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Algebraic expressions reference

Words to algebraic expressions reference sheet

A printable guide to the language of algebra. Connect words with addition, subtraction, products, quotients, equality and grouping, with examples that explain operand order.

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Read each phrase beside its expression. Identify which quantity comes first and whether a whole sum or difference must be grouped.

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A4

Reference handout
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Use meaning, order and grouping together

The reference connects six groups of language with mathematical examples: addition, subtraction, multiplication, division, equality and grouped quantities. It explains reversed phrases such as subtracted from and warns against choosing an operation from one isolated word.

This is a fixed handout, so it has no random question set or separate answer edition. Change the paper size, printed language or teacher note before downloading.

Learning objective

What this activity builds

Read the relationship between quantities before choosing an operation or writing an expression.

Worked example

Write an expression for six less than twice a number n.

2n − 6.

Twice the number is 2n. Six less than that quantity means subtract 6 from 2n. The word order does not make 6 the first operand.

Teaching notes

Make the practice count

  • Ask learners to restate a phrase in their own words.
  • Test the meaning with a small number before writing the general expression.
  • Contrast twice a number plus three with twice the sum of a number and three.
  • Read context: a word such as of does not always specify one operation.

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This fixed reference teaches operation order, reversal, division order, equality, and grouped quantities in the selected print language.

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Configured PDF · Words and Algebraic Expressions · US Letter

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Math SheetNameScoreTeacherDateWords and Algebraic ExpressionsUse meaning, order, and grouping to turn words into algebra.AdditionAddition joins quantities. “More than” reverses the spoken order but not the addends’ value.the sum of x and 5x+55 more than xSubtractionSubtraction order matters: the quantity named after “from” or “than” comes first.5 less than xx-55 subtracted from xMultiplicationA coefficient multiplies the complete factor that follows it; a fractional coefficient means that fraction of a quantity.the product of 3 and x3x3 times x1 over 2 of x12xthe product of 1 over 2 and xDivisionThe dividend is divided by the divisor. In “4 divided into x,” x is the dividend and 4 is the divisor.4 divided into xx4x divided by 4x divided into 44xx must not be zero because a divisor cannot be zero.EqualityAn equals sign says that both sides have the same value; it is not a cue to start calculating.the sum of x and 2 = 3 times yx+2=3yBoth expressions name the same value.Grouped quantitiesParentheses make one quantity. An outside factor multiplies every term inside the group.2 times the grouped quantity (the sum of x and 3)2(x+3)2x + 6Context matters: words such as “of,” “shared,” and “sold for” do not always name one operation.math-sheet.comPage 1 / 1

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