Number & Operations - Fractions

Extend understanding of fraction equivalence and ordering.

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × 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 recognize and generate equivalent fractions.

Equivalent fractions

Equivalent Fractions

4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

Compare fractions with half and one

Compare Fractions with Half and One

Build fractions from unit fractions.

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1/b.

4.NF.3.a Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.

Add fractions (sums up to 1)

Add Fractions (Sums up to 1)

Add fractions (sums greater than 1)

Add Fractions (Sums greater than 1)

Subtract fractions

Subtract Fractions

4.NF.3.b Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model.

Add fractions (sums up to 1)

Add Fractions (Sums up to 1)

Add fractions (sums greater than 1)

Add Fractions (Sums greater than 1)

Subtract fractions

Subtract Fractions

4.NF.3.c Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

Mixed numbers

Mixed Numbers

Fractions greater than 1

Fractions greater than 1

Mixed numbers as fractions

Mixed Numbers as Fractions

Add mixed numbers using models

Add Mixed Numbers Using Models

Add mixed numbers

Add Mixed Numbers

Subtract mixed numbers using models

Subtract Mixed Numbers Using Models

Subtract mixed numbers

Subtract Mixed Numbers

4.NF.3.d Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.

4.NF.4.a Understand a fraction a/b as a multiple of 1/b.

Multiply unit fractions by a whole

Multiply Unit Fractions by a Whole

4.NF.4.b Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.

Multiply fractions by a whole

Multiply Fractions by a Whole

4.NF.4.c Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.

Understand decimal notation for fractions, and compare decimal fractions.

4.NF.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 and 100.

Hundredths

Hundredths

Tenths and hundredths

Tenths and Hundredths

4.NF.6 Use decimal notation for fractions with denominators 10 or 100.

Decimal place value (numbers less than 1)

Decimal Place Value (numbers less than 1)

Decimal place value (numbers greater than 1)

Decimal Place Value (numbers greater than 1)

Represent decimals less than 1

Represent Decimals less than 1

Represent decimals greater than 1

Represent Decimals greater than 1

Decimals and fractions - tenths

Decimals and Fractions - Tenths

Decimals and fractions - hundredths

Decimals and Fractions - Hundredths

Decimals and fractions - mixed numbers

Decimals and Fractions - Mixed Numbers

4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Compare decimals less than 1

Compare Decimals less than 1

Compare decimals greater than 1

Compare Decimals greater than 1

Order decimals less than 1

Order Decimals less than 1

Order decimals greater than 1

Order Decimals greater than 1