ATI TEAS 7 FULL STUDY GUIDE MATH

1 kilometer = ____ meters

1,000

Steps to change a fraction to a percent.

1. divide the numerator and denominator. 2. multiply by 100 and add a percent sign.

How do you add like fractions?

Add the numerators. Example: 2/5 + 1/5 = 3/5

How do you subtract like fractions?

Subtract the numerators. Example: 8/9 - 2/9 = 6/9 = 2/3

What is the subtraction property of equality?

Subtract the same number from both sides of the equation. Example: x + a = b x + a - a = b - a x = b - a

What is the rate of change for some quantity?

The rate of change for some quantity is the ratio of the quantity's difference over a specific time period to the length of that time period. Example: if an automobile increases its speed from 50 mph to 100 mph in 10 seconds, the rate of change of its speed is 100 mph - 50 mph / 10 s = 50 mph/10 s = 5 mph/s.

The top number of a fraction is the __________________________.

numerator

What are the formulas used to convert Celsius to Fahrenheit and vice versa?

°F = 9/5(°C + 32) °C = 5/9(°F - 32)

1 cubic centimeter is equivalent to _______________.

1 milliliter

2 ways to convert a decimal to a percent.

1. multiply the decimal by 100 and add a percent sign. 2. move the decimal point 2 places to the right.

1 pint = ____ cups

2

1 quart (qt) = _____ pints (pt).

2

1 quart = ____ pints

2

1 meter (m) = _____ feet (ft).

3.28

1 cup = ___ oz

8

Formula for calculating the area of a parallelogram.

A = bh Area = base times height.

What is a percent or percentage?

A fraction of some quantity. "percent" means "per hundred."

What is an improper fraction?

A fraction where the numerator is larger than the denominator.

What is a proper fraction?

A fraction where the numerator is smaller than the denominator.

What is a proportion?

A proportion is an equation of two ratios.

What is a linear equation?

An equation where 2 expressions are set equal to each other. ax+b=c a is a non-zero constant b and c are constants the exponent on a linear equation is always 1 there is no more than one solution to a linear equation

What is the simple way for solving a binomial?

FOIL. First Outside Inside Last

How to subtract polynomials.

Rewrite the second polynomial using an additive inverse. Change the minus sign to a plus sign, and change the sign of every term inside the parentheses. Then add the polynomials.

What is the subtraction property of inequality?

Subtracting the same number from both sides of the inequality. Example: x + 3 > 9 x + 3 - 3 > 9 - 3 x > 6

What is the term "product."

The result of the multiplication operation.

T/F: A negative value squared is a positive solution.

True.

Basic formula for the rate of change of some quantity.

x(f) - x(i) / t(f) - t(i) where t(f) is the "final" (or ending) time and t(i) is the "initial" (or starting) time. x(f) is the (final) quantity at (final) time t(f). x(I) is the (initial) quantity at (initial) time t(i). The numerator is the difference between the 2 quantities. The denominator is the difference in time.

1 Kiloliter (kL) = ____ Liters (L).

1,000

1 liter (L) = _____ milliliters (mL).

1,000

1 metric ton (t) = _______ kilograms (kg).

1,000

How many meters (m) in 1 kilometer (km)?

1,000 m in 1 km.

The amount of millimeters (mm), centimeters (cm), and decimeters (dm) in 1 meter (m).

1,000 mm in 1 m. 100 cm in 1 m. 10 dm in 1 m.

1 mile (mi) = ____ yards (yd)

1,760

The 4 properties to help solve a linear equation.

1. Addition property of equality 2. Subtraction property of equality 3. Multiplication property of equality 4. Division property of equality

The following 5 steps can make solving word problems easier.

1. Read the problem for understanding. 2. Visualize the problem by drawing a picture or diagram. 3. Make a plan by writing an expression to represent the problem. 4. Solve the problem by applying mathematical techniques. 5. Check the answer to make sure it answers the question asked.

Steps to change a percent to a fraction.

1. Remove the percent sign and write the value as the numerator with a denominator of 100. 2. Simplify the fraction.

The 3 steps in solving a complex linear equation.

1. Simplify each side of the equation. This includes removing parentheses, removing fractions, and adding like terms. 2. Use addition and subtraction properties of an equation to move the variable to one side of the equation and all number terms to the other side of the equation. 3. Use multiplication and division properties of an equation to remove the value in front of the variable.

The 3 steps in solving a complex linear inequality.

1. Simplify each side of the inequality. This includes removing parentheses, removing fractions, and adding like terms. 2. Use addition and subtraction properties of an inequality to move the variable to one side of the equation and all number terms to the other side of the equation. 3. Use multiplication and division properties of an inequality to remove the value in front of the variable. Reverse the inequality sign if multiplying or dividing by a negative number.

The 2 steps to solve a two-step linear equation.

1. Use addition and subtraction properties of an equation to move the variable to one side of the equation and all number terms to the other side of the equation. 2. use multiplication and division properties of an equation to remove the value in front of the variable.

How do you change a decimal to a fraction?

1. Write the decimal divided by 1 with the decimal as the numerator and 1 as the denominator. 2. Multiply the numerator and denominator by 10 for every number after the decimal point. Example: if there is 1 decimal place, multiply by 10. If there are 2 decimal places, multiply by 100. 3. Reduce the fraction completely. Example: 0.37 1. 0.37/1 2. 0.37 x 100/1 x 100 = 37/100 3. 37/100 (this fraction does not reduce)

Steps to multiply a fraction by a mixed number or multiplying 2 mixed numbers.

1. change the mixed number to an improper fraction. 2. multiply the numerators. 3. multiply the denominators. 4. write the improper fraction as a mixed number. 5. reduce if necessary.

Steps to multiply a fraction by a whole number.

1. change the whole number to a fraction with a denominator of 1. 2. multiply the numerators together. 3. multiply the denominators together. 4. rewrite the final answer as a mixed number.

Steps to changing a fraction to a decimal.

1. divide the numerator by the denominator. Add zeros after the decimal point as needed. 2. complete the process when there is no remainder or the decimal is repeating.

Steps to adding or substracting fractions without like denominators.

1. find the lowest common denominator (the lowest common multiple). 2. convert the LCD by multiplying the fraction by the necessary numerical value written as a fraction equal to 1. 3. Add or subtract the numerators.

Steps to divide a fraction by a fraction.

1. leave the first fraction alone. 2. find the reciprocal of the second fraction. 3. multiply the first fraction by the reciprocal of the second fraction. 4. Rewrite the fraction as a mixed number and reduce the fraction completely.

How to multiply fractions.

1. multiply the numerators together. 2. multiply the denominators together.

2 ways to convert a percent to a decimal.

1. remove the percent sign and divide the decimal by 100. 2. move the decimal point 2 places to the left.

Steps to divide a fraction by a whole or mixed number.

1. write any whole number as a fraction with the denominator of 1. write any mixed numbers as improper fractions. 2. leave the first fraction (improper fraction) alone. 3. find the reciprocal of the second fraction. 4. multiply the first fraction by the reciprocal of the second fraction. 5. rewrite the fraction as a mixed number and reduce the fraction completely.

1 liter (L) = _____ quarts (qt).

1.06

1 mile (mi.) = _____ kilometer (km)

1.61

1 centimeter = ___ millimeters.

10

How many meters (m) in 1 dekameter (dam)?

10 m in 1 dam.

1 meter = ____ centimeters

100

How many meters (m) in 1 hectometer (hm)?

100 m in 1 hm.

1 pint (pt) = _____ fluid ounces (fl. oz).

16

1 pound (lb) = ____ ounces (oz).

16

1 ton (T.) = _______ pounds (lbs.).

2,000

1 kilogram (kg) = _____ pounds (lbs.).

2.2

1 inch (in.) = ___ centimeters (cm)

2.54

1 ounce (oz.) = ______ grams (g).

28.3

1 gallon (gal.) = ______ liters (L).

3.79

1 ounce (oz) = _____ milliliters (mL)

30

1 gallon (gal) = ____ quarts (qt).

4

1 gallon = ____ quarts

4

1 mile (mi) = ____ feet (ft)

5,280

Formula for calculating the area of a rectangle.

A = lw Area = length times width.

Formula for calculating the area of a square.

A = s^2 Area = the side length squared.

What is a mixed number?

A mixed number is a whole number and a proper fraction.

What can an improper fraction be changed to?

A mixed number.

What is a ratio?

A ratio expresses the relationship between two numbers and is expressed using a colon or fraction notation. Ratios should generally appear in lowest terms. Mathematically, ratios act just like fractions. Example: 8:13 is the same as 8/13.

What is a two-step linear equation?

A two-step linear equation is in the form ax+b=c. a is a non-zero constant b and c are constants there are 2 basic steps to solving this equation

What is the addition property of equality?

Adding the same number to both sides of the equation. Example: x - a = b x - a + a = b + a x = a + b

What is the addition property of inequality?

Adding the same number to both sides of the inequality. Example: x - 3 < 9 x - 3 + 3 < 9 + 3 x < 12

What is a polynomial?

An expression that contains exponents, as well as variables, constants, and operations.

How to add polynomials.

Combine like terms and write the solution from the term with the highest exponent to the term with the lowest exponent.

What is the division property of equality?

Divide both sides of the equation by the same number. ax = b ax/a = b/a x = b/a

What is the division property of inequality (when multiplying by a positive number)?

Divide both sides of the inequality by the same number. Example: 3x ≤ 9 3x/3 ≤ 9/3 x ≤ 3

What is the division property of inequality (when multiplying by a negative number)?

Divide both sides of the inequality by the same number. Example: -3x ≤ 9 -3x/-3 ≤ 9/-3 x ≥ -3 (note the reversal of the inequality sign)

How do you change an improper fraction to a mixed number?

Divide the denominator into the numerator. The result is the whole number. The remainder is the numerator of the proper fraction, and the value of the denominator does not change. Example: 5/2 is 2 1/2 because 2 goes into 5 twice with a remainder of 1.

What is a linear inequality?

It is similar to a linear equation, but it contains an inequality sign (< , > , less than or equal, greater than or equal). The major difference is the solution is an infinite number of values.

Term for fractions with the same denominator.

Like fractions.

What is the multiplication property of equality?

Multiply both sides of the equation by the same number. Example: x/a = b x/a x a = b x a x = ab

What is the multiplication property of inequality (when multiplying by a negative number)?

Multiply both sides of the inequality by the same number. Example: x/-3 ≥ 9 x/-3 x -3 ≥ 9 x -3 x ≤ -27 (note the reversal of the inequality sign)

What is the multiplication property of inequality (when multiplying by a positive number)?

Multiply both sides of the inequality by the same number. Example: x/3 ≥ 9 x/3 x 3 ≥ 9 x 3 x ≥ 27

How do you change a mixed number to an improper fraction?

Multiply the whole number by the denominator and add the result to the numerator. The results become the new numerator. Example: 2 1/2 is 5/2 because 2 times 2 plus 1 is 5 for the new numerator.

What are perfect squares?

Numbers with whole number square roots, such as 1, 4, 9, 16, and 25.

What is the RANGE?

The difference between the highest and lowest values in a data set. Example: 2, 3, 4, 5, 6, 6, 7, 8. The highest value is 8 and the lowest value is 2, for a range of 6.

What is the MEDIAN?

The middle number of a data set when written in order. If there are an odd number of items, the median is the middle number. If there are an even number of items, the medium is the mean of the middle two numbers. Example: 2, 3, 4, 5, 6, 6, 7, 8. The middle two numbers are 5 and 6. The mean of those is 5.5, so the median is 5.5.

What is the area of a 2-dimmensional object?

The number of unit squares that fit inside a two-dimensional object. A unit square is one unit long by one unit wide, which includes 1 foot by 1 foot and 1 meter by 1 meter.

What is the MODE?

The number or numbers that occur most often. There can be no modes, one mode, or many modes. Example: 2, 3, 4, 5, 6, 6, 7, 8. Since 6 appears twice and no other number do, it is the mode.

What is the square of a number?

The number raised to the power of 2.

What is the cube of a number?

The number raised to the power of 3.

What is the least common denominator?

The smallest number that can be divided evenly into the denominators of all fractions being compared.

What is the MEAN?

The sum of all numbers in a data set divided by the number of elements in the set. Example: 2, 4, 7, 6, 8, 5, 6, and 3. The mean are the numbers added divided by 8, which is 5.125.

T/F: A positive exponent in scientific notation represents a large number, while a negative exponent represents a small number.

True.

T/F: Any number to the power of 0 will equal 1.

True.

T/F: The negative exponent rule reveals that numbers with a negative power are equal to a fraction.

True.

T/F: When multiplying signed numbers, if the numbers have the same sign, their product is positive.

True.

T/F: multiplying or dividing both sides of the inequality by a negative number reverses the sign of the inequality.

True.

The bottom number of a fraction is the __________________________.

denominator