What is a fraction of something or a group of things?
It is an equal part!
So far we have looked at equal parts when one thing is divided. We expressed this as a fraction of that shape or of the number line e.g. 1/2, 1/4, 2/3, 1/5, 4/6 etc.
When we compared shapes to one another and renamed each shape ‘the whole‘ we found that we could explain the value of any given shape acording to its relationship to the other shapes e.g. one large rectangle = five smaller rectanlges, therefore each smaller one is one fifth IF the larger one is ‘the whole’. IF the smaller one is ‘the whole’ then the larger one = 5.
This brought us to ‘irregular fractions‘.
We learned that an irregular fraction has a NUMERATOR that is larger in value than the DENOMINATOR. We also learned that the line dividing these two numbers is called the VINICULUM.
An ‘irregular fraction’ can be changed into a ‘mixed number’ or a ‘whole number with a fraction beside it’. We found that this can be done by using division (divide the numerator by the denominator) and expressing the left-over as a fraction again.
Now we can convert ‘irregular fractions’ to ‘mixed numbers’ and vice versa. There are a few experts in our group now who can help others do this.
We also looked at equivalent fractions, decimal fractions and percents. We created a table to show the most common equivalents. If we know these by heart, then many calculations come easier!
We used fraction pies to combine different fractions to see if we could fit them into the pie. We found that some combinations fitted exactly and others left parts missing or needed to squeeze together to actually fit.
If we wrote these examples as number sentences this is what they looked like:
1/3 + 1/6 + 1/2 = 1
1/5 + 1/4 + 1/3 + 1/10 + 1/8 (does not equal) 1
1/8 + 1/8 + 1/8 + 1/5 + 1/10 + 1/4 + x =1
We found that in order to figure out these equations we needed to find common denominators for all the fractions. This wasn’t so easy! Knowing something about factors and multiples helps to find a common denominator. There are some people in the group who could explain that when the denominator changes then whatever you had to do to the denominator to get the new one – you have to do to the numerator.
e.g 1/3 + 1/6 + 1/2 = 1 …. 2/6 + 1/6 + 3/6 = 6/6 = 1 Here we multiplied the first fraction by 2 (top and bottom) to make it into sixths and we multiplied 1/2 by 3 (top and bottom) to make it into sixths. Then we could add all the sixths together.
Oh… and when the numerator and denominator are the same number they equal 1 – every time, no matter what. So 10/10 =1, 54/54 = 1, and even 1,496/1,496 = 1.
Try some of these ‘addition of fractions’ number sentences. Fractions addition worksheet.
Fractions of a group of things
When we tried to find a fraction of a group of things we used the ‘bar method’.
Our stragey was:
1. Write the worded problem
2. Draw the problem
3. Write the algorithm (or number sentence)
A pie maker made 64 pies for 8 schools. If each school received one eighth of the pies, how many did each school receive?
Here some more examples of using the bar method with fractions:
Try some of these problems involving fractions of groups or larger numbers. Worded problems link.