Historical Counting Systems: Background You’ll Need 2

  • Simplify using math words and symbols

Translate Word Phrases of Addition to Math Notation

Mathematics often presents itself as a unique language with its own vocabulary and symbols. To streamline problem-solving, it’s helpful to translate common mathematical terms into their symbolic counterparts. The following table serves as a guide to convert verbal expressions of addition into their equivalent mathematical symbols.

Operation Words Example Expression
Addition
plus [latex]1[/latex] plus [latex]2[/latex] [latex]1+2[/latex]
sum the sum of [latex]3[/latex] and [latex]4[/latex] [latex]3+4[/latex]
increased by [latex]5[/latex] increased by [latex]6[/latex] [latex]5+6[/latex]
more than [latex]8[/latex] more than [latex]7[/latex] [latex]7+8[/latex]
total of the total of [latex]9[/latex] and [latex]5[/latex] [latex]9+5[/latex]
added to [latex]6[/latex] added to [latex]4[/latex] [latex]4+6[/latex]
Translate and simplify the following:

[latex]28[/latex] increased by [latex]31[/latex]

Translate Word Phrases of Subtraction to Math Notation

In everyday language, we often talk about taking away or comparing amounts. In math, this is known as subtraction. The words we use in conversation can be directly translated to subtraction symbols, which you’ll see in math problems. The table below shows how common phrases that describe taking away or comparing quantities are expressed in the universal language of math.

Operation Word Phrase Example Expression
Subtraction
minus [latex]5[/latex] minus [latex]1[/latex] [latex]5 - 1[/latex]
difference the difference of [latex]9[/latex] and [latex]4[/latex] [latex]9 - 4[/latex]
decreased by [latex]7[/latex] decreased by [latex]3[/latex] [latex]7 - 3[/latex]
less than [latex]5[/latex] less than [latex]8[/latex] [latex]8 - 5[/latex]
subtracted from [latex]1[/latex] subtracted from [latex]6[/latex] [latex]6 - 1[/latex]
Translate the following into numerical form and then simplify:

  1. The difference of [latex]13[/latex] and [latex]8[/latex]
  2. Subtract [latex]24[/latex] from [latex]43[/latex]

Translate Word Phrases of Multiplication to Math Notation

Turning words into math symbols is like finding shortcuts to solve problems faster. For multiplication, we use different phrases to mean ‘put together in groups.’ This table helps you to see how phrases like ‘times’ and ‘twice’ can be written using multiplication signs or dots, making them ready for quick calculations.

Operation Word Phrase Example Expression
Multiplication
times [latex]3[/latex] times [latex]8[/latex] [latex]3\times 8, 3\cdot 8, (3)(8)[/latex], [latex](3)8, \text{ or } 3(8)[/latex]
product the product of [latex]3[/latex] and [latex]8[/latex] [latex]3\times 8, 3\cdot 8, (3)(8)[/latex], [latex](3)8, \text{ or } 3(8)[/latex]
twice twice [latex]4[/latex] [latex]2\cdot 4[/latex]

Translate the following to math notation and simplify:

the product of [latex]12[/latex] and [latex]27[/latex].

Translate Word Phrases of Division to Math Notation

When we share things equally or find out how many times one number fits into another, we’re doing division. The words ‘divided by’ and ‘quotient of’ are keys that tell us to divide. This table shows how these words change into division symbols.

Operation Word Phrase Example Expression
Division
divided by [latex]12[/latex] divided by [latex]4[/latex] [latex]12\div 4[/latex]
quotient of the quotient of [latex]12[/latex] and [latex]4[/latex] [latex]\frac{12}{4}[/latex]
divided into [latex]4[/latex] divided into [latex]12[/latex] [latex]4\overline{)12}[/latex]
Translate the following into numerical notation and simplify:

the quotient of [latex]51[/latex] and [latex]17[/latex].