Problem 114 - Prealgebra

Question

In the following exercises, translate each phrase into math notation and then simplify. $$ 115 \text { more than } 286$$

Step-by-Step Solution

Answer

401

Step 1: Identify the Key Components

The phrase '115 more than 286' indicates that we are adding 115 to 286.

Step 2: Translate the Phrase into Math Notation

'115 more than 286' can be translated into the mathematical expression: 286 + 115

Step 3: Simplify the Expression

Add the two numbers together to get: 286 + 115 = 401

Key Concepts

headline of the respective core concept

When translating phrases into math notation, you begin by identifying key terms in the text. For instance, phrases like 'more than' typically indicate addition. In the exercise '115 more than 286', the words 'more than' tell us that we should add the two numbers.

Next, we translate the words into a math equation. We change '115 more than 286' into a numerical expression, which results in:

• 286 + 115

This step is essential because it transforms words into a format we can work with mathematically.

Finally, we simplify the equation to get the answer:

• 286 + 115 = 401

headline of the respective core concept

Simplification in math means making an expression easier to understand or solve. Once we have translated our phrase into a math equation, the next step is to simplify it.

In this exercise, simplifying means simply performing the arithmetic operation of addition. We start with:

• 286 + 115

To solve this, we align the numbers vertically, ensuring the digits are in the correct columns. Then, we add each column starting from the rightmost digit (units place):

• 6 + 5 = 11 (write down 1, carry over 1)
• 8 + 1 + 1 (carried over) = 10 (write down 0, carry over 1)
• 2 + 1 (carried over) = 4

Therefore, 286 + 115 simplifies to 401.

headline of the respective core concept

Basic arithmetic is the foundation of all mathematics. It includes the basic operations we use every day: addition, subtraction, multiplication, and division.

Addition is one of the key operations in arithmetic. It combines two numbers to make a larger one. The symbols used are the plus sign (+) and the equals sign (=). For example, if we add 286 and 115, we perform the following operation:

• 286 + 115
• 6 + 5 = 11 (1 in units place, carry over 1)
• 8 + 1 + 1 = 10 (0 in tens place, carry over 1)
• 2 + 1 = 4 in the hundreds place

Practicing these basic arithmetic operations helps build strong math skills. Once mastered, they aid in solving complex problems.