Problem 63 - Prealgebra

Question

Simplify the given expression. \(\frac{11}{8}+8.2\)

Step-by-Step Solution

Answer

The simplified expression is 9.575.

Step 1: Identify the Types of Numbers

In the given expression \(\frac{11}{8}+8.2\), we have a fraction \(\frac{11}{8}\) and a decimal number \(8.2\). To simplify this expression, we need to convert the fractional part into a decimal or vice versa.

Step 2: Convert the Fraction to a Decimal

Convert the fraction \(\frac{11}{8}\) into a decimal. Divide 11 by 8 to get \(1.375\). So the expression becomes \(1.375 + 8.2\).

Step 3: Add the Decimal Numbers

Add \(1.375\) and \(8.2\). Align the decimal points and add:\[\begin{array}{c} 1.375 \+ 8.200 \\hline 9.575\end{array}\]Therefore, \(1.375 + 8.2 = 9.575\).

Step 4: Present the Simplified Expression

The final simplified expression is \(9.575\).

Key Concepts

Fractions to Decimals Conversion

Converting fractions to decimals is a helpful skill, especially when you need to perform arithmetic operations involving both fractions and decimals. To convert a fraction to a decimal, simply divide the numerator by the denominator. This means you take the top number of the fraction and divide it by the bottom number. In our exercise, \[\frac{11}{8}\]we divide 11 by 8. When you carry out this division, you will get 1.375.
Here’s a quick reminder of how to handle this:

• Write the division problem: 11 divided by 8.
• Perform the division: 11 ÷ 8 = 1.375.
• Now, you can use this decimal, 1.375, for further calculations.

Remember, turning fractions into decimals can make calculations involving mixed numbers seamless, as decimals are often easier to work with for addition and subtraction tasks.

Adding Decimal Numbers

Adding decimal numbers might seem a bit tricky at first, but it's straightforward once you understand the process. When you add decimals, always line up the decimal points to ensure each digit is in the correct place value column. This aligns the digits so you can add them just like whole numbers.
In our example, you need to add 1.375 to 8.2:

• Write the numbers under each other, aligning the decimal points:
• Recall that 8.2 can be written as 8.200 to match the number of decimal places.
• Add from right to left, following normal addition rules.

Here's how it looks:\[\begin{array}{c}1.375 \+8.200 \\hline9.575\end{array}\]

Things to keep in mind:

• Ensure to carry over values if the sum of digits in a column is 10 or greater.
• Align numbers by their decimal points for accurate results.

Practicing with various decimal numbers will help to boost your confidence and accuracy with these types of operations.

Simplifying Expressions

Simplifying expressions is all about making them easier to understand or use by combining like terms or converting different forms of numbers. In arithmetic, simplifying might mean performing all calculations until the expression is in its simplest form.
For our given example, simplifying involved first aligning both numbers in the same format (both as decimals) and then performing the addition. Once you have the decimal results, like in:\[1.375 + 8.2 = 9.575\]your expression is simplified to 9.575.

How to simplify expressions effectively:

• Ensure all parts of the expression are in compatible forms, like all decimals or all fractions, before proceeding.
• Perform operations like addition or subtraction following proper arithmetic rules.
• Double-check calculations to confirm accuracy.

By simplifying expressions thoughtfully, you make complex arithmetic more approachable and understandable. This helps streamline your math work and increase accuracy.