Problem 769 Simplify. $$ 10(0.1 d) $$... [FREE SOLUTION]

Chapter 1: Problem 769

Simplify. $$ 10(0.1 d) $$

Short Answer

Expert verified

The simplified expression is $d$.

Step by step solution

- Understand the Problem

We need to simplify the expression $10(0.1d)$. This means we need to eliminate the parentheses and simplify the multiplication.

- Distribute the 10

Distribute the factor 10 to the term inside the parentheses: $10 \times 0.1d$.

- Multiply the Numbers

Perform the multiplication: $10 \times 0.1 = 1$. Therefore, $10 \times 0.1d = 1d$.

- Simplify the Final Expression

The expression can be simplified to $d$, since $1d$ is the same as $d$.

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Key Concepts

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

Distributive Property

The Distributive Property is a fundamental algebra concept. It allows you to multiply a single term by each term inside parentheses. For instance, in the expression
\[a(b + c)\rightarrow ab + ac\]
you distribute 'a' to both 'b' and 'c'. Let's break it down:

'a' multiplies 'b' yielding 'ab'
'a' multiplies 'c' yielding 'ac'

So, \[a(b + c) = ab + ac\]. This property helps to remove parentheses in an expression, making it easier to work with. In our problem, the distributive property allows us to simplify \[10(0.1d)\rightarrow (10 \times 0.1d)\].

Multiplication of Decimals

Multiplying decimals might seem tricky, but it's simple with a few steps. Consider the numbers without the decimal point. Multiplicate these as you would whole numbers. Then, count the total number of decimal places in both numbers. Place the decimal into the product so it has that many places. For instance:

Multiply 10 and 0.1
Ignore the decimal and think of it as 10 and 1
10 times 1 equals 10

0.1 has one decimal place, so place the decimal one position from the right. This gives you 1. Therefore, \[10 \times 0.1 = 1\].

Algebraic Simplification

Algebraic simplification is crucial for solving equations easily. It involves reducing expressions to their simplest form. In our example, after distributing and multiplying the decimals, we get \[1d\rightarrow d\].

Combine like terms: if possible
Reduce coefficients of variables
Eliminate unnecessary terms

The final expression in the problem is simplified to 'd'. Simplification makes equations easier to solve and understand.

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91影视

Simplify. $$ 10(0.1 d) $$

Short Answer

Step by step solution

- Understand the Problem

- Distribute the 10

- Multiply the Numbers

- Simplify the Final Expression

Key Concepts

Distributive Property

Multiplication of Decimals

Algebraic Simplification

One App. One Place for Learning.

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