Math+A

= **Math A** ▀ ▄▀ ▄▀= ✿ **Naomi** **Galindo** **&** **Amber Garza ✿ ** The following page shows what will be on our 2011 7th grade Math final. It starts from what we did in the first semester all the way until now.

=Chapter 8: Solving Equations= toc **Lesson 8-1** : //**Equations and Variables**// hhhhh When you have an equation you will usually see something like ** hhhhhhhhhhhhhhhhhhhhhhh 6+y=12** ** hhhhhhhhhhhhhhhhh "y"** is the **variable.** hhhhhhhhhhhhhhhhhh So, **6+y=12** is the **equation**.

**Lesson 8-2** : //**Equations: Addition and Subtraction**// hhhhhhh When you have an equation you will usually see something like **x+5=7**. hhh You solve these kind of problems by, since this problem involves addition, you subtract 5 from both sides. hhhhhhhhhhhhhhhhhhh hhhhhhhhhhhhhhhhhhhhhhhhhhhhhh *So, **x+5=7** hhhhhhhhhhhhh *Since 5-5=0 you can cancel it and you are left with **x=7-5** hhhhhhhhhhhhhhhhhhhhhhhhhh hhhhhhhh which turns into
 * hhhhhhhhhhhhhhhhhhhhhhhhhh hhh -5= -5 **
 * hhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh x=2**

**Lesson 8-3** : //**Equations: Multiplication and Division**//

**Lesson 8-4** : //**Equations: Decimals and Fractions**//

**Lesson 8-5** : //**Combined Operations**//

**Lesson 8-6** : //**Word Sentences and Equations**// "An equation such as //32n = 80// can be given meaning in the real world in many ways.  hhhh a.) If a car goes 32 mi/h, how many hours //(n)// would it take to go 80 miles?  hhhhhhhhhhhhhhhhhhhhhhhhhhhh **32mi/h x //n// hours = 80 mi**   hhhh b.) If peaches cost 32¢ a pound, how many pounds //(n)// can you buy for 80 ¢?    hhhhhhhhhhhhhhhhhhhhhh **32¢/lb x //n// pounds = 80¢**

** Lesson 8-7 ** : //**Translating Problems into Equations**// This chapter is manly about making equations with word problems.

[|Translating_Problems_into_Equations..png]

**Lesson 8-8** : //**A Problem Solving Model: Writing Equations**// //** hhhhh **//__** Solving a Word Problem Using an Equation **__ ** Step 1: **Read the problem carefully. Make sure that you understand what it says. You may need hhhhhhhhhh to read it **more than once**. ** Step 2: **Decide what numbers are asked for. Choose a variable and use it with the given conditions of  hhhhhhhhhh the problem to represent the number(s) asked for. ** Step 3: ** Write an equation based on the given conditions. ** Step 4: ** Solve the equation and find the required numbers. ** Step 5: ** Check your results with the words of the problem. Give the answer.

=Chapter 9: Percents=

**Lesson 9-1** : //**Percents and Fractions**// Percent means **part of a hundred.** They are not only expressed as 70% or 50% but they can also be turned into fractions. **For example**, 50% = 50/100 (which can be reduced to 1/2) because it is **part of a hundred**.

**Lesson 9-2** : //**Percents and Decimals**// Just like fractions, you can turn percents into **decimals.** But there is a special rule of turning percents into fractions. Every number has a decimal point, but some you just don't see; they are imaginary. With percents move the decimal point to the left two times, **every time!** **For example,** 80% is also written as .80 OR 6% is .06

**Lesson 9-3** : //**Computing with Percents**// You can also "compute" with percents. You just have to follow what the problem says. hhhhhhhhhhhhhhhhhhhhhh What number is 8% of 75? hhhhhhhhhhhhhhhhhhhhhhhhhhh n= 0.08 x 75 hhhhhhhhhhhhhhhhhhhhhhhhhhhhhh n=6
 * For example,**

**Lesson 9-4** : //**Percents of Increase and Decrease**// There are **two** different formulas when dealing with percent of increase or decrease. percent of change= __amount of change__ hhhhhhhhhhhhhhh original amount hhhhhhhhhhhhhhhhhhh OR  amount of change= percent of change x original amount

**Lesson 9-5** : //**Discount and Markup**// "A **discount** is a decrease in the price of an item. A **markup** is an increase in the price of an item." (296)

**Lesson 9-6** : //**Commission and Profit**// **Formulas:**

hhhhhhhh amount of commission= percent of commission x total sales
 * ** Commission :**

hhhhhhhh profit= total income- total costs
 * **Profit** :

hhhhhhhhh percent of profit= __profit__ hhhhhhhhhhh hh total income
 * **Percent of profit:**

**Lesson 9-7** : //**Simple Interest**//

Let //**l**// = simple interest charged ** hhh //P//=** amount borrowed, or **principal** ** hhh //r//=** annual rate ** hhh //t//=** time in years for which the amount is borrowed ** hhhh **So, **interest= principal x rate x time**, or **I= Prt.**

**Lesson 9-8** : //**Compound Interest**// hhhhhh In order to find compound interest you must use the formula //**I= Prt. The principal** is the amount of money on which interest is paid. **The interest** is the amount of money paid for the use of money. **The rate** is a quotient of measures in different kinds of unit, for example 35 km/h.// =Chapter 10: Areas & Volumes=

** Lesson 10-1 : //Area of Rectangles and Parallelograms//** The formula for the area of a rectangle is Area of rectangle= length x width or **//A=lw//** Example: hhhh Say there is a rectangle with a length of 9 in. and a width of 4 in.. You would then multiple the length and width to get the area. hhhhhhhhhhhhhhhhhhhhhhhh //**A=lw**// // hhhhhhhhhhhhhhhhhhhhhhhh **A****=9 in. x 4 in.= 36 in.**// // hhhhhhhhhhhhhhhhhhhhhhh**h** **The area is 36 in.**// The formula for the area of a rectangle is Area of parallelogram= base x height or //**A=bh**// Example:

hhhh A parallelogram has a height of 30 m and the base is 25 m. So you would multiple the base and the height hhh and the product would be the area.

ffffffffffffffffffffffffffffffffffffffffffff //**A=bh**// //** ffffffffffffffffffffffffffffffff A=25 m x 30 m= 750 m**// //** ffffffffffffffffffffffffffffff The area would be 750 m**//

gg gg ** Lesson 10-2 : //Area of Triangles and Trapezoids//** The formula for the area of a triangle is Area of Triangle= base x height/ 2 or **//A=bh/2//** Example:

hhhhhhh A triangle has a base of 8 cm and a height of 5 cm. After identifying the base and height you would multiply the two together and then divide the product by two. the quotient would then be your area.

hhhhhhhhhhhhhhhhhh //**A=bh/2**// //** hhhhhhhhhhhhhh A= 8 cm x 5 cm= 40 cm**// //** hhhhhhhhhhhhhh A= 40 cm/2= 20 cm**// //** hhhhhhhhhhhhhh The area would be 20 cm**//

The formula for the area of a trapezoid is Area of trapezoid= (sum of bases) x height/2 or **//A=(b1+ b2)h/2.//** Example:

hhhhhhhhhhhhhhhh A trapezoid has two bases. The first is 25 m while the other is 37 m. It also has a height of 19. You would first add the two bases together. After adding the bases you get the sum of the two numbers and dived them by two. once again the quotient is the area.

hhhhhhhhhhhhhhhh **//A= (b1+ b2) h/2//** **// hhhhhhhhhhhhhh A= (25 m + 37 m) 19 m/2//** **// hhhhhhhhhhhhhh A= 62 m x 19 m/2//** **// hhhhhhhhhhhhhh A= 1178 m/2 = 589 m//** **// hhhhhhhhhhhhhh The area would be 589 m //**

** Lesson 10-3 : //Area of Circles//** The formula for the area of a circle is **//Area of a circle = pi x (radius) squared.//** Pi can equal either **//3.14//** //or// **//22/7.//**

** Lesson 10-4 ://Using Symmetry to Find Area//** We call a figure that can be split in two with both pieces matching //**symmetric with respect to a line**//. The line that separates these two is called a //**line of symmetry**//.A figure may have more than one line of symmetry. Figures can also be //**respectful towards a point**//. A figure is respectful towards a point if for every point on that figure there is an opposite point on the figure that corresponds.

** Lesson 10-5 : //Polyhedrons//** A **//polyhedron//** is a figure formed of polygonal parts of planes that enclose a region of space. An example of a polyhedron are boxes. The **//edge//** of a polyhedron is where the faces intersect into segments. The endpoints of these edges are the **//vertices//**. Here are two different types of polyhedrons: **//Cube//**: a three dimensional shape having square faces **//Prism//**: a polyhedron that has two congruent polygonal regions called **//bases//**

** Lesson 10-6 : //Volume of Prisms//** The formula for the volume of a prism is Volume of prism= base area x height or **//A=Bh.//** Example: hhhhhhhhhh A prism's base has a length of 5 cm and the width of 3 cm. The height of the whole prism is 4 cm. You would first find the area of the base with the given measurements. After finding the area of the base you would multiply that by the height of the prism. The product would be your area.

hhhhhhhhhhhhh **//A= Bh//** **// hhhhhhhhhhh A= (5cm x 3 cm) 4 cm//** **// hhhhhhhhhhh A= 15 cm x 4 cm//** **// hhhhhhhhhhh A= 60 cm//** **// hhhhhhhhhhh The area would be 60 cm.//**

** Lesson 10-7 : //Volumes of Cylinders//** The formula for the volume of a cylinder is Volume for cylinder= Base area x height or **//V=Bh//** Method: hhhhhhhhhh To find the volume of a cylinder is very simple but if careless mistakes are made it can turn out really wrong. You first must solve the area of the base. Since the base of a cylinder is a circle you must know how to solve for the area of a circle. (see lesson 10-3) After finding the area of the base you get the result of that and multiply it by the height. The end product would be your area.

** Lesson 10-8 : //The Mass of an Object//** The **//mass//** of an object is a measure of the amount of material it contains. In order to find the mass of an object you must know the weight of the material used in the object. Most objects will be weighed in grams while the heavier objects will be weighed in kilograms or metric tons.You must find the volume of the object before you can find its total mass. =Chapter 11: Integers & Graphs=

**Lesson 11-1** : //**Negative Numbers**// The distance from 0 to graph a number is called //**the absolute value.**// we all know the **//positive integers//** 1,2,3,4.etc. but what about the negative numbers? **//Negative numbers//** include -1,-2,-3,-4, etc.. They are all the numbers to the left of a number line. ) is neither a positive nor negative integer. It is simply just another integer. The farther to the right on a number line a number is, the greater the number is.

**Lesson 11-2** : //**Adding Integers**// There are two rules to adding integers. //**Rule 1:** The sum of two positive integers is a positive integer// //**Rule 2:** The sum or two negative integers is a negative integer.// //**Rule 3:** If both numbers have the same absolute value the answer will be// **zero**

hhhhh When one number is negative and the other is positive in an addition problem the answer may be either negative or positive. If a negative number is being added you would move to the right on the number line but if the number being added is positive you would move to the right on the number line. ** Lesson 11-3 : //Subtracting Integers//**

The following is a video by Julie Harland on youtube. It teaches you how to subtract integers.
 * *Before you watch this you must know how to add integers! **

media type="youtube" key="0sMIJkFV1uw" height="240" width="274"

** Lesson 11-4 and Lesson 11-5 : //Products with Negative Integers//** There are some basic rules to multiplying by integers both negative and positive: //** Rule 1: ** The product of a positive number times another positive number is always positive // // Rule 2: The product of a negative number times another negative number is always a negative // //**Rule 4:** The product of zero and any integer is zero// //** Rule 5: ** The product of -1 and any integer equals the opposite of that integer //
 * //Rule 3//**//: The product of a negative number and a positive integer is always a negative number//

** Lesson 11-6 :** //**Quotients of Integers**// There are three basic rules you must know to divide by negative and positive integers : //**Rule 1:** The quotient of two positive or two negative integers is positive.// //**Rule 2:** The quotient of a positive integer and a negative integer is negative//

Lesson 11-7 : **//Solving Equations//** hhhhhh After learning how negative numbers work and how to add, subract, multiply, and divide by them you are ready to do equations using negative numbers. This is a very simple thing to do but if careless mistakes are made your answer may come out really wrong.

Example: hhhhhhhh //**y+ 7 + 2**// //** hhhhhhh y + 7 -7 = 2 -7 **// //** hhhhhh y = 2 + -7 **// //** hhhhhh y = -5 **//

For additional help, visit: =Yourteacher.com=

 username: chinquapin password: yourteacher and click "Pre-Algebra"

=Our Sources...= //Mathematics: Structure and Method "McDougal Littell/ Houghton Mifflin"// __Subtracting Integers__. Dir. VideosbyJulieHarland. Youtube, 2009.