Do ratios form a proportion
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This document discusses ratios and proportions. It defines a ratio as a comparison of values and shows examples of ratios written in different formats like 3:1 or 3 to 1. Ratios can be scaled up or down by multiplying both values by the same number. A proportion is a statement that two ratios are equal to each other. To determine if ratios form a proportion, you cross multiply the terms - if you get the same number, the ratios are proportional; if the numbers are different, they are not proportional. Examples are provided to illustrate determining proportionality through cross multiplying.
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All about-my-family
This document provides a brief introduction to the author and their family and pets. The author has been teaching math for 15 years, including 10 years teaching math online, and their goal is to help others love math as much as they do.
Ratio slideshow
The document discusses ratios and how to express them in different formats. Ratios can be expressed using a colon, "to", or as a fraction. They can represent a part-to-part comparison between two parts, or a part-to-whole comparison of a part to the total. Examples are given of simplifying ratios by finding the greatest common factor.
Order of operations
Order of Operations (PEMDAS) provides rules for the sequence of mathematical operations to avoid confusion. It dictates that operations within parentheses should be performed first, followed by exponents, then multiplication and division from left to right, and finally addition and subtraction from left to right. The document provides an overview of the PEMDAS method and examples for the reader to practice applying the order of operations.
All about-my-family
This document provides a brief introduction to the author and their family and pets. The author has 14 years of experience teaching math and has taught online for 9 years, and their passion is helping students love math as well.
Trig notes
This document introduces trigonometric ratios, which compare the sides of a right triangle. It defines the three primary ratios: sine, cosine, and tangent. Sine is the ratio of the opposite side to the hypotenuse. Cosine is the ratio of the adjacent side to the hypotenuse. Tangent is the ratio of the opposite side to the adjacent side. Several examples are provided to demonstrate calculating trigonometric ratios given a right triangle and to find angles or sides using inverse trigonometric functions.
U4 l4 quadratic formula powerpoint
This document provides instruction on solving quadratic equations using the quadratic formula. It explains that the quadratic formula can be used to solve any quadratic equation, even those that cannot be factored. It defines the discriminant (b^2 - 4ac) as an important part of the formula, as the sign of the discriminant determines the number and type of roots. A negative discriminant means there are two complex roots, zero means there is one real root, and a positive discriminant means there are two real roots that can be rational or irrational depending on whether the discriminant is a perfect or non-perfect square. An example problem demonstrates finding the discriminant, describing the roots, and solving a quadratic equation using the formula. Practice
Relations & functions
The document summarizes key concepts about relations and functions including:
1) It defines relation, domain, range, and function.
2) It provides examples of relations that are and are not functions using ordered pairs, tables, and mappings.
3) It shows how to determine if a relation is a function using a vertical line test and mappings.
4) It gives examples of finding the domain and range of relations and determining if other relations are functions.
The y intercept and the slope
This document explains how to graph linear functions in slope-intercept form by plotting the y-intercept and using the slope. It outlines three steps: 1) Plot the y-intercept point on the y-axis. 2) Use the slope to rise up and run over to plot the next point. 3) Connect the dots with a line to graph the function. It also provides extra examples to demonstrate the process.
Solving inequalities one step
Solving inequalities is similar to solving equations, except the inequality sign changes if multiplying or dividing by a negative number. There are multiple numbers that can satisfy an inequality rather than a single solution. Notation for inequalities includes > for greater than, >= for greater than or equal to, < for less than, and <= for less than or equal to. Examples show solving basic linear inequalities involving addition, subtraction, multiplication, and division.
Lesson solving two step equations when -x = #
This document provides instructions for solving two-step equations. It outlines the six key steps: 1) divide the equation with an equal sign, 2) undo addition/subtraction to isolate the variable, 3) simplify, 4) undo multiplication, 5) simplify to solve for the variable, and 6) always check the answer by substituting it back into the original equation. It then provides five practice problems for students to solve.
Solving equations one & two step
1) The document defines terms, constants, coefficients, and discusses how to solve one-step and two-step equations. It provides examples of solving equations involving addition, subtraction, multiplication and division.
2) Sample one-step equations are provided along with the steps to solve each type. Equations involving addition, subtraction, multiplication and division are worked through as examples.
3) A two-step practice problem is given along with the answers. Solving two-step equations is introduced.
Solving one step equations
This document provides examples of how to solve one-step equations by adding, subtracting, multiplying, and dividing. It includes 3 examples for each operation: adding by isolating the variable term on one side of the equation and adding its opposite to both sides; subtracting by isolating the variable term and subtracting its opposite from both sides; multiplying by isolating the variable term and dividing both sides by its coefficient; and dividing by isolating the variable term and multiplying both sides by the reciprocal of its coefficient.
Solving equations
This document discusses solving two-step equations and provides examples of solving equations such as 2x + 1 = 4, X - 2 = 3 + 3, X + 2x = 6, and -x + 4 = 10. The solutions to these example equations are provided as x = 3/2, x = 8, x = 2, and x = -6, respectively.
Ratio powerpoint
The document discusses ratios and provides examples using Lucky Charms cereal. It states there are 287 marshmallow pieces and 2,583 oat pieces in one box of Lucky Charms. This ratio of marshmallows to oats can be written in three ways: as a fraction, using the word "to", or using a colon. The document also discusses writing ratios in simplest form and explaining their meanings.
Ratio slideshow
The document discusses ratios and how to express them in different formats. Ratios can be expressed using a colon, "to", or as a fraction. They can compare parts to parts (part-to-part ratios) or parts to the whole (part-to-whole ratios). Examples are given of simplifying ratios by finding the greatest common factor and converting ratios to their simplest form.
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Do ratios form a proportion
- 1. Do ratios form a proportion?
- 2. What is a ratio? A ratio compares values. Above you see 3 blue squares and 1 red square. This can be written 3 different ways to show it is a ratio: 3:1 3 to 1 1 3 Another example:
- 3. Scale up or scale down . . . A ratio can always be scaled up or scaled down. For example: 3:1 is the same as 6:2 It may be easier to see if you think of it like equivalent fractions and set them equal: 2 6 1 3 Here the numerator (top) and denominator (bottom) are both multiplied by 2 so the ratio is still the same.
- 4. Proportion A proportion says that two ratios are equal. Example: Another example: 4 2 2 1 3 1 12 4
- 5. How do you know if ratios form a proportion? Remember a proportion is a statement that two ratios are equal. When you are given a problem the way to check to see if they are proportional is to cross multiply: 20 * 5 =100 25 * 4 = 100 5 4 25 20 We need to check to see if these are proportional. - First cross multiply - Then we see if we get the same number. - If we have the same number they are proportional. 100 = 100 So these are proportional!
- 6. Let’s look at a few more examples . . . Are the ratios below proportional? Cross multiply first 8 * 40 = 320 10 * 32 = 320 You end up with the same number. Are the ratios below proportional? Cross multiply first 10 * 5 = 50 20 + 4 = 80 You do not have the same number. 40 32 10 8 320=320 So they are proportional! 5 4 20 10 50 ≠ 80 So they are NOT proportional!