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Chapter 1: Problem 5

Translate the English phrase into a mathematical statement and simplify. Twice 14

Short Answer

Expert verified
28

Step by step solution

01

Understand the Phrase

The phrase 'twice 14' means that 14 is multiplied by 2.
02

Translate to Mathematical Expression

Write the phrase as a mathematical expression: \[ 2 \times 14 \]
03

Simplify the Expression

Multiply the numbers: \[ 2 \times 14 = 28 \]

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Key Concepts

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

Translation of Phrases to Expressions
In mathematics, it's common to translate words and phrases into numbers and symbols. This helps us solve problems more easily. For example, in the phrase 'twice 14,' the word 'twice' means 'two times.' So, we can replace 'twice' with the multiplication symbol (*). This gives us the expression:

\( 2 \times 14 \).

It's important to understand what each word in a phrase means in mathematical terms. Words like 'sum,' 'product,' 'difference,' and 'quotient' each have specific meanings.
  • 'Sum' means addition.
  • 'Product' means multiplication.
  • 'Difference' means subtraction.
  • 'Quotient' means division.
Translating phrases into mathematical expressions is a crucial first step in solving many math problems.
Multiplication
Multiplication is one of the basic arithmetic operations. It's a quick way to add groups of the same size. For instance:

\[ 2 \times 14 \] means you have two groups of 14.

Here's how you can multiply step-by-step:
  • Start with the first number, in this case 2.
  • Then take the second number, 14.
  • Multiply the two numbers together. You can think of it as adding 14 to itself:
    \[ 14 + 14 = 28 \]
Multiplication can also be shown through repeated addition, making it easier to understand:
Two groups of 14 added together give us:
\[ 2 \times 14 = 28 \].

Understanding multiplication will help you solve various mathematical problems more quickly and accurately.
Simplification of Expressions
Simplification involves making an expression easier to understand or work with while keeping its value the same. In our example, we have the mathematical expression
\[ 2 \times 14 \].

To simplify it, we perform the multiplication: \[ 2 \times 14 = 28 \].

Here are the basic steps for simplification:
  • Perform operations following the order of operations (PEMDAS/BODMAS): Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
  • Simplify each part of the expression step by step.
  • Combine like terms if necessary.
Simplification makes expressions easier to understand and work with. It's a fundamental skill in math that will be useful in solving both simple and complex problems.

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Most popular questions from this chapter

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