Problem 59 - Algebra 1: Concepts and Skills

Question

Use the distributive property and mental math to simplify the expression. $$ 2(2.90) $$

Step-by-Step Solution

Answer

The simplified expression is 5.80

Step 1: Applying the Distributive Property

In this case, the distributive property was simply used to separate the multiplication into one multiplication problem. Because there are not multiple terms in the parentheses being added or subtracted, the expression can be restated as \( 2 * 2.90 \) directly.

Step 2: Perform the Multiplication

Using multiplication for 2 and 2.90 yields \( 2 * 2.90 = 5.80 \)

Key Concepts

Mental Math

Mental math refers to the practice of performing calculations in your head, without the use of pencil, paper, or calculators. It is a valuable skill that enhances number sense and promotes a deeper understanding of mathematical principles. Simplifying expressions using mental math requires familiarity with arithmetic operations and the ability to manipulate numbers quickly and accurately.

When applying mental math to multiplication, like in the exercise given with the expression 2(2.90), we often use strategies such as breaking numbers down into more manageable parts, or using known multiplication facts as stepping stones. For instance, recognizing that 2 is the same as 1 + 1 can simplify your calculations, so you are doubling the number 2.90 instead of using a more complex multiplication method.

Simplify Expressions

The process of simplifying expressions makes equations more straightforward to solve. It typically involves reducing equations to their simplest form by performing all possible arithmetic operations and combining like terms.

Using the Distributive Property

The distributive property is a key tool for simplifying expressions, especially when dealing with numbers inside parentheses. It allows us to multiply a single term by each individual term inside the parentheses. However, when there is only one term within the parentheses, as in the provided exercise 2(2.90), the distributive property simply aids in rewriting the expression in a multiply-ready form, which in this instance, is straightforward multiplication.

Multiplication

Multiplication is one of the four essential operations in arithmetic. It can be thought of as repeated addition. To multiply is to add a number (the multiplicand) to itself a certain number of times (the multiplier). In our example, we are asked to multiply 2 by 2.90. Since we are working with a whole number and a decimal, we can use mental math to recognize that multiplying by 2 simply doubles the number. Therefore, 2.90 doubled is 5.80, giving us an efficient path to the answer without complex calculations. This is a fundamental concept in understanding how to simplify and solve expressions using multiplication.