TRANSLATING ENGLISH PHRASES TO MATHEMATICAL SYMBOLS AND VICE-VERSA || GRADE 7 MATHEMATICS Q2
Translating English Phrases to Mathematical Symbols
Introduction to Translation of Expressions
- The video aims to teach how to translate English phrases into mathematical symbols and vice versa, focusing on algebraic expressions. Familiarity with terms related to addition, subtraction, multiplication, and division is essential for this process.
Key Terms for Operations
Addition
- Important keywords include "the sum of," "added to," "increased by," "plus," "more than," and "exceeds by." These terms indicate the operation of addition.
Subtraction
- Keywords for subtraction are "the difference of," "diminish by," "decrease by," "minus," "subtracted from," and "less than." Understanding these terms helps in identifying subtraction operations.
Multiplication
- For multiplication, phrases like “of” (e.g., “one-half of 24,” “three-fourths of a number”) indicate the need for multiplication in translation. It can also be represented side-by-side as a product.
Division
- Division is indicated by terms such as “split into,” “ratio,” “all over,” and “divided by.” The concept of exponents is introduced with terms like square or cube, which represent powers in mathematics.
Translating Specific Phrases into Algebraic Expressions
Examples of Addition and Subtraction
- Translating phrases like “x plus 5” results in expressions such as x + 5 . Similarly, phrases like “five less than x” translate to x - 5 . Care must be taken regarding the order when translating addition and subtraction statements.
More Complex Translations
- The phrase “the sum of m plus eight” translates directly to m + 8 , while “seven minus eight” becomes 7 - 8 . Understanding context is crucial for accurate translations.
Further Examples Involving Multiplication and Division
- Phrases indicating multiplication include:
- “The product of nine and n” translates to 9n .
- “Twice a number” means 2x where x represents the number.
- “The quotient of a number and ten” translates to x/10 . Here, understanding that 'quotient' indicates division is key.
Additional Examples
- Other examples include:
- “Ten less b” translates to 10 - b .
- “Three-fourths of a number” indicates multiplication resulting in 3/4x .
- “The product of twelve and a number decreased by eight” combines both operations leading to an expression like 12x - 8. This highlights the importance of recognizing multiple operations within one phrase.
Conclusion on Translation Techniques
- The video emphasizes that translating English phrases into mathematical symbols requires careful attention to keywords that denote specific operations (addition, subtraction, multiplication, division). Mastery over these concepts allows for effective communication between verbal descriptions and mathematical representations. Understanding how different operations interact within complex phrases enhances clarity in translation tasks.
Operation Order of Operations
Understanding Mathematical Expressions
- The discussion begins with the concept of translating mathematical expressions, specifically focusing on "the sum of twice a number and five." This highlights the importance of using variables (e.g., 2 times x increased by 5) in algebraic expressions.
- The phrase "the difference of x and three times y" is introduced as an example of subtraction in algebra. It emphasizes how to articulate mathematical operations verbally.
- The expression "the square of a minus four times b" is explained, showcasing how to express squared terms and their relationships with other variables.
- The speaker elaborates on multiplication through the example "three times the sum of x and nine," reinforcing that multiplication can be represented in various ways within expressions.
- A complex expression involving division is discussed: "the quotient of the sum and difference of a and b." This illustrates how to structure fractions involving both addition and subtraction, emphasizing clarity in mathematical language.