Mental Math
Part of the Expressions & Data section of Coddy's Pre-Algebra journey. Lesson 12 of 52.
What is 3 × 14? Split 14 into 10 and 4. Three groups of 14 are three groups of 10 and three groups of 4, so 3(10 + 4) is 3 × 10 + 3 × 4, which is 30 + 12, or 42. Multiplying a sum is the same as multiplying each part and adding the results.
This is the distributive property: a(c + d) = ac + ad. The number outside the parentheses is shared out, or distributed, to every part inside. It works with a difference too, as a(c - d) = ac - ad.
It turns hard products into easy ones. 6 × 99: 99 is 100 - 1, so the product is 6 × 100 - 6 × 1, which is 600 - 6, or 594. Rounding to a friendly number and then correcting is how quick mental arithmetic works.
Challenge
Work out 7 × 98 without long multiplication. Write 98 as 100 - 2 and distribute the 7 in your first line, then finish one step per line.
Try it yourself
Simplify the expression
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Expressions & Data
1Variables and Expressions
What a Variable IsWriting ExpressionsExpressions from StoriesTwo OperationsRecap: Expressions2Evaluating Expressions
Substituting a ValueNegative InputsPowers in ExpressionsFormulasRecap: Evaluating5Patterns and Sequences
Continuing a PatternThe Common DifferenceThe nth TermWriting the RuleRecap: Sequences3The Distributive Property
Number PropertiesMental MathDistributing LettersDistributing a MinusRecap: Distributing