Use modeling and reasoning to multiply a whole number times a fraction or a fraction times a whole number. Use the breaking into 1s strategy to solve problems where the whole number is a multiple of the denominator, as well as when it is not.
Transition to adding 2 fractions with equal denominators and sums greater than 1. What's 3/4 + 2/4? Their units are the same – they have common denominators – so add their quantities or numerators. 3 fourths + 2 fourths = 5 fourths, or 1 and 1 fourth. Using fraction notation, 3/4 + 2/4 = 5/4 = 4/4 + 1/4 = 1 1/4. Prerequisites: 4-98
Transition from adding to multiplying fractions. What's 2 x 1/4? Draw a bar model to see 2 groups of 1 fourth is 1 fourth+1 fourth = 2 fourths. Using fraction notation, 2 x 1/4 = 1/4+1/4 = 2/4 = 1/2. Shortcut? 2 x 1/4 = (2x1)/4 = 2/4. What's 3 x 1/3? 3 x 1 third = (3x1) thirds = 3 thirds. Using fraction notation, 3 x 1/3 = (3x1)/3 = 3/3 = 1. Prerequisites: 4-98
Find a fraction of a whole number by breaking numbers into 1s. What's 1/3 x 2? Think of 2 as 1+1. Draw a bar model or number bond to see 1/3 x (1+1) = (1/3 x 1)+(1/3 x 1) = 1/3+1/3 = 2/3, or 2 x 1/3. Since 1/3 x 2 = 2 x 1/3, transition to using the commutative property, when ready. What's 4/5 x 2? It's 2 x 4/5 = 8/5 = 1 3/5. Prerequisites: 4-99