TRANSLATING

Objectives of the Lesson

• Identify Keywords: Recognizing keywords that signify the four fundamental operations in mathematics.

• Translate Phrases: Converting English phrases into mathematical expressions and vice versa.

Importance of Translation in Algebra

• English to Mathematical Translation: Not all problems in algebra are constructed mathematically; many appear as English phrases.

• Translation Needs: Understanding how to translate these phrases into mathematical expressions is essential for problem-solving.

Variables and Expressions

• Variable: A symbol (usually a letter) that represents an unknown number or quantity in mathematical problems.

• Expression: A combination of variables and constants joined together by the operations of addition, subtraction, multiplication, or division.

  • Examples of Expressions:

    • 2x + y

    • 5x

    • x - 8

Translating Mathematical Phrases to Verbal Phrases

Common Operations and Their Phrases

• Addition (+):

  • plus,

  • increased by,

  • added to,

  • the sum of,

  • total,

  • more than.

• Subtraction (-):

  • minus,

  • decreased by,

  • subtracted from,

  • the difference of,

  • less than,

  • diminished by.

• Multiplication (×):

  • times,

  • multiplied by,

  • the product of,

  • twice,

  • thrice.

• Division (÷):

  • divided by,

  • the quotient of,

  • ratio of.

Examples of Translations

Simple Examples

1. Eight less a number n:

   • Mathematical Phrase: 8 - n

   • Note: The order matters; "less" indicates a switch in order.

2. Eight more than a number x:

   • Mathematical Phrase: x + 8

Commutative Properties

• Commutative Property: Addition and multiplication are commutative, meaning that changing the order of addends or factors does not change the result.

  • For example:

    • 5 + x = x + 5

    • 3 * 4 = 4 * 3

Additional Examples

3. Five plus a number:

   • Mathematical Phrase: 5 + x

   • Also can be expressed as x + 5.

4. The product of eight and a number n:

   • Mathematical Phrase: 8n

   • Alternatively: 8 • n.

More Complex Translations

5. The difference of five and twice a number plus three:

   • Mathematical Phrase: 5 - (2p + 3)

6. The quotient of thrice a number and two:

   • Mathematical Phrase: ( \frac{3n}{2} )

   • Note: "Thrice" means multiplied by 3.

Conclusion

• Students should practice translating various phrases to strengthen their understanding of mathematical expressions.

Thank You for Listening!

• Students are encouraged to ask questions and seek clarification on doubts.