Basic Math Examples

$10 = (\frac{10 - y (1 + 0.0004)}{1 - 0.5 \cdot 10^{- 3}}) + y (1 + 0.0004)$

Step 1

Rewrite the equation as $\frac{10 - y (1 + 0.0004)}{1 - 0.5 \cdot 10^{- 3}} + y (1 + 0.0004) = 10$ .

$\frac{10 - y (1 + 0.0004)}{1 - 0.5 \cdot 10^{- 3}} + y (1 + 0.0004) = 10$

Step 2

Simplify $\frac{10 - y (1 + 0.0004)}{1 - 0.5 \cdot 10^{- 3}} + y (1 + 0.0004)$ .

Tap for more steps...

Step 2.1

Convert $1$ to scientific notation.

$\frac{10 - y (1 + 0.0004)}{1 \cdot 10^{0} - 0.5 \cdot 10^{- 3}} + y (1 + 0.0004) = 10$

Step 2.2

Move the decimal point in $- 0.5$ to the left by $3$ places and increase the power of $10^{- 3}$ by $3$ .

$\frac{10 - y (1 + 0.0004)}{1 \cdot 10^{0} - 0.0005 \cdot 10^{0}} + y (1 + 0.0004) = 10$

Step 2.3

Factor $10^{0}$ out of $1 \cdot 10^{0} - 0.0005 \cdot 10^{0}$ .

$\frac{10 - y (1 + 0.0004)}{(1 - 0.0005) \cdot 10^{0}} + y (1 + 0.0004) = 10$

Step 2.4

Subtract $0.0005$ from $1$ .

$\frac{10 - y (1 + 0.0004)}{0.9995 \cdot 10^{0}} + y (1 + 0.0004) = 10$

Step 2.5

Move the decimal point in $0.9995$ to the right by $1$ place and decrease the power of $10^{0}$ by $1$ .

$\frac{10 - y (1 + 0.0004)}{9.995 \cdot 10^{- 1}} + y (1 + 0.0004) = 10$

Step 2.6

Add $1$ and $0.0004$ .

$\frac{10 - y \cdot 1.0004}{9.995 \cdot 10^{- 1}} + y (1 + 0.0004) = 10$

Step 2.7

Simplify each term.

Tap for more steps...

Step 2.7.1

Move $10^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{(10 - y \cdot 1.0004) \cdot 10}{9.995} + y (1 + 0.0004) = 10$

Step 2.7.2

Simplify the numerator.

Tap for more steps...

Step 2.7.2.1

Multiply $1.0004$ by $- 1$ .

$\frac{(10 - 1.0004 y) \cdot 10}{9.995} + y (1 + 0.0004) = 10$

Step 2.7.2.2

Factor $0.0004$ out of $10 - 1.0004 y$ .

Tap for more steps...

Step 2.7.2.2.1

Factor $0.0004$ out of $10$ .

$\frac{(0.0004 (25000) - 1.0004 y) \cdot 10}{9.995} + y (1 + 0.0004) = 10$

Step 2.7.2.2.2

Factor $0.0004$ out of $- 1.0004 y$ .

$\frac{(0.0004 (25000) + 0.0004 (- 2501 y)) \cdot 10}{9.995} + y (1 + 0.0004) = 10$

Step 2.7.2.2.3

Factor $0.0004$ out of $0.0004 (25000) + 0.0004 (- 2501 y)$ .

$\frac{0.0004 (25000 - 2501 y) \cdot 10}{9.995} + y (1 + 0.0004) = 10$

Step 2.7.2.3

Multiply $10$ by $0.0004$ .

$\frac{0.004 (25000 - 2501 y)}{9.995} + y (1 + 0.0004) = 10$

Step 2.7.3

Factor $9.995$ out of $9.995$ .

$\frac{0.004 (25000 - 2501 y)}{9.995 (1)} + y (1 + 0.0004) = 10$

Step 2.7.4

Separate fractions.

$\frac{0.004}{9.995} \cdot \frac{25000 - 2501 y}{1} + y (1 + 0.0004) = 10$

Step 2.7.5

Divide $0.004$ by $9.995$ .

$0.0004002 \frac{25000 - 2501 y}{1} + y (1 + 0.0004) = 10$

Step 2.7.6

Divide $25000 - 2501 y$ by $1$ .

$0.0004002 (25000 - 2501 y) + y (1 + 0.0004) = 10$

Step 2.7.7

Apply the distributive property.

$0.0004002 \cdot 25000 + 0.0004002 (- 2501 y) + y (1 + 0.0004) = 10$

Step 2.7.8

Multiply $0.0004002$ by $25000$ .

$10.0050025 + 0.0004002 (- 2501 y) + y (1 + 0.0004) = 10$

Step 2.7.9

Multiply $- 2501$ by $0.0004002$ .

$10.0050025 - 1.00090045 y + y (1 + 0.0004) = 10$

Step 2.7.10

Add $1$ and $0.0004$ .

$10.0050025 - 1.00090045 y + y \cdot 1.0004 = 10$

Step 2.7.11

Move $1.0004$ to the left of $y$ .

$10.0050025 - 1.00090045 y + 1.0004 y = 10$

Step 2.8

Add $- 1.00090045 y$ and $1.0004 y$ .

$10.0050025 - 0.00050045 y = 10$

Step 3

Move all terms not containing $y$ to the right side of the equation.

Tap for more steps...

Step 3.1

Subtract $10.0050025$ from both sides of the equation.

$- 0.00050045 y = 10 - 10.0050025$

Step 3.2

Subtract $10.0050025$ from $10$ .

$- 0.00050045 y = - 0.0050025$

Step 4

Divide each term in $- 0.00050045 y = - 0.0050025$ by $- 0.00050045$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $- 0.00050045 y = - 0.0050025$ by $- 0.00050045$ .

$\frac{- 0.00050045 y}{- 0.00050045} = \frac{- 0.0050025}{- 0.00050045}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $- 0.00050045$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{- 0.00050045 y}{- 0.00050045} = \frac{- 0.0050025}{- 0.00050045}$

Step 4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 0.0050025}{- 0.00050045}$

Step 4.3

Simplify the right side.

Tap for more steps...

Step 4.3.1

Divide $- 0.0050025$ by $- 0.00050045$ .

$y = 9.99600159$