Numbers, Algebra, Measurement & Data Review

Flashcards covering fundamental concepts of numbers, algebra, statistics, geometry, and measurement systems based on the lecture transcript.

How do you convert a fraction to a decimal?

Divide the numerator (top number) by the denominator (bottom number).

What is the procedure for converting a decimal to a percentage?

Multiply the decimal by $100$ and add the percent sign ($\%$), which is equivalent to moving the decimal point two places to the right.

How is a percentage converted back into a decimal?

Divide the percentage by $100$, move the decimal point two places to the left, and remove the percent sign.

What is the rule for adding or subtracting fractions?

Find a common denominator, add or subtract the numerators, and keep the common denominator.

How are fractions multiplied?

Multiply the numerators together and the denominators together.

What is the process for dividing fractions?

Multiply the first fraction by the reciprocal (inverse) of the second fraction.

How do you determine the number of decimal places in the product of two decimals?

The number of decimal places is the sum of the decimal places in the factors.

What is the procedure for dividing decimals?

Make the divisor a whole number by moving the decimal point to the right, move the decimal point in the dividend the same number of places, and then perform division.

When comparing two fractions $\frac{a}{b}$ and $\frac{c}{d}$, how is cross-multiplication used?

If $ad > bc$, then $\frac{a}{b} > \frac{c}{d}$.

What is the goal when solving equations with one variable?

To isolate the variable on one side of the equation using inverse operations.

What are the Addition and Subtraction Properties of Equality?

If $a = b$, then $a + c = b + c$ and $a - c = b - c$.

How do you calculate the percentage of a number?

Convert the percentage to a decimal and multiply it by the number.

What is the formula for percentage increase or decrease?

$$\frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%$$

How is the Sale Price calculated when a discount is involved?

$$\text{Sale Price} = \text{Original Price} - \text{Discount Amount}$$

What is the standard rule for rounding?

If the digit to the right of the place value is $5$ or greater, round up; if it is less than $5$, keep the digit the same.

What property is used to solve the proportion $\frac{a}{b} = \frac{c}{d}$?

Cross-multiplication: $ad = bc$.

How does a rate differ from a ratio?

A ratio compares two quantities, while a rate is a ratio that compares two quantities with different units, often involving time.

What is the difference between an expression and an equation?

An expression is a combination of numbers, variables, and operations without an equal sign, while an equation contains an equal sign showing two expressions are equal.

In statistics, how is the Mean calculated?

Sum of all values divided by the number of values.

What is the Median of a data set?

The middle value when the data is arranged in order; for an even number of values, it's the average of the two middle values.

How is the Range of a data set determined?

The difference between the highest and lowest values in the data set.

What characterizes a negative correlation on a scatter plot?

As one variable increases, the other tends to decrease, and points generally go downwards from left to right.

What is the formula for the circumference of a circle?

$C = 2\pi r$ or $C = \pi d$

What is the formula for the area of a triangle?

$$A = \frac{1}{2}bh$$

What is the volume formula for a cylinder?

$$V = \pi r^{2}h$$

How many feet are in one mile?

$$5280\,\text{ft}$$

What is the conversion factor between inches and centimeters?

$$1\,\text{inch} \approx 2.54\,\text{cm}$$

How many fluid ounces are in one cup?

$$8\,\text{fl\,oz}$$

What is the formula for the area of a rectangle?

$A = lw$ where $l$ is the length and $w$ is the width.

What is the formula for the volume of a rectangular prism?

$V = lwh$ where $l$ is the length, $w$ is the width, and $h$ is the height.

How do you calculate the simple interest?

$I = Prt$ where $I$ is the interest, $P$ is the principal amount, $r$ is the rate, and $t$ is the time in years.

What is the formula for converting Celsius to Fahrenheit?

$$F = \frac{9}{5}C + 32$$

What is the relationship between area and volume in geometry?

Area measures the extent of a surface, while volume measures the space occupied by a three-dimensional object.

What is the difference between permutations and combinations?

Permutations consider the arrangement of items, while combinations focus on the selection of items without regard to order.

What is the formula for calculating the probability of an event?

$$P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$

What is the Pythagorean theorem?

In a right triangle, $a^2 + b^2 = c^2$ where $c$ is the hypotenuse, and $a$ and $b$ are the other two sides.

What is the formula for the area of a circle?

$A = \pi r^2$ where $r$ is the radius of the circle.

How do you calculate the mean of a set of numbers?

Add all the numbers together and divide by how many numbers there are.

What is the concept of median in statistics?

The median is the value that separates a data set into two equal halves.