Problem 74 - Algebra 1: Concepts and Skills

Question

Add. Write the answer as a decimal. (Skills Review pp. 759, 767) $$0.58+\frac{2}{5}$$

Step-by-Step Solution

Answer

The sum is 0.98.

Step 1: Convert Fraction to Decimal

Firstly, the fractional term needs to be converted to a decimal. The fraction provided is \(\frac{2}{5}\). Diong the division of the numerator (2) by the denominator (5), the result is 0.4.

Step 2: Perform Addition

Now, perform the addition operation with both decimal numbers. Add the decimal obtained from step 1, 0.4, to the other decimal term 0.58. The result is 0.98.

Key Concepts

Fraction to Decimal Conversion

To tackle problems involving both fractions and decimals, it's essential to understand how to convert a fraction to a decimal. In our example, we have the fraction \(\frac{2}{5}\). Converting this to a decimal is straightforward and involves a simple division operation. Here’s how you can do it:

• Identify the numerator and the denominator in the fraction. In \(\frac{2}{5}\), 2 is the numerator, and 5 is the denominator.
• Divide the numerator by the denominator. So, you calculate \(2 \div 5\).
• The result of the division gives you the decimal equivalent. \(2 \div 5 = 0.4\).

This method will help you convert any fraction into a decimal, making it easier to perform further arithmetic operations, such as addition.

Basic Arithmetic

Basic arithmetic operations are the foundation of mathematics, consisting of addition, subtraction, multiplication, and division. In problems like the one presented, where you need to add decimals, knowing the basics of addition is crucial.For adding decimals:

• Make sure the decimal points are lined up vertically. This ensures each digit is in the correct place value position.
• Start adding from the rightmost digits (smallest place value) to the leftmost (biggest place value), just like in whole number addition.
• Carry over any value greater than 10 to the next left column.

Incorporating these simple rules can help handle decimal addition correctly, leading to accurate results, such as \(0.58 + 0.4 = 0.98\).

Problem Solving Steps

Approaching a math problem systematically can simplify the process and enhance understanding. For the given task of adding \(0.58\) and \(\frac{2}{5}\), follow these problem-solving steps to organize your approach:

• Identify what you need to find. In this case, the sum expressed as a decimal.
• Convert all parts of the problem into the same format, e.g., converting fractions to decimals so everything matches up.
• Perform any straightforward calculation that follows. For example, adding \(0.58 + 0.4\) directly after converting \(\frac{2}{5}\) to \(0.4\).
• Double-check each step to confirm accuracy and avoid any mistakes.

Practicing these steps strengthens problem-solving skills, ensures accuracy, and builds confidence when dealing with decimals and fractions.