**Fifth Grade Math**

This book, with over 250 problems, covers the following topics:

Algebra, Decimals, Fractions, Geometry, Measurement, Multiplying Large Numbers, Probability, Word Problems, and more.

If you are homeschooling (or if you are just trying to get extra practice for your child), then you already know that math workbooks and curriculum can be expensive. Homeschool Brew is trying to change that! We have teamed with teachers and parents to create books for prices parents can afford. We believe education shouldn’t be expensive.

The problem portion of the book may also be purchased individually in "Fifth Grade Math Problems."

Algebra, Decimals, Fractions, Geometry, Measurement, Multiplying Large Numbers, Probability, Word Problems, and more.

If you are homeschooling (or if you are just trying to get extra practice for your child), then you already know that math workbooks and curriculum can be expensive. Homeschool Brew is trying to change that! We have teamed with teachers and parents to create books for prices parents can afford. We believe education shouldn’t be expensive.

The problem portion of the book may also be purchased individually in "Fifth Grade Math Problems."

## Print Copy: Fifth Grade Math

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**Excerpt**

**Algebra**

Algebra is a part of math in which letters are substituted for numbers. Algebra uses both letters and numbers to create equations. In math, there are ways to represent relationship between numbers. One very common type of relationship is a linear relationship. A linear relationship is when one side of an equation equals the other side of the equation and is represented by a linear equation. A linear equation has a variable, such as x or y.

For example, x + 3= 8

It is important to understand that in a linear equation, one side MUST equal the other side. When working with a linear equation, it does not matter how many variables are in the equation or what operations the equation includes, the sides will always be equal.

Equations An equation is a mathematic sentence. An equation says that two things are equal. An equal sign is always used in an equation. An example of an arithmetic equation is 3 + 5 = 8. The left side (3 + 5) is equal to the right side (8). In an equation, both sides must always be equal. An example of an algebraic equation is 3 + x = 8. The left side (3 + x) is equal to the right side (8). In the algebraic equation, the value of x could be substituted for a number that would make the equation true and make both sides equal.

In an equation, many different operations can be used. There can be addition, subtraction, multiplication and division. There could also be exponents or parentheses. It may be necessary to use the order of operations to solve equations.

There are times when you may be given some information and you need to figure the rest of the information out on your own. For example, you know how much it costs to buy 1 item, but you need to figure out how much it will cost you to buy 6 items. An equation will be able to help you figure out the problem. In situations where you may not have all of the information you need, you can use what is called a variable to help you.

Variables A variable is a symbol that represents something else. Variables represent a number or value that is unknown. The most common symbols used for variables are “x” and “y.” The value of the symbol changes based on the problem that it is in. For example:

C= v × 4

In this problem, C is the total cost, 4 is how much it costs to buy a bag of chips and v is the variable. If you want to purchase 5 bags of chips, you could substitute the v for 5. You would then be able to figure out that 5 × 4= 20 and you would be spending $20 for 5 bags of chips. If you want to purchase 8 bags of chips, you could substitute the v for 8. You would then be able to figure out that 8 × 4= 32 and you would be spending $32 for 8 bags of chips.

When you are faced with a mathematical problem in which all of the numbers or values are not known, you will need to use a variable to represent that unknown value or values.

For example, there are 7 children in the neighborhood. Three of the children are girls. The other children are boys. How many boys are there? You do not know the value of the number of boys, so you would represent that value with a variable such as x. You would then represent this equation as 7 = x + 3.

Variables are used in equations. An equation is a statement about numbers. For example:

3 + 2 = 2 + 3 or 4 + x = x + 4

Representing a Variable Variables can be represented in a number of different ways. Variables can be represented as a box . However, variables are most often represented as a letter. Some of the common letters that are used for variables are: x, y, n, t, a, b, c. Letters are often used to represent a variable because a letter can stand for something. In the case of the bags of chips, you could have represented the total cost as T and the cost of the bag of chips as c for chips. The letter x is the most commonly used variable as x often stands for unknown.

Using letters to represent variables saves space and gives you much more freedom to represent the problem in the way that makes sense to you.

Using Variables Variables should be treated the same as numbers despite the fact that they are letters. They should be treated this way because they represent a number. For example:

2 + x = 5 should be treated the same as 2 + 3 = 5

When a variable is being added or subtracted it will be represented as x + 4 or x – 4. You should then add the variable or subtract the variable just as you would a number.

When a variable is being multiplied it will be represented as 2x or 2(x). When a variable is being divided it will be represented as x/2 .

You should then multiply the variable or divide the variable just as you would a number.

Solving Equations When solving equations, the most important thing is getting the variable by itself!

Step 1: Identify the variable

Step 2: Identify the operation

Step 3: Identify the opposite of the operation (for example, the opposite of addition is subtraction)

Step 4: Use the opposite operation to move the number on the same side as the variable to the other side of the equal sign

Step 5: If there is a number attached to the variable, move that number to the other side of the equal sign using the opposite operation

Step 6: Write the answer to the equation as the variable = the answer

One-step equations are equations that have one variable and one operation.

For example, x + 5 = 10 or 2x = 6

In the example x + 5 = 10, x is the only variable and addition is the only operation. In the example 2x = 6, x is the only variable and 2 is being multiplied to x. After identifying the variable and the operation, identify the opposite of the operation. The opposite of addition is subtraction.

To solve a one-step equation, the x must be isolated, or be by itself on one side.

x + 5 = 10

To get the x by itself, you must move the 5 from the left side of the equation to the right side of the equation. To do that, do the opposite of addition, which is subtraction. Subtract 5 from both sides.

x + 5 = 10

-5 -5

That leaves you with x = 5

To solve the equation 2x = 6, you must get the x by itself. Identify x as the only variable and the operation as multiplication. Since the 2 is being multiplied to x, the only way to move it is to do the opposite operation, which is to divide both sides by 2.

2x = 6

--- ---

2 2

That leaves you with x = 3

Two- step equations are equations that have more than one operation. When solving a two-step equation, it is still most important to get the variable by itself.

2x – 4 = 4

In this example, the two operations are subtraction and multiplication. After identifying the variable as x and the two operations, figure out the opposite of the operations. The opposite of subtraction is addition and the opposite of multiplication is division.

Always start by moving the number that is not closest to or attached to the variable. Start by adding 4 to both sides.

2x – 4 = 4

+4 +4

That leaves 2x = 8. To get the variable by itself, do the opposite of multiplication which means you will divide both sides by 2

2x = 8

---- ----

2 2

x = 4