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Pre Algebra Problems

Pre algebra problems are termed as the basic rules of mathematics that are very essential for the understanding, the concept of algebra at a higher level.

Pre algebra problems include fractions, percentages, the number theory, decimals, types of numbers, exponents, the PEMDAS rule, the greatest common factors etc. The fractions are defined as some part of the whole. Like $\frac{2}{3}$, $\frac{7}{5}$, $\frac{9}{2}$ are the examples of fractions.
Percentages
, which are defined as the part out of the total of 100, as a denominator.

For Example: 20% of 50 is calculated as $\frac{20}{100}$ $\times$ 50 = 10 which is equal to 10.

The Number Theory, which includes factors, which are defined as the break up of a given number into multiples of other numbers less than equal to a given number. Out of these factors of a number, we choose, the least common factors and Greatest common factors, which are helpful for performing the four mathematical operations on fractions, including addition, subtraction, multiplication and division. The rule or the order of these operations to solve a problem, which follows the PEMDAS rule, meaning first, the brackets will be open, then the division will be performed, and then multiplication followed by addition and subtraction in the end.

PEMDAS Rule

Decimals which are also a way of representing the fractions only, in points system. Like 0.4, 0.8, 1.9, 5.6 are the examples of decimal numbers.

Exponents, which are defined as the power of a number, that is, how many times a number is multiplied by itself. For example if we have number 2 multiplied by itself five times that is $2 \times 2 \times 2 \times 2 \times 2$ then we can write it as $2^{5}$.

Algebraic Expression: An algebraic expression is an expression built up from constants, variables, and a finite number of algebraic operations.

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Properties

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The basic properties of addition and multiplication which are followed by every integer, includes:

1. The commutative law of addition and multiplication
$a + b = b + a$ and $a \times b = b \times a$. 
For example: $2 + 3 = 3 + 2$ and $2 \times 3 = 3 \times 2$

2. The Associative Law under addition and multiplication
$(a + b) + c = a + (b + c)$ and $(a \times b) \times c = a \times (b \times c)$
For example $(2 + 3) + 5 = 2 + (3 + 5) and (5 \times 3) \times 10 = 5 \times (3 \times 10)$.
3. The Distributive Law
$a \times (b + c) = a \times b + a \times c$ and $a + (b \times c) = (a + b) \times (a + c)$. 
For example: $3 (6 + 5) = 3 \times 6 + 3 \times 5$.

Examples

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Below are some pre algebra problems:

1. Simplify 2x + 5 (3x + 4x)
To simplify this, we apply the PEMDAS rule 
Simplify the brackets first, we get 2x + 5(7x). 
Multiply 5 by 7x, we get 
2x + 35x 
Now add both the terms.
This can be simplified to 37x

2. Solve for x.
3x + 22 = 12 x + 4
We subtract 4 from both sides, we get
3x + 22 - 4 = 12x + 4 - 4
3x + 18 = 12x 
Subtract 3x from both sides, we get
3x + 18 - 3x = 12x - 3x
18 = 9x
Now we can divide both sides by 9, which gives x = 2

3. What is 15 % of 640?
To solve this, we multiply $\frac{15}{100}$$ \times 640$, we get 96.
Hence we can say that 15 % of 640 is 96.


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