Parentheses rule

The bracket rules describe in arithmetic and elementary algebra rules for resolving brackets in pure sums and differences , so expressions in which only occur plus and minus. Colloquially, other rules that describe the use of brackets in mathematical expressions, as allowed by the distributive law, are also called rules of brackets .

Rules of brackets in the narrower sense

The following applies to the resolution of brackets in sums and differences:

If there is a plus sign in front of the bracket, the bracket can simply be left out.

{\ displaystyle a + (b + c) = a + b + c}

{\ displaystyle a + (bc) = a + bc}

If there is a minus sign in front of the bracket, the bracket may only be omitted if the characters within the bracket are reversed.

{\ displaystyle a- (b + c) = abc}

{\ displaystyle a- (bc) = a-b + c}

Examples

${\ displaystyle 5+ (1-5) = 5 + 1-5 = 1}$
${\ displaystyle 3 - (- 3 + 7) = 3 + 3-7 = -1}$
${\ displaystyle (n + 1) - (n-1) = n + 1-n + 1 = 2}$

Rules of brackets in a wider sense

If brackets appear in mathematical expressions, the operations (e.g. plus or times) inside the brackets are always carried out before those outside the brackets.

example 1

(2 + 5) · 3 = 7 · 3 = 21, (first the “+”, then the “·” because of the brackets), but

2 + 5 3 = 2 + 15 = 17, point calculation before line calculation .

Example 2

(2 x 3) 2 = 6² = 36, but

2 x 32 = 2 x 9 = 18.

Individual evidence

↑ Kreul, Hans .: Mathematics made easy: 781 problems with solutions . Special edition the 6th, rework. Ed. Of the textbook "Moderner Vorkurs der Elementarmathematik", 4th ed. German, Thun 1994, ISBN 3-8171-1356-0 .

[1] Kreul, Hans .: Mathematics made easy: 781 problems with solutions . Special edition the 6th, rework. Ed. Of the textbook "Moderner Vorkurs der Elementarmathematik", 4th ed. German, Thun 1994, ISBN 3-8171-1356-0 .