Exploring the Distributive Property in Multiplication

In this video, Jeff Jacobson introduces the distributive property, explaining its concept and application in mathematics. He demonstrates how to use the distributive property with both numerical and algebraic expressions, including variables. The video also covers mental math techniques using the distributive property and how to apply it to mixed numbers. Finally, Jeff provides examples of simplifying expressions using this property, emphasizing the importance of understanding like terms and order of operations.

What does the distributive property allow us to do with a number outside parentheses?

• Add it to each term inside the parentheses

• Multiply it by each term inside the parentheses

• Divide it by each term inside the parentheses

• Subtract it from each term inside the parentheses

What does the distributive property equate to in the expression 7(3 + 2)?

• 21

• 35

• 25

• 14

Why can't we simply add 3 + X in the expression 7(3 + X)?

• Because X is an unknown variable

• Because 3 and X are like terms

• Because addition is not allowed in algebra

• Because the distributive property does not apply to variables

In the expression 7(3 + X), what does 7 times X equal?

• 21

• X7

• 7X

• 10

How can the distributive property help in mental math for 8 * 53?

• By converting 53 into 50 + 3 and distributing 8

• By adding 8 to 53

• By directly multiplying 8 and 53

• By dividing 53 by 8

What is the result of using the distributive property on 6 * 35?

• 220

• 215

• 210

• 225

What is 1/2 times 2 and 3/4 simplified using the distributive property?

• 1 and 3/8

• 4 and 1/2

• 2 and 1/2

• 3 and 1/4

How do we simplify 1/2 times 2 + 1/2 times 3/4 using the distributive property?

• 2 and 1/4

• 1 and 1/2

• 2

• 1 and 3/8

What is a common mistake when applying the distributive property?

• Forgetting to distribute to every term

• Distributing to terms outside the parentheses

• Multiplying terms instead of adding them

• Adding terms instead of multiplying them

When simplifying 9(6 + 2X + 3), what should you do first?

• Combine like terms inside the parentheses

• Distribute 9 to each term immediately

• Multiply 9 by 6 only

• Ignore the variable X