4.NF

Number and Operations – Fractions

4.NF.1Explain 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.4.NF.2Compare two fractions with different numerators and different denominators, (e.g. by creating common numerators or denominators, 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 relational symbols >, <, =, or ≠, and justify the conclusions, (e.g. by using visual fraction models.).4.NF.3Understand a fraction a/b with a > 1 as a sum of fractions 1/b.4.NF.3aUnderstand addition and subtraction of fractions as joining and separating parts referring to the same whole.4.NF.3bDecompose 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.4.NF.3cAdd and subtract mixed numbers with like denominators, e.g. by replacing each mixed number with an equivalent fraction (simplest form is not an expectation), and/or by using properties of operations and the relationship between addition and subtraction.4.NF.3dSolve 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.4Apply and extend previous understandings of multiplication (refer to 2.OA.3, 2.OA.4, 3.OA.1, 3.NF.1, 3.NF.2) to multiply a fraction by a whole number.4.NF.4aUnderstand a fraction a/b as a multiple of 1/b. For example, use a visual fraction model to represent 5/4 as 5 copies of 1/4, recording the conclusion by the equation 5/4 = 5 ⋅ 1/4.4.NF.4bUnderstand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number. For example, use a visual fraction model to express 3 ⋅ 2/5 as 6 ⋅ 1/5, recognizing this product as 6/5. (In general, n ⋅ a/b = n⋅a/b.).4.NF.4cSolve word problems involving multiplication of a fraction by a whole number (e.g. by using visual fraction models and equations to represent the problem.) 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.5Express 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. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.4.NF.6Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.4.NF.7Compare 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 relational symbols >, < =, or ≠, and justify the conclusions, (e.g. by using a visual model.).
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