Many students (and adults!) miss the notion that conceptually, we can think of fraction multiplication this way:
1/2 × 3/4 can be seen as HALF of 3/4... which is 3/8.
Or, 5/6 × 1 1/2 can be thought of as 5/6 OF 1 1/2 , which is 1 1/4.
This interpretation (called "scaling") gives a very simple meaning to this operation, and it is especially important because it EXTENDS to decimals and percentages:
You see, 1/2 × 3/4 can be written as 50% of 3/4 = 50% × 3/4 = 0.5 × 3/4 = 0.5 × 0.25.
Or, 5/6 × 1 1/2 becomes (about) 83% of 1 1/2. Or maybe you turn it around and get 1 1/2 × 5/6 = 150% of 5/6. Being able to think FLEXIBLY of fractions/decimals/percentages really helps you (and your students) find all kinds of tie-ins with real-world situations.
from Homeschool Math Blog http://ift.tt/2dcNsUl
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