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.
Examples: 3/8 = 1/8 1/8 1/8 ; 3/8 = 1/8 2/8 ; 2 1/8 = 1 1 1/8 = 8/8 8/8 1/8.
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.
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?
Identify apparent features of the pattern that were not explicit in the rule itself.
For example, given the rule "Add 3" and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers.
Record the results of comparisons with symbols 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.
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.) 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.