Math - Numbers and Fraction Operations

Number and Operations – Fractions (NF)

Note: Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


  • 4.NF.A  Extend understanding of fraction equivalence and ordering.
    • 4.NF.A.1  Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to understand and generate equivalent fractions.
    • 4.NF.A.2  Compare two fractions with different numerators and different denominators (e.g., by creating common denominators or numerators and by comparing to a benchmark fraction).
      1. Understand that comparisons are valid only when the two fractions refer to the same size whole.
      2. Record the results of comparisons with symbols >, =, or <, and justify the conclusions.
  • 4.NF.B  Build fractions from unit fractions by applying and extending previous understanding of operations on whole numbers.
    • 4.NF.B.3  Understand a fraction a/b with a > 1 as a sum of unit fractions (1/b).
      1. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
      2. Decompose a fraction into a sum of fractions with the same denominator in more than one way (e.g., 3/8 = 1/8 + 1/8+1/8; 3/8 = 2/8 + 1/8; 2 1/8 = 1 + 1 + 1/8 + or 2 1/8 = 8/8 + 8/8 + 1/8).
      3. Add and subtract mixed numbers with like denominators (e.g., by using properties of operations and the relationship between addition and subtraction and/or by replacing each mixed number with an equivalent fraction).
      4. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators.
    • 4.NF.B.4  Build fractions from unit fractions.
      1. Understand a fraction as a multiple of a unit fraction. In general, = a x .
      2. Understand a multiple of as a multiple of a unit fraction, and use this understanding to multiply a whole number by a fraction. In general, n x = .
      3. Solve word problems involving multiplication of a whole number by a fraction. For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
  • 4.NF.C  Understand decimal notation for fractions, and compare decimal fractions.
    • 4.NF.C.5  Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 (tenths) and 100 (hundredths). For example, express 3/10 as 30/100, and and 3/10 + 4/100 = 34/100. (Note: Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators, in general, is not a requirement at this grade.)
    • 4.NF.C.6  Use decimal notation for fractions with denominators 10 (tenths) or 100 (hundredths), and locate these decimals on a number line.
    • 4.NF.C.7  Compare two decimals to hundredths by reasoning about their size. Understand that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <.

*Please note that students at CTA Independence are accelerated in math therefore are learning the level one year above their current grade.