Order of operations
When an expression contains several operations, start with brackets. Next calculate powers, then multiplication and division, and finally addition and subtraction. Operations with the same priority are calculated from left to right.
In 2 + 3 · 4 do the multiplication first: 3 · 4 = 12. Then 2 + 12 = 14.
With brackets, the problem changes: (2 + 3) · 4 = 5 · 4 = 20. Write one step per line so you can see what you have calculated.
Calculating with fractions
Simplifying and extending
Simplify: Divide the numerator and denominator by the same number.
Example: 1218 = 12 : 618 : 6 = 23
Extend: Multiply the numerator and denominator by the same number.
Example: 25 = 2 · 35 · 3 = 615
What does a fraction look like?
A fraction is a part of a whole. The bars below show ⅓, ½ and ¾ — compare them:
When we add fractions, the «parts» must be the same size. That is why we need a common denominator:
Addition and subtraction
The fractions must have a common denominator:
Example: 13 + 14 = 412 + 312 = 712
Multiplying fractions
Example: 23 · 57 = 1021
Dividing fractions
We invert the second fraction and multiply:
Example: 34 : 25 = 34 · 52 = 158
Algebra with fractions
The same rules apply to letters:
Example: 2x + 3x + 1 = 2(x + 1) + 3xx(x + 1) = 5x + 2x(x + 1)
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