By Fatskills Exam Guides Team — the exam nerds behind 28,500+ quizzes and 2.1M practice questions across 500+ global exams.
A fraction is a way to represent a part of a whole as a ratio of two integers. A decimal is a way to represent a number using a base-10 system with a dot as the separator. A percentage is a way to represent a value as a part of 100. Conversions and comparisons between these three types of numbers are essential in various fields, such as finance, science, and engineering.
Fractions, decimals, and percentages are used extensively in data analysis, science, engineering, economics, and decision-making. For instance, in finance, interest rates are often expressed as percentages, while stock prices are often displayed as decimals. In science, measurements are often reported as decimals, while percentages are used to express probabilities or changes in values.
Fractions are equivalent if they represent the same ratio. For example, $\frac{1}{2}$ and $\frac{2}{4}$ are equivalent fractions.
Decimals can be converted to fractions by writing the decimal as a fraction with a denominator of the form $10^b$, where $b$ is the number of digits after the decimal point. For example, $0.5 = \frac{5}{10} = \frac{1}{2}$.
Percentages can be converted to decimals by dividing by 100. For example, 25% = 0.25.
Fractions can be compared by converting them to equivalent decimals or by finding a common denominator.
The LCM of two numbers is the smallest number that is a multiple of both. The LCM is used to find a common denominator for fractions.
Determine whether the problem involves equivalent ratios, decimal representations, percentage conversions, or comparisons of fractions.
Write down the given information and identify the unknown quantity.
Select the method that is most suitable for the problem. For example, if the problem involves equivalent ratios, use the method of finding equivalent fractions.
Apply the chosen method to solve the problem. Show all work and explain the reasoning.
Check the answer by converting it to a different form, such as a decimal or percentage.
Convert the fraction $\frac{3}{8}$ to an equivalent fraction with a denominator of 24.
$$\frac{3}{8} \cdot \frac{3}{3} = \frac{9}{24}$$
Convert the decimal 0.375 to a fraction.
$$0.375 = \frac{375}{1000} = \frac{3}{8}$$
Convert the percentage 12.5% to a decimal.
$$12.5\% = \frac{12.5}{100} = 0.125$$
Converting a fraction to a decimal or percentage without finding a common denominator or using the wrong conversion method.
Using inconsistent units when comparing fractions, such as comparing a fraction to a decimal or percentage.
Failing to find a common denominator when comparing fractions.
Practice converting fractions to decimals and percentages, and vice versa.
Use a calculator to check your answers and ensure accuracy.
Check your work by converting the answer to a different form.
Use graphing calculators to check your answers and visualize data.
Use statistical software to analyze data and perform calculations.
Use symbolic math tools to solve equations and perform calculations.
Stock prices are often displayed as decimals, while interest rates are expressed as percentages.
Measurements are often reported as decimals, while percentages are used to express probabilities or changes in values.
Design specifications are often expressed as fractions or decimals, while tolerances are expressed as percentages.
What is the decimal representation of the fraction $\frac{3}{8}$? A) 0.25 B) 0.375 C) 0.5 D) 0.625
What is the percentage equivalent of the decimal 0.125? A) 10% B) 12.5% C) 15% D) 20%
What is the fraction equivalent of the percentage 25%? A) $\frac{1}{4}$ B) $\frac{1}{2}$ C) $\frac{2}{3}$ D) $\frac{3}{4}$
Ratios and proportions are used to compare quantities and express relationships between variables.
Algebraic expressions are used to represent equations and inequalities.
Calculus is used to study rates of change and accumulation.
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