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Imagine two people solve the exact same math problem, 3+4×23 + 4 \times 2, but one gets 11 and the other gets 14.
Both did their arithmetic correctly, so how can one number sentence lead to two completely different results?

The Standard Rule vs. Brackets

In math, the standard order of operations says we always multiply and divide before we add and subtract.
When we add brackets (also called parentheses), they act like a VIP pass that forces us to calculate whatever is inside them first.
Without brackets in 3+4×23 + 4 \times 2, we compute 4×2=84 \times 2 = 8 first, then 3+8=113 + 8 = 11.
With brackets in (3+4)×2(3 + 4) \times 2, the brackets override standard order, giving 7×2=147 \times 2 = 14.
What happens when brackets surround a subtraction or division step instead?

Controlling Subtraction and Division

Consider the expression 20−8+320 - 8 + 3. Normally, addition and subtraction have equal priority, so we move from left to right: 20−8=1220 - 8 = 12, and 12+3=1512 + 3 = 15.
If we place brackets around 8+38 + 3 to make 20−(8+3)20 - (8 + 3), we must add first: 8+3=118 + 3 = 11, leaving 20−11=920 - 11 = 9.