Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 137

Chapter 1, Problem 137

Use the distributive property to calculate each value mentally. 72∙17+28∙17

Verified step by step guidance

Recognize that both terms, \(72 \times 17\) and \(28 \times 17\), share a common factor of 17.

Apply the distributive property: \(a \times c + b \times c = (a + b) \times c\). So rewrite the expression as \((72 + 28) \times 17\).

Add the numbers inside the parentheses: calculate \(72 + 28\).

Multiply the sum by 17: calculate \((72 + 28) \times 17\).

This approach simplifies the calculation by reducing two multiplications into one multiplication after addition.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. For example, a(b + c) = ab + ac. This property helps simplify calculations by breaking them into easier parts.

Mental Math Strategies

Mental math involves performing calculations in your head without paper or a calculator. Using properties like distributive property allows you to simplify complex expressions into smaller, manageable parts, making mental computation faster and more efficient.

Factoring Common Terms

Factoring common terms means identifying and extracting a shared factor from terms in an expression. In the expression 72*17 + 28*17, 17 is common and can be factored out as 17(72 + 28), simplifying the calculation.

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