Like terms are terms that have the same variable part i.e. they only differ in their coefficients. Combining like terms is very often required in the process of simplifying equations.

For example:

2x and –5x are like terms

a and are like terms

6x and 5y are unlike terms

Like terms can be added or subtracted from one another.

Solving Equations using Multiplication or Division

Removal of Brackets - Distributive Property

Sometimes removing brackets (parenthesis) allows us to simplify the expression. Brackets can be removed by using the distributive property. This is often useful in simplifying equations.

Cross multiplication allows you to remove denominators from fractions in an equation. Note that this technique applies only towards simplifying equations, not to simplifying expressions.

For example, if you have the equation:

then you can multiply the numerator of one fraction with the denominator of the other fraction (across the = sign) as shown:

to obtain the equation

(2 × 6) = a × 3

Example 1:

Simplify:

Solution:

Step 1: Cross Multiply

4 × a = 8 × 5
4a = 40

Step 2: Isolate variable a

Answer: a = 10

Solve equations easily by cross-multiplying when there are two fractions.

Have a look at the following video for more examples on simplifying equations:

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