200 \cdot 5$

Step 4.7.5

Multiply $200$ by $5$ .

$1000$

Step 5

Multiply both sides by $1000$ .

$1000 y = 1000 (\frac{1791}{1000} x + \frac{816}{25})$

Step 6

Simplify the right side.

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Step 6.1

Simplify $1000 (\frac{1791}{1000} x + \frac{816}{25})$ .

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Step 6.1.1

Combine $\frac{1791}{1000}$ and $x$ .

$1000 y = 1000 (\frac{1791 x}{1000} + \frac{816}{25})$

Step 6.1.2

Apply the distributive property.

$1000 y = 1000 \frac{1791 x}{1000} + 1000 (\frac{816}{25})$

Step 6.1.3

Cancel the common factor of $1000$ .

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Step 6.1.3.1

Cancel the common factor.

$1000 y = 1000 \frac{1791 x}{1000} + 1000 (\frac{816}{25})$

Step 6.1.3.2

Rewrite the expression.

$1000 y = 1791 x + 1000 (\frac{816}{25})$

Step 6.1.4

Cancel the common factor of $25$ .

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Step 6.1.4.1

Factor $25$ out of $1000$ .

$1000 y = 1791 x + 25 (40) \frac{816}{25}$

Step 6.1.4.2

Cancel the common factor.

$1000 y = 1791 x + 25 \cdot 40 \frac{816}{25}$

Step 6.1.4.3

Rewrite the expression.

$1000 y = 1791 x + 40 \cdot 816$

Step 6.1.5

Multiply $40$ by $816$ .

$1000 y = 1791 x + 32640$

Step 7

Rewrite the equation.

$1791 x + 32640 = 1000 y$

Step 8

Move all terms containing variables to the left side of the equation.

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Step 8.1

Subtract $1000 y$ from both sides of the equation.

$1791 x + 32640 - 1000 y = 0$

Step 8.2

Move $32640$ .

$1791 x - 1000 y + 32640 = 0$

Step 9

Subtract $32640$ from both sides of the equation.

$1791 x - 1000 y = - 32640$

Step 10