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Chapter 8: Problem 6

Use the distributive property to compute each value. $$ 8(9-7) $$

Short Answer

Expert verified
The result of \( 8(9-7) \) is 16.

Step by step solution

01

Identify the Distributive Property

The distributive property states that for any three numbers \( a \), \( b \), and \( c \), the expression \( a(b+c) \) is equal to \( ab + ac \). This property also applies to subtraction, so \( a(b-c) \) is equal to \( ab - ac \). We will apply this to the expression \( 8(9 - 7) \).
02

Apply the Distributive Property

We use the distributive property on \( 8(9 - 7) \) as follows: \( 8 \times 9 - 8 \times 7 \).
03

Compute the Individual Products

Calculate the product of 8 and 9: \( 8 \times 9 = 72 \). Next, calculate the product of 8 and 7: \( 8 \times 7 = 56 \).
04

Subtract the Products

Now subtract the products obtained in Step 3: \( 72 - 56 = 16 \).
05

Review the Solution

The final result of \( 8(9 - 7) \) using the distributive property is 16.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Subtraction
Subtraction is one of the basic arithmetic operations. It involves taking one number away from another. In the context of our exercise, we have the expression \(9 - 7\). This means we take away 7 from 9.
  • When subtracting, we start with the 'minuend,' which is the initial number, 9 in this case.
  • We subtract the 'subtrahend,' which is 7 here, from the minuend.
  • The result is called the 'difference.'

So, \(9 - 7 = 2\), which is the difference. Subtraction helps us in breaking down expressions, especially when using properties like the distributive property.
Grasping Arithmetic Operations
Arithmetic operations are fundamental in mathematics. They include addition, subtraction, multiplication, and division. Each operation has its properties and uses in simplifying math problems.
  • Addition: Combining two or more numbers.
  • Subtraction: Removing a number from another.
  • Multiplication: Scaling one number by another.
  • Division: Splitting a number into equal parts.

In our problem, we emphasize multiplication and subtraction as part of using the distributive property. Understanding these operations and how they interact forms the foundation of math problem-solving.
Exploring Product Calculation
Product calculation refers to the process of multiplying numbers. For example, in the expression \(8(9 - 7)\), we use the distributive property which involves multiplying \(8\) by each number inside the parenthesis separately.
  • First, calculate \(8 \times 9 = 72\).
  • Then, calculate \(8 \times 7 = 56\).

These are individual products obtained using multiplication. Lastly, we subtract the products: \(72 - 56\), which gives the final value of 16. Product calculation is crucial in using the distributive property effectively.

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Most popular questions from this chapter

Estimate the sum: \(43,892+92,106\).

Use the distributive property to compute each product. \(35 \cdot 12\)

Use the distributive property to compute each value. \(25 \cdot 12\)

Compute each product using the distributive property. \(19 \cdot 85\)

Estimate each calculation using the method of rounding. After you have made an estimate, find the exact value and compare this to the estimated result to see if your estimated value is reasonable. Results may vary. $$ 8,092 \div 239 $$
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