Whole Numbers and Fractions Operations

The rules of order of operations are: parentheses, exponents, multiplication and division, and finally addition and subtraction.

To solve problems involving mixed numbers, convert the mixed number to an improper fraction, perform the required operation, and then convert the result back to a mixed number.

The steps to simplify a fraction are: find the greatest common divisor (GCD) of the numerator and denominator, divide both by the GCD, and rewrite the fraction in its simplest form.

To convert a decimal to a fraction, write the decimal as a fraction with a denominator equal to a power of 10 (e.g., 10, 100, 1000), and then simplify the fraction.

Rounding off numbers is used to approximate a value to a certain degree of accuracy, making calculations easier and more efficient.

To multiply fractions, multiply the numerators (numbers on top) and multiply the denominators (numbers on the bottom), then simplify the resulting fraction.

It ensures that the solutions are meaningful and practical, and can be applied to real-world scenarios, taking into account the limitations and constraints of the problem.

Ratio and proportion enable the comparison of like and unlike quantities by providing a common basis for measurement, allowing for the identification of equivalent ratios and proportional relationships. This facilitates the solution of skill problems by enabling the calculation of unknown quantities and the identification of patterns and relationships.

Calculating percentages involves finding a percentage of a value, whereas decimal equivalents involve converting a percentage to a decimal value. These concepts are applied in solving real-world problems, such as calculating discounts, interest rates, and growth rates, by providing a convenient and efficient way to perform calculations.

Simple calculations involving whole numbers, fractions, and decimal numbers demonstrate an understanding of ratio and proportion by showing the ability to identify and apply equivalent ratios, and to perform calculations that involve proportional relationships.

Using percentage to solve problems provides a convenient and efficient way to perform calculations, and is particularly useful in applications involving proportions, scaling, and growth rates. This concept is closely related to ratio and proportion, as it involves the calculation of proportional relationships and equivalent ratios.

The area of the rectangular tank's surfaces in contact with the water is 2(lw + lh + wh) = 2(53 + 52 + 3*2) = 2(15 + 10 + 6) = 2(31) = 62 square meters.

The volume of the pipe is V = πr²h = π(0.5/2)²(10) = π(0.0625)(10) ≈ 1.96 cubic meters.

The volume of the prism is V = (base * height) * length = (5 * 8) * 12 = 40 * 12 = 480 cubic meters.

The circumference of the saw blade is C = 2πr = 2π(0.25) ≈ 1.57 meters.

The area of the gutter is A = (1/2)h(b1 + b2) = (1/2)(2)(3 + 5) = (1/2)(2)(8) = 8 square meters.