Now, the one thing that's not obvious is why did this work? So I have four objects, and if I were to divide into groups of two, so I want to divide it into groups of two.
When adding and subtracting fractions the denominators must be the same. If we wish to combine or take away parts we must be talking about the same sized parts, otherwise it would get confusing.
Here are some examples and solutions of fraction word problems. The second example shows how blocks can be used to help illustrate the problem. More examples and solutions using the bar modeling method to solve fraction word problems are shown in the videos. Bar Modeling with Fractions Examples: 1) Grace thought that a plane journey would take 7/10 hr but the actual journey took 1/5 hr longer.
The bar modeling method, also called tape diagrams, are use in Singapore Math and the Common Core.
Multiply by a form of one to change the denominators into a common size.
Essentially, we’re dividing the fractions into smaller sized pieces until they’re the same size. Truthfully, any common denominator will do, but people prefer to find the smallest one.
Well, 4 divided by 2, I have two groups of two, so that is equal to 2. You have eight groups of 1/2, so this is equal to 8.
Why is dividing by 1/2 the same thing as multiplying essentially by 2. And to do that, I'll do a little side-- fairly simple-- example, but hopefully, it gets the point across. So that is one group of two and then that is another group of two, how many groups do I have? That's the seventh, and then that's the eighth.
So hopefully that makes some sense or gives you a more tangible feel for what it means when you take 1/2 of 3/4.
But let's think about it in terms of the eights. Well, you have one section of eight here, two sections of eight there, three sections of eight, so it is 3/8.