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To subtract integers, add the opposite of the number being subtracted. This works because subtraction is the inverse of addition. The document provides examples of subtracting integers in word problems, algebraic expressions, and evaluating expressions by substituting values for variables. It also includes a warm up section with more practice problems subtracting and evaluating expressions with integers.
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The document provides information about a pre-algebra class that covers topics like the number line and rational numbers. It includes warm-up problems, homework assignments, and discussions of investigations into extending the number line and using it to represent number sentences for changes in temperature. The class materials are aimed at helping students understand rational numbers and how to use the number line to compare numbers and represent number sentences.
10.3
This document provides examples of using quadratic functions in intercept form. It demonstrates how to identify the x-intercepts from the function, graph the function by plotting intercepts and the vertex, write a function given intercepts and a point, and model a real-world scenario like a dolphin's leap using a quadratic function. Key aspects covered include the intercept form equation, finding the vertex and axis of symmetry, and completing the steps to graph or write a quadratic function based on given information.
New week 1
The document provides information about a pre-algebra class, including:
1) Instructions for students to write down their homework, review class expectations, and get out notebooks.
2) Details about classroom rules and expectations for students.
3) An overview of the upcoming unit on operations with integers which will cover comparing and ordering numbers on a number line.
New week 10
This document contains a multi-part math problem about using similar triangles to estimate heights and distances. Part A asks students to use similar triangles to find the height of a building from given measurements. Part B asks students to use the mirror method with their group to estimate the height of an object and provide their measurements and explanation. Part C compares the estimates from Parts A and B and asks if they seem reasonable. Follow-up questions involve pooling the class data and comparing estimates from the two methods.
New week 9
The document contains instructions and information about using similar triangles to estimate heights and distances that are difficult to measure directly. It discusses using shadows and mirrors to form similar triangles and estimate heights of objects. Measurements are taken of shadows, mirrors, and distances that allow heights to be calculated through properties of similar triangles. Students work through examples estimating heights of buildings using these methods.
11.6
This document provides an example of how to use the work formula to solve problems involving work done at a steady rate. It gives the formula for work rate as the amount of a job completed in a given time. It then works through two examples - one calculating the time for two people to complete a job together, and another multiple choice problem calculating the time for one person to complete a job alone based on work rates.
11.5
This document discusses solving rational equations by using the cross product property. It provides three examples of solving rational equations:
1) Solving a simple rational equation with a single rational expression on each side. The solutions are -6 and 2.
2) Solving a rational equation with rational expressions on both sides. The solution appears to be 2, but it is an extraneous solution.
3) Solving a rational equation by factoring the denominators to find the least common denominator (LCD).
11.4
1) To add or subtract rational expressions with the same or different denominators, we first find the least common denominator (LCD), which is the least common multiple of the denominators.
2) We then rewrite the rational expressions with the LCD as the common denominator before adding or subtracting the numerators.
3) Once the rational expressions have been rewritten with the same denominator, we can perform the addition or subtraction operation as we would with numerical fractions.
New week 8
Raphael wants to make enlarged posters of his advertisement to display at a sale. He has an 8.5" by 11" ad and wants to enlarge it as much as possible using the copy machines at his local copy shop, which can enlarge documents between 50-200% and have paper sizes of 8.5" by 11", 11" by 14", and 11" by 17". The best option would be to use the 11" by 17" paper and enlarge the ad 150% to make it a similar, larger poster without trimming off the edges of the paper.
11.1
This document provides examples of direct and inverse variation, including how to identify, graph, and write equations for direct and inverse variation relationships. It also contains examples of solving work problems using inverse variation.
Key points covered include:
- Direct variation is when y=kx and inverse variation is when y=k/x, where k is the constant of variation.
- Example 1 shows how to identify if an equation represents direct, inverse, or neither type of variation.
- Examples 2 and 3 demonstrate how to graph inverse variation equations.
- Examples 4, 5, and 6 show how to write inverse variation equations from tables of data or real-world context and solve problems using inverse variation equations.
New week 6
This document provides instructions and materials for a math lesson on similarity and scale factors. It includes examples of similar figures with questions about their side lengths, scale factors, and areas. It also discusses how police use measurements and similar figures to determine characteristics like a criminal's height from surveillance photos. Students are asked to use a photo of a teacher holding an object of known size to calculate the teacher's height, and to explain how police may have used a similar technique to determine a robber's height from a store surveillance photo.
9.9
The document provides examples of factoring polynomials completely. It begins by outlining guidelines for factoring polynomials completely, such as factoring out the greatest common monomial factor, looking for differences of squares or perfect square trinomials, and factoring trinomials and polynomials with four terms by grouping. It then works through examples of factoring various polynomials completely by applying these guidelines. These include factoring trinomials, solving a polynomial equation, and solving a multi-step problem involving factoring a polynomial to find dimensions.
9.8
The document discusses factoring polynomials using the difference of squares pattern and perfect square trinomial pattern. It provides examples of factoring expressions involving these patterns, including solving polynomial equations. The examples illustrate factoring expressions with variables and evaluating expressions to solve vertical motion problems.
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1.5 7th
- 2. Subtracting Two Integers Words Numbers Algebra To subtract an 3 – 7 = 3 + (-7) a – b = a + (- b) integer, add its opposite. 5 – (-8) = 5 + 8 a – (-b) = a + b
- 3. Example 1: Subtract 1. -5–9 2. - 8 – (- 6) 3. 8 – (- 4) 4. - 11 – ( - 6)
- 4. Example 2: Evaluate each expression 1. 9 – h for h = -8 2. - 7 – m for m = -5 3. l-3 – k l + l -3l for k = 12
- 5. Warm up 1.5 Subtract 1. – 6 – ( -4) 2. - 3 – 3 3. 4 – ( - 5) Evaluate the expression 4. 9 – s for s = - 5 5. - 4 – w + 5 for w = 21