Hesi A2 Math| EVERYTHING YOU NEED TO KNOW ! |Full Review|

The video introduces a comprehensive review for the HESI A2 mathematics section, advising students taking TEAS or Kaplan exams to follow along as much of the math content is universal. It outlines the test format, including the provision of scratch paper, pencil, and a digital calculator, and lists the basic math skills covered, such as fractions, decimals, Roman numerals, percentages, and algebra. The importance of understanding mathematical vocabulary is emphasized for correctly interpreting problems.

The video defines essential math terms, explaining an exponent as a number indicating multiplication times (e.g., 25 to the second power means 25*25). An expression is a mathematical sentence with constants and variables (e.g., 3x-4). A factor divides evenly into another number. A fraction bar separates the numerator (top) and denominator (bottom). An improper fraction has a numerator greater than or equal to the denominator (e.g., 25/5). Least Common Denominator (LCD) is the smallest common multiple of two numbers (e.g., 15 for 3 and 5). Other terms defined include common denominator, constant, digit (0-9), dividend, divisor, remainder, terminating decimal, and variable.

This section covers basic arithmetic operations, reminding viewers that a calculator will be provided on the HESI exam. Examples include subtraction (12 - 8.99 = 3.01), multiplication (23 * 5 = 115), and division (672 / 6 = 112). The presenter demonstrates how to use a calculator and suggests working backward from answer options for division problems if unsure. A long division example for 672 / 6 is shown using the DMSB (Divide, Multiply, Subtract, Bring down) acronym.

The video reviews decimal arithmetic, showing how to align numbers for addition (2.61 + 3.1 = 5.71, 12.37 + 5.00 = 17.37) and multiplication (3.41 * 7 = 23.87, 0.002 * 3.4 = 0.0068). Emphasis is placed on careful decimal placement during calculations.

This part explains Roman numeral values: I=1, V=5, X=10, L=50, C=100, D=500, M=1000. It covers rules for addition (VI = 6) and subtraction (IV = 4, where a smaller numeral precedes a larger one). The concept of a 'vinculum' or horizontal bar above numerals to indicate multiplication by 1,000 for larger numbers is introduced (e.g., becomes 5,000). Several practice problems, including complex ones, are demonstrated for conversion to Hindu-Arabic numerals.

The video outlines crucial metric conversions for length, volume, and weight. Key conversions include 1 km = 1,000 m, 1 m = 100 cm, 1 gal = 128 oz or 4 quarts, 1 oz = 30 ml, 1 kg = 1,000 g, and 2.2 lb = 1 kg. A visual aid (Gallon Man) is used to illustrate gallon-to-quart-to-pint-to-cup relationships. The mnemonic 'King Henry Died by Drinking Chocolate Milk' (Kilo, Hecto, Deca, Basic Unit, Deci, Centi, Milli) is presented as a tool for metric unit conversion by shifting the decimal point.

Using the 'King Henry' mnemonic, the video provides examples for converting between metric units: 0.73 kg to grams (730 g), 5.0 L to milliliters (5,000 mL), 4.6 cm to millimeters (46 mm), and 0.12 cm to kilometers (0.0000012 km). The process involves moving the decimal point based on the number of steps between units on the mnemonic scale.

This section covers conversions between standard units like miles, yards, and feet, and also kilograms, pounds, and grams. It's noted that conversion factors may be provided on the HESI. The method involves setting up proportions to solve for the unknown value. Examples include converting miles to yards, yards to miles, feet to yards, and vice-versa. For weight, explicit rules are given for multiplying or dividing by 2.2 for pounds/kilograms and by 1,000 for grams/kilograms, followed by practice problems.

Important rules for fractions are highlighted: for addition and subtraction, denominators must be the same; for multiplication, multiply straight across; for division, flip the second fraction and then multiply. Examples for finding the Least Common Denominator (LCD) are shown (e.g., LCD of 4 and 9 is 36, LCD of 8 and 12 is 24). Fraction addition problems are demonstrated, including those with different denominators where finding the LCD is necessary.

Fraction subtraction examples are provided, emphasizing the need for common denominators. A complex mixed fraction subtraction problem (25 1/7 - 12 5/7) illustrates the concept of 'borrowing' from the whole number to avoid negative fractions. A word problem involving cutting a board is translated into a subtraction fraction problem, solved by finding the LCD. Another mixed fraction subtraction problem (5 2/3 - 3 4/5) further demonstrates the borrowing technique after finding a common denominator.

Fraction division is explained by the rule: flip the second fraction and multiply. Examples include (4/5) / (1/7) and (12/15) / (3/5). The results are often improper fractions, which are then converted to mixed numbers using long division and reduced to their lowest terms. A specific example demonstrates simplifying 60/45 to 1 1/3. Division of a whole number by a mixed fraction and a mixed fraction by a whole number are also covered, requiring conversion to improper fractions.

Fraction multiplication is straightforward: multiply numerators and denominators straight across. Examples include (3/5) * (2/3) and (7/9) * (1/9). The video shows how to reduce fractions to their lowest terms after multiplication. It also covers multiplying a whole number by a fraction and a mixed fraction by a whole number, converting whole numbers to fractions (e.g., 6/1) and mixed fractions to improper fractions first.

This section explains how to convert fractions to decimals using a calculator (e.g., 3/4 = 0.75) or manual long division. The long division method for 3/4 is meticulously demonstrated, adding a decimal point and zeros to the numerator. Another example, 5/8, is also converted using long division. For repeating decimals like 2/3 (0.666...), it's noted how to represent them (e.g., 0.6 with a bar over it).

To convert decimals to fractions, understanding place values is crucial. The last digit's place value determines the denominator (e.g., 0.02, the 2 is in the hundredths place, so it's 2/100). Examples include converting 0.02 (reduces to 1/50), 0.9 (9/10), 0.08 (reduces to 2/25), and 3.055 (becomes 3 11/200). The integral part of the decimal becomes the whole number in a mixed fraction.

Converting fractions to ratios involves simply replacing the fraction bar with a colon (e.g., 3/4 becomes 3:4). For proportions involving an unknown (x), they are set up as equal fractions, and cross-multiplication and division are used to solve for x. Several practice problems for solving proportions are demonstrated, including a word problem involving chips and cost, solved using two different proportional methods.

To convert decimals to percentages, move the decimal point two places to the right and add a percentage sign (e.g., 0.13 becomes 13%). For fractions, divide the numerator by the denominator and then multiply by 100 (e.g., 9/10 becomes 90%). The video shows examples like 0.002 to 0.2% and 5/6 to 83.33%.

Understanding the wording of percentage problems is key. For 'What is X out of Y as a percentage?', set up as X/Y = X/100 and cross-multiply (e.g., 15 out of 75 = 20%). For 'What is X of Y?', set up as X/Y = Given Percent/100 (e.g., What is 28 of 100 is 28). For 'X is Y% of what number?', set up as X/Unknown = Y/100 (e.g., 65 is 25% of what number is 260). Distinct formulas for each type of problem are presented.

Algebra fundamentals begin with the order of operations (Please Excuse My Dear Aunt Sally: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Integer rules for multiplication and division are reviewed (positive*positive=positive, negative*negative=positive, positive*negative=negative). For algebraic expressions, when dividing, subtract exponents; when multiplying, add exponents. Examples of dividing and multiplying monomials are worked through, demonstrating exponent rules and simplification.

Examples of solving for a variable in an equation (e.g., -7k - 4 = -21) are shown, emphasizing isolating the variable by performing inverse operations on both sides. Evaluating algebraic expressions (e.g., -xy(x-y)+y with given values for x and y) involves substituting the values and following the order of operations. The importance of writing out each step on scratch paper is highlighted.

Simplifying complex algebraic expressions, particularly those involving multiplication of monomials with multiple variables, is demonstrated. The strategy of counting the total exponents for each variable before combining coefficients is used. The FOIL method (First, Outer, Inner, Last) is introduced for multiplying two binomials (e.g., (5x+2)(3x+3)), leading to combining like terms for the final simplified expression.

The video explains how to convert between 12-hour clock time and military time. AM times in military format usually have a leading zero (e.g., 4 AM is 0400). PM times are found by adding 12 to the regular time (e.g., 4 PM is 1600). Special attention is given to 12 AM (0000 or 2400) and 12 PM (1200). Practice questions involve converting both directions, highlighting the common confusion points.