The initial branch of algebra is pre-algebra. Students are prepared for the algebra classes in high school through this. Pre-algebra and Pre-algebra formulas are necessary to completely understand algebra. This teaches pupils some fundamental pre-algebra formulas that they can use in their daily lives to calculate things like speed, profit, and loss.

Pre-algebra formulae are used to teach students how to use variables to solve fundamental mathematical equations.

It’s common for pupils to believe that pre-algebra and algebra are interchangeable, but this is untrue. Before the end, you will be able to distinguish between algebra and pre-algebra.

**These are the topics covered in Pre-algebra.**

**Number theory**

- Whole numbers
- Roman numerals
- Rational numbers
- Real numbers
- Integers
- Pythagorean theorem
- Absolute value

**Factors and Multiples**

- Factors
- Multiples
- Prime numbers
- Composite numbers
- Prime factorizations

**Linear Equations**

- Algebraic expressions
- By substitution, solve the linear system
- Linear equations
- Linear equation solutions
- Equation solver system
- Variable expressions

**Ratio and Proportions**

- Ratio
- proportion

**Exponent and Square Root**

- Fractions
- Exponents
- Order of operation
- Square roots

**Statistics**

- Mean, median, mode
- Probability

**Pre-algebra formulas**

Here are some important and useful Pre-algebra formulas

**Speed**

The speed (s) of an object is equal to the distance (d) traveled by the object per unit of time (t).

Speed (s)= Distance (d) / Time (t)

**Pythagoras theorem**

Pythagoras theorem is the theorem to find the hypotenuse of a right-angled triangle. According to this theorem, the square of the hypotenuse of a right-angled triangle is equal to the sum of the square of the base and the height of the triangle. It is one of the most important Pre-Algebra formulas.

Hypotenuse (h)2 = Base (b)2 + Height (h)2

**Profit**

Profit on an object is defined as the difference between the selling price and the cost price. In the case of profit, the selling price of an object is always greater than the cost price of the object. The selling price is the price at which shopkeepers sell the product. And the cost price is the price on which he (shopkeeper) bought the product.

Profit on an object (P) = selling price of an object (Sp) – cost price of an object (Cp)

**Loss**

Loss on an object occurs when the cost price of an object is greater than the selling price of that object. In other words, the Loss on an object is defined as the difference between the cost price and the selling price.

Loss on an object (L) = Cost price of object (Cp) – selling price of the object (Sp)

**Discount**

A discount is defined as the ratio of the discount percentage given on the product to the maximum retail price (MRP) of that product, multiplied by 100.

Discount (d) = ( discount percentage (d%) / maximum retail price (MRP) ) * 100

**The slope of a line**

The slope of a line joining two points ( X1, Y1 ) and ( X2, Y2 ) is equal to the change in the y-axis value over the change in the x-axis.

( Y2 – Y1 ) / ( X2 – X1 ) = M

**Point slope formula**

The point slope formula or the equation of the straight line is equal to

(Y – Y1) / ( X -X1 ) = M

Where M is the slope of the line and ( X1, Y1 ) is the point line that passes through. X and Y are the equation’s variables.

**Distance between two points of a line**

Distance between two points of a line is equal to the square root of the sum of the square of the change in the value of the x-axis and the change in the value of the y-axis.

Distance between two points of a line (d) = √[ (X2- X1)2 + ( Y2 – Y1)2 ]

**Mean**

Mean is defined as the average of given observations and is calculated by dividing the sum of the observations by the total number of observations.

mean = total of the given observations / total number of the observations

**Probability**

Possibility of an event happening is defined as the Probability. It is calculated by dividing the number of favorable cases by the total number of cases of a sample space. The probability of an event happening is always greater than 0 and less than 1. That is 0<P<1.

probability of an event (PA) = number of favorable cases (NA) / total number of cases (NS)

**Differences between algebra and Pre-algebra**

Pre-Algebra | Algebra |

Pre-algebra gives the basic knowledge of algebra to the students. | Algebra increases the complexity and the understanding of the topics learned in Pre-Algebra. |

Pre-Algebra is essential to understanding Algebra 1 and Algebra 2. | Algebra is the main branch of mathematics which consist of Pre-Algebra, Algebra 1, and Algebra 2. |

**Differences between algebra and Pre-algebra**

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**Conclusion**

We have covered pre-algebra and pre-algebra formulae in this post since they are crucial to comprehending algebra. At the end of the post, I have made a distinction between algebra and pre-algebra for those who were unsure about algebra and pre-algebra.

I hope you have liked reading this post on pre-algebra basics of Pre-algebra and Pre-algebra formulas. And I hope am able to clear all your queries about Pre-algebra and Pre-algebra formulas. For more posts related to education visit our website regularly.

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