ATI TEAS Version 7 Mathematics Numbers and Algebra (How to Get the Perfect Score)

This paragraph introduces the ATIT (Advanced Trauma and Injury Treatment) Mathematics exam, specifically the version 7. It covers the objectives and the two main parts of the exam, with the focus on the first part: numbers and algebra. The paragraph outlines the 18 out of 34 questions that will be encountered, which include converting fractions, decimals, and percentages; performing arithmetic operations; comparing and ordering rational numbers; solving equations with one variable; and applying estimation strategies and rounding rules to word problems. It also mentions the use of proportions, ratios, rates of change, expressions, equations, and inequalities.

This section delves into the fundamentals of fractions, decimals, and percentages. It explains how fractions are written and their relationship to division, with examples provided. The paragraph also covers how to convert fractions to decimals by division and to percentages by multiplying by 100. The concept of place values in decimals and the process of identifying and calculating percentages are thoroughly explained, with an emphasis on moving decimal places to convert between these forms.

This paragraph continues the discussion on numerical conversions, focusing on the methods to convert fractions to decimals and vice versa. It explains the process of dividing the numerator by the denominator to convert a fraction to a decimal and then multiplying by 100 to convert it to a percentage. The reverse process of converting decimals to fractions by dividing by place values is also detailed, along with simplifying fractions to their lowest terms. The paragraph concludes with converting percentages to decimals and fractions, emphasizing the importance of moving decimal places correctly.

The order of operations (PEMDAS) is introduced, explaining the sequence in which mathematical operations should be performed. This includes handling parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (also from left to right). The paragraph provides examples of multi-step problems that demonstrate the application of these rules, including dealing with parentheses and exponents in various combinations.

This section distinguishes between rational and irrational numbers. Rational numbers are those that can be expressed as a fraction of two integers, with examples provided, such as negative one-half and three-fourths. Irrational numbers, on the other hand, cannot be expressed as fractions, with examples including Pi and the square root of 16. The paragraph also discusses how to order rational numbers from least to greatest and vice versa, emphasizing the use of decimals for clarity during exams.

The paragraph discusses how to compare rational numbers using number lines and various symbols like greater than, less than, and equal to. It introduces inverse arithmetic operations, explaining that the inverse of addition is subtraction, and the inverse of multiplication is division. The concept is applied to solving simple equations with one variable, demonstrating how to isolate the variable using these inverse operations.

This section focuses on solving equations with one variable, starting with identifying terms such as constants, variables, and coefficients. It then moves on to solving proportional relationships and inequalities with one variable, using inverse arithmetic to isolate the variable. The paragraph provides examples of solving equations step by step, emphasizing the importance of checking the solution by substituting it back into the original equation.

The paragraph outlines a step-by-step approach to solving word problems, emphasizing the importance of reading the problem carefully, identifying given and needed information, determining the problem type, setting up the correct equation, and checking the work. An example of a word problem involving a plumber's service charge is provided, demonstrating how to apply the steps to find the total cost.

This section addresses word problems that involve percentages, which represent a fraction of 100. It explains how to solve problems involving percentage increases or decreases by identifying the original amount, the percentage change, and the new amount. Examples are given, including a store discount and a population increase, demonstrating how to set up and solve equations to find the new amounts after the percentage change.

The paragraph introduces the metric system, which is widely used in healthcare for measurements of length, weight, volume, and temperature. It emphasizes the importance of area and volume measurements in square and cubic units, respectively. The section also covers estimation and rounding of numbers to improve speed and accuracy in math problems, providing examples of rounding to the nearest whole number based on the value in the tenths place.

This section explains how to solve word problems using proportions, which are ratios that equal another ratio. The steps for solving proportions include reading the problem, drawing a diagram, determining the unknown quantity, identifying equivalent ratios, writing a proportion, and cross-multiplying to solve. An example of a shelter with dogs and cats is given to illustrate the process. The paragraph also distinguishes between direct proportions, where the relationship is constant (Y = kX), and non-direct proportions, where an additional constant is involved.

The paragraph discusses the use of ratios and rates of change to solve problems. It defines a ratio as a comparison of two numbers by division and a rate as a ratio used to compare different units. The unit rate is found by simplifying a ratio to one unit, and the rate of change represents the speed of change in a quantity. Examples are provided to show how these concepts can be applied to solve problems, such as predicting future populations based on average rates of change.

This final paragraph covers the concepts of expressions, equations, and inequalities. Expressions are mathematical phrases without an equal sign, while equations include an equal sign and represent a balanced state. Inequalities, on the other hand, use symbols like greater than or less than to show a relationship where one value is not equal to another. The paragraph explains how to solve inequalities, emphasizing the importance of inverse arithmetic and the rules for reversing inequality signs when multiplying or dividing by negative numbers.