To add the fractions, first find a common denominator, which is 6. Converting the fractions to equivalent forms gives 3/6 and 2/6, and their sum is 5/6.

Adding -3 and 7 involves combining a negative and a positive number. The positive value outweighs the negative, resulting in 4.

Adding decimals 0.5 and 0.7 gives 1.2 by summing the tenths. This demonstrates a basic addition of decimal numbers.

Multiplying 6 by 4 yields 24. This is a straightforward multiplication fact that is essential in mathematics.

Following the order of operations, multiplication is performed before addition. Multiplying 3 by 4 gives 12, then adding 2 results in 14.

Multiply the numerators (3 x 2 = 6) and the denominators (4 x 5 = 20) to obtain 6/20, which simplifies to 3/10. This question reinforces the concept of multiplying fractions.

Dividing 1/2 by 2/3 is the same as multiplying 1/2 by 3/2, which equals 3/4. This problem demonstrates how to divide fractions in a practical situation.

Dividing both sides of the equation by 3 gives x = 12/3, which simplifies to 4. This reinforces the method for solving simple linear equations.

A 20% discount on $50 amounts to 0.2 x 50 = $10 off, so subtracting the discount from the original price results in $40. This problem applies percentage calculations to find the sale price.

Dividing 3 by 5 results in 0.6, which is the decimal representation of the fraction 3/5. Converting between fractions and decimals is an important skill in math.

The area of a rectangle is calculated by multiplying its length by its width. Multiplying 8 cm by 3 cm gives an area of 24 cm².

A square has four equal sides, so its perimeter is 4 times the side length. Multiplying 5 cm by 4 gives a perimeter of 20 cm.

A ratio of 3:4 means that for every 3 boys, there are 4 girls. With 21 boys, dividing 21 by 3 gives 7, and multiplying 7 by 4 results in 28 girls.

The decimal 0.25 can be written as 25/100, which simplifies to 1/4 when reduced. This conversion is a basic exercise in relating decimals to fractions.

Calculating 2² gives 4 and 3² gives 9; adding them together results in 13. This problem reinforces the use of exponents and basic addition.

Subtracting 5 from both sides of the equation gives 2x = 12, and dividing by 2 yields x = 6. This problem strengthens skills in solving linear equations.

Average speed is calculated by dividing the total distance by the total time. Dividing 180 km by 3 hours results in an average speed of 60 km/h.

Divide both the numerator and the denominator by 8 to simplify 16/24 to 2/3. This exercise is designed to reinforce fraction reduction techniques.

Subtracting 3x from both sides gives 2x - 2 = 6. Adding 2 to both sides yields 2x = 8, so dividing by 2 results in x = 4. This problem tests the ability to solve linear equations with variables on both sides.

Let the width be x and the length be 2x. The perimeter is 2(x + 2x) which is 6x; setting 6x equal to 36 meters gives x = 6 meters. This question integrates basic algebra with geometry to determine dimensions.