How to solve equations for grade 5?
An equation is an equation in which there is an unknown term - x. Its value and need to find.
The unknown value is called the root of the equation. To solve an equation means to find its root, and for this you need to know the properties of the equations. The equations for Grade 5 are simple, but if you learn to solve them correctly, you will not have problems with them in the future.
Main property of equations
If both sides of the equation change by the same amount, it continues to be the same equation with the same root. Let's solve a few examples to better understand this rule.
How to solve equations: addition or subtraction
Suppose we have an equation of the form:
- a + x = b - here a and b are numbers, and x is the unknown term of the equation.
If we add (or subtract from) the value of c to both sides of the equation, it will not change:
- a + x + c = b + c
- a + x - c = b - c.
We use this property to solve the equation:
- 37 + x = 51
Subtract the number 37 from both parts:
- 37 + x-37 = 51-37
- x = 51-37.
The root of the equation is x = 14.
If we look closely at the last equation, we see that it is the same as the first. We simply transferred the 37 term from one part of the equation to the other, replacing the plus by the minus.
It turns out that any number can be transferred from one part of the equation to another with the opposite sign.
- 37 + x = 37 + 22
Let's perform the same action, transfer the number 37 from the left side of the equation to the right:
- x = 37-37 + 22
Since 37-37 = 0, then we simply reduce and get:
- x = 22.
Identical terms of the equation with the same sign, located in different parts of the equation, can be reduced (crossed out).
Multiplication and division of equations
Both parts of the equation can also be multiplied or divided by the same number:
If the equality a = b is divided or multiplied by s, it will not change:
- a / c = b / s
- ac = bc
- 5x = 20
We divide both sides of the equation by 5:
- 5x / 5 = 20/5.
Since 5/5 = 1, then we multiply this multiplier and the divisor on the left side of the equation and get:
- x = 20/5, x = 4
- 5x = 5a
If both sides of the equation are divided by 5, we get:
- 5x / 5 = 5a / 5.
5 in the numerator and denominator of the left and right parts are reduced, it turns out x = a. Hence, the same factors in the left and right sides of the equations are reduced.
Let's solve one more example:
- 13 + 2x = 21
We transfer the term 13 from the left side of the equation to the right with the opposite sign:
- 2x = 21 - 13
- 2x = 8.
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