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Scan for outdated or missing drivers - takes under a minuteDriver Scan →Clear out junk files and repair common Windows errorsFree Scan →Fix the driver behind crashes, sound loss and screen glitchesFind Drivers →Addition combines quantities to make a sum; multiplication forms a product. In an expression such as 4 + 3 × 7, multiply first and then add, so the result is 25. Parentheses can change that order: (4 + 3) × 7 equals 49.
What do multiply and add mean?
Addition combines quantities. For example, 4 + 2 = 6: the sum of 4 and 2 is 6.
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Multiplication forms a product. For whole numbers, it can be understood as counting equal-sized groups: 4 × 2 means four groups of two, for a total of 8. The dot in 4 · 2 is another multiplication symbol, so 4 · 2 + 1 means multiply 4 by 2, then add 1. (OpenStax explains these operations and notation in its introduction to the language of algebra.)
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When an expression includes both, which comes first?
In standard arithmetic notation, multiplication and division are evaluated before addition and subtraction, unless parentheses or other grouping specify a different order. For 4 + 3 × 7, calculate 3 × 7 = 21 first, then 4 + 21 = 25. Likewise, 3 + 5 · 2 = 13: multiply 5 by 2, then add 3.
This convention makes an unparenthesized expression readable in a consistent way. If you mean to add before multiplying, show that grouping with parentheses: (4 + 3) × 7. Add first to get 7, then multiply by 7, giving 49. The Open University’s guide to the sequence of arithmetic calculations likewise explains how grouping clarifies or changes the order.
How do parentheses affect the result?
Parentheses tell the reader to treat the enclosed calculation as a group. Compare:
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4 + (3 × 7): multiply inside the parentheses, then add; the result is 25.(4 + 3) × 7: add inside the parentheses, then multiply; the result is 49.
The first expression makes the usual multiplication-before-addition order explicit. The second deliberately changes it. When an expression could be misread, parentheses make the intended calculation clear.
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How should equal-priority operations be handled?
Multiplication and division share one priority level, as do addition and subtraction. When operations at the same level appear together, evaluate them from left to right. PEMDAS is a memory aid, not a rule that multiplication always outranks division or addition always outranks subtraction.
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For example, in 20 ÷ 5 × 2, work left to right: 20 ÷ 5 = 4, then 4 × 2 = 8. In 10 − 3 + 2, calculate 10 − 3 = 7, then 7 + 2 = 9. Parentheses can make a different grouping explicit.
How is this different from the distributive property?
The order-of-operations convention tells you how to read a written expression. The distributive property is a mathematical relationship between multiplication and addition: multiplying a sum by a number gives the same result as multiplying each addend by that number and adding the products.
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2 × (3 + 4) = 2 × 3 + 2 × 4 = 14
This property can help simplify expressions, but it does not remove the need to follow grouping and precedence when evaluating the original expression. The National Academies’ Adding It Up, Chapter 3, discusses arithmetic concepts including these relationships.
What if you are entering the calculation in Excel?
Excel follows the familiar precedence convention: multiplication is calculated before addition, and parentheses can change the calculation order. Microsoft’s documentation on calculation operators states, “Using parentheses allows you to change that calculation order.” For example, an Excel formula corresponding to 4 + 3 × 7 is =4+3*7; to add first, enter =(4+3)*7.
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