Problem 167 In the following exercises, simp... [FREE SOLUTION]

91影视

Prealgebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2016 Edition

Chapter 5: Problem 167

In the following exercises, simplify. $$1.15(26.83+1.61)$$

Short Answer

Expert verified

32.706

Step by step solution

- Distribute the Coefficient

Distribute the factor 1.15 to both terms inside the parentheses. This means multiplying 1.15 by 26.83 and 1.15 by 1.61 separately.

- Perform the Multiplications

Calculate the individual multiplications: $ 1.15 \times 26.83 = 30.8545 $ and $ 1.15 \times 1.61 = 1.8515 $.

- Add the Results

Finally, add the results obtained from the multiplications: $ 30.8545 + 1.8515 = 32.706 $.

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Key Concepts

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

Distributive Property

To simplify the expression $1.15(26.83 + 1.61)$, we first need to apply the distributive property. The distributive property states that a term outside the parentheses can be multiplied by each term inside the parentheses. This means that you'll multiply the 1.15 by every term within the parentheses separately.

When you see an expression like $a(b + c)$, the distributive property allows you to rewrite it as $a \times b + a \times c$. In our example, we apply this property as follows:

$$1.15(26.83 + 1.61)$$
is converted to:
$$1.15 \times 26.83 + 1.15 \times 1.61$$
After distributing, we move on to the actual multiplication step.

Multiplication

Now that we have used the distributive property to break down the expression, the next step involves multiplying each term.

For the expression $1.15 \times 26.83 + 1.15 \times 1.61$, we separately perform the two multiplication operations:

\begin{align*} 1.15 \times 26.83 &= 30.8545 \ 1.15 \times 1.61 &= 1.8515 \ \text{Thus,} & \text{we get the intermediate results:} \ & 30.8545 \text{ and } 1.8515. \end{align*}
These steps illustrate how to deal with each part of the expression before moving on to addition.

Addition

The final step in simplifying the expression involves summing up the products we calculated in the previous step.

We found that:

$1.15 \times 26.83$ equals $30.8545$
$1.15 \times 1.61$ equals $1.8515$

Now, we add these two results together:\[ 30.8545 + 1.8515 = 32.706 \]

Combining the results from the multiplication gives us the final simplified value of the expression:

$$1.15(26.83 + 1.61) = 32.706$$
This shows how the separate steps of distributive property, multiplication, and addition come together to simplify the expression.

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91影视

In the following exercises, simplify. $$1.15(26.83+1.61)$$

Short Answer

Step by step solution

- Distribute the Coefficient

- Perform the Multiplications

- Add the Results

Key Concepts

Distributive Property

Multiplication

Addition

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