This is the second page where we look at questions such as:
‘How many sixths make two and a half?’
Children need to know that there are six sixths in one whole one and also need to understand equivalent fractions and that a half is equivalent to three sixths.
Many children fail to grasp this in primary school, probably because they have never really got to grips with equivalent fractions and it might be necessary to go back and practice this first before attempting these questions.
How many fractions make…(pg 2)
Here is another page where the remainders from division are written as fractions. Children need a good knowledge of tables to work out the division ‘in their heads’ and this is probably best suited to Year 4, aged8/9+ years old.
The remainder goes on the top line (numerator) and the bottom number (denominator) is the number you have divided by.
This is a much neater finish to the question as the whole number is divided completely, with no messy remainders. Some of the fractions could be cancelled down to their simplest form, although this is not essential at this stage.
Division with fraction remainders (pg 2)
Several different sets of skills and knowledge needed for these questions. Firstly knowledge of measurements eg that there are 1000 metres in a kilometre, 1000 ml in a litre etc, as well as a couple of Imperial measures thrown in as an extra challenge.
Continue reading “Year 6 Maths: Fractions”
Here we have some quite tricky questions on fractions, suitable for Year 6. The key to these is to think carefully about how many parts or fractions of a number make one whole one and to understand equivalent fractions.
Understanding equivalent fractions is the key to understanding fractions generally and it is a good start to know that ten tenths make one whole one, as do six sixths etc.
How many fractions make…. (pg 1)
Year 5 Maths Worksheet: relate fractions and division
Only six questions on this worksheet, but plenty of important concepts. Firstly, that division can be represented as a fraction, and, of course, a fraction can be thought of as a division.
Secondly, an improper fraction (where the top number is larger than the bottom number) can be shown as a mixed number (a whole number and a proper fraction). This can be done by dividing the numerator (top number) by the denominator (bottom number) to find the whole part with the remainder being the numerator of the new fraction. The denominator remains the same.
Relate division and fractions (pg 2 )
Reading and writing fractions remain a bit of a mystery for many children, but our cunning foxes can help. This worksheet looks at how to read and write fractions from halves to tenths using numbers or words. As well as reading a fraction such as 1/3 as one third, it can also be read as a division sum: 1 divided by 3, or 1 divided into 3 equal parts, but this comes a little later.
These pages can be found in our Year 4 section, under Counting and Numbers.
Writing fractions in words or numbers
Once the idea of equivalent fractions has been understood it becomes possible to compare two fractions to see which is the larger. The first thing to remember is that the larger the number on the bottom of the fraction, the smaller each part of the fraction is. So 4/100 is much smaller than 4/25.
Now this is also easy if the bottom number (denominator) is the same in each fraction eg 1/5 is smaller than 3/5.
The difficulty comes when the numbers are not the same. How do you compare 3/5 with 7/10?
The easiest way is to make the bottom number of each fraction the same, and in the case above this will mean converting the 3/5 into tenths. We can do this by multiplying the 5 by 2 to make 10 and we have to do the same with the top number, multiplying the 3 by 2. In this way 3/5 can be converted to 6/10.
3/5 and 6/10 are equal, or equivalent.
It is now easy to see that 6/10 is smaller than 7/10, so 3/5 must also be smaller than 7/10. Job done!
Later it will become harder to convert so that the denominators are the same; sometimes you have to multiply both fractions by different numbers, but this comes later! At the moment it is important to get the basics correct.
Equivalent fractions: comparing
One of the hardest ideas to get over to children is equivalent fractions, but it is one of the most vital. These pages look at some of the easier equivalence, using sixths, eighths and tenths and relating them to halves. It is a good idea to have as much practical work as possible, either shading in or cutting into pieces. The aim is for the child to see a developing pattern of numbers: if the numerator doubles and the denominator also doubles then the fractions will remain equal. Tricky, as children are unused to the idea of different numbers being equal to each other.
These pages can be found in our Year 4 resources, under Counting and Number.
Fractions equal to a half
This worksheet looks at the relationship between fractions and division. It is important that children understand that finding one half of a number is equivalent to dividing by 2, that finding one quarter of a number is the same as dividing the number by 4 and to find one fifth is equivalent to dividing by 5. Plenty of practice is needed with this before children go on to find, for example, two fifths, or three fifths of numbers.
Most of these questions should be calculated mentally, although rough jottings may help. It might be a help to remember that finding a quarter of a number can be found by halving and then halving again. A fifth can be found by dividing by ten and doubling the answer, although if the number is not divisible by 10 it might be easier to do a quick pencil and paper calculation.
Find fractions of numbers (p2)
Here we have some more work on understanding equivalence in fractions.
The first question looks at simple equivalence between halves, fifths, tenths etc and asks which fractions are less than a half. The quick way to work this out is to see if the top number (numerator) is less than double the bottom number (denominator) – if it is then it is less than one half.
The second question requires an understanding that a fraction such as four fifths can be changed to an equivalent fraction such as eight tenths by multiplying both the numerator and denominator by the same number (in this case 2, but it will not always be 2). All the fractions need to be changed to the same denominator which in this case would be 30.
The other questions are all aimed at improving understanding of equivalence.
More ordering fractions