8/12 simplifies to 2/3 by dividing both the numerator and denominator by 4. This is the simplest form of the fraction.

Subtracting 5 from 12 gives x = 7. This is a straightforward linear equation.

0.5 is equivalent to the fraction 1/2 when expressed in simplest form. Converting between decimals and fractions is a fundamental skill.

Dividing 3 by 4 gives 0.75. This conversion from a fraction to a decimal is a common calculation.

The area of a rectangle is found by multiplying the length by the width: 5 × 3 = 15. This basic geometry principle is essential for many problems.

Dividing both sides of the equation by 2 gives x - 3 = 7, and adding 3 to both sides results in x = 10. This reinforces basic algebraic manipulation.

The commutative property states that numbers can be added in any order without affecting the sum. This fundamental property is key to understanding many mathematical operations.

When multiplying exponents with the same base, you add the exponents: 2^(3+2) = 2^5, which equals 32. This tests the basic rules of exponents.

First, distribute the 3 to get 6x + 12, then subtract 2x to combine like terms, resulting in 4x + 12. This question applies distributive and combining like terms techniques.

Multiplying both sides of the equation by 4 yields 3y = 36, and then dividing by 3 gives y = 12. This reinforces solving simple linear equations.

The slope-intercept form is written as y = mx + b, where m is the slope and b is the y-intercept. This form is essential for graphing and understanding linear relationships.

The given ratio indicates that for every 3 men there are 4 women. Since 12 men represent 3 parts (with each part equal to 4), there must be 4 × 4 = 16 women.

First, simplify the expression inside the parentheses: 3 - 1 equals 2. Then, multiplying 2 by 2 gives 4, and subtracting 4 from 5 results in 1.

The fractions 3/5, 6/10, and 9/15 all simplify to 0.6, while 4/7 is approximately 0.571. This question tests the ability to recognize equivalent fractions.

The volume of a rectangular prism is calculated by multiplying its length, width, and height: 4 × 3 × 2 = 24 cubic units. This problem reinforces spatial reasoning and volume computation.

First, distribute 1/2 to get (1/2)x - 2, then add 3 to obtain (1/2)x + 1. Setting this equal to 2x - 1 and solving for x leads to x = 4/3. This problem requires careful handling of fractions and variable isolation.

In the slope-intercept form y = mx + b, the y-intercept is the constant term b. Here, the y-intercept is -5.

First, find the number by dividing 15 by 0.25, which gives 60. Then, calculate 60% of 60 by multiplying 60 by 0.6 to get 36. This problem emphasizes percentage calculations.

Expanding (2x)^3 gives 8x^3, and dividing by x^2 subtracts the exponents, resulting in 8x^(3-2) = 8x. This problem reinforces the properties of exponents.

Solve the second equation for y (y = x - 1) and substitute into the first equation to get 2x + (x - 1) = 7, which simplifies to 3x = 8 and x = 8/3. Then, substituting back gives y = 5/3. This demonstrates solving systems using substitution.