LI: To be able to subtract mixed fractions using regrouping.
Last week, we practiced adding and subtracting proper fractions. Write down what you can remember about the method we use to do so.
Watch the following video to recap how to do so:
- Today, we are going to use a strategy called regrouping to subtract mixed numbers fractions. We will do this with fractions that have different denominators.
- In order to subtract the fractions, it is important that we first of all make both denominators the same. Then it is possible to subtract the fractions.
- Look at the example below:
1 and 4/9 - 16/18.
- To make both denominators the same, we can divide 18 by 2 (remember that we must also now divide the numerator by 2). This gives us the fraction 8/9.
- Our question now reads: 1 and 4/9 - 8/9.
- We cannot take 8 from 4 without removing the whole number. So, in order to solve this question, we will have to regroup the fraction with one of the whole numbers.
- 1 whole and 4/9 = 9/9 + 4/9 = 13/9
- 13/9 - 8/9 = 5/9.
Watch the video below to recap the instructions with further examples:
LI: I can multiply proper fractions and simplify them.
In this lesson, you will be learning how to multiply a fraction by another fraction and then, if possible, simplify your answer.
- There are three common methods that we can use to multiply fractions. Any of the three methods are suitable in order to solve problems when multiplying two fractions together.
- The first is to use a bar model to help multiply.
- The second involves multiplying both the numerators together and then the denominators.
- Example: 3/7 x 2/5
1. Multiply the numerators together (3x2) to get 6
2. Multiply the denominators together (7 x 5) to get 35.
3. Simplify if possible. In this example we cannot simplify. So our answer is 6/35
- Finally, the third method requires us to visualise the calculation like a butterfly. We would then look at the numbers diagonally to find the greatest common factor and then simplify both diagonal sides by this common factor. This should result in us not needing to simplify at the very end.
- Example: 2/6 x 9/10
- Now it is possible to simply multiply the numerators together and then the denominators together.
LI: I can answer word problems that involve multiplying fractions together.
In this lesson you shall be building on your learning from yesterday by continuing to multiply fractions together, however you shall be using word problem questions to do so.
- We shall start with an example and look at how we identify the important information in word problems.
Meera has a bag of sweets. 3/8 are fizzy. Of the fizzy sweetsm 2/5 are red.
What fraction of the sweets are both red and fizzy.
- In this question we first need to look at the whole bag of sweets. We are told that 3/8 are fizzy and of those fizzy sweets, 2/5 are red. As we are looking for the fraction that are both fizzy and red we need to find what 2/5 out of 3/8 is equal to.
- In other words, this is the same as the calculation 2/5 x 3/8.
- From yesterday's learning, we know that in this calculation we have to multiply the numerators together and then the denominators together to get our answer and simplify if possible.
- Try the same method for the following question:
A group of children play musical instruments. 2/6 of the children play woodwind instruments. Of these children, 3/5 play the flute. What fraction of all the children play the flute.
- Again, as we are finding 3/5 of 2/6 we shall need to multiply.
- What answer did you get?
- Was it one of the following?
- 6/30 or 1/5
- If so you have completed the calculation accurately. 1/5 shows our simplified answer.
LI: I can divide fractions by whole numbers.
- Study the question 4/5 ÷ 2.
- What do you think we need to do to solve this question?
- We are going to use a method that we like to call: keep, change, flip to solve it!
- So what does this mean?
- Step 1: Keep = Keep 4/5 the same in our calculation
- Step 2: Change = Change the whole number into a fraction so 2 becomes 2/1 AND change the divide symbol into a multiplication sign.
4/5 x 2/1
- Step 3: Flip = Invert (swap over) the fraction so that it now becomes 1/2
4/5 x 1/2.
- Now we are able to solve the question as we have learnt in the previous lessons that multiplying fractions needs us to multiply the numerators together and then the denominators together.
- So 4/5 x 1/2 = 4/10 or 2/5
LI: I can solve word problems involving dividing fractions by whole numbers.
In this lesson, we are going to develop our knowledge of dividing fractions by an integer through the use of solving word problems.
- We shall start with an example:
Lauren has a chocolate bar. She wants to share 3/4 of it with her five friends. What fraction of the chocolate bar will each friend get?
- To solve this fraction we need to recognise that we are dividing a fraction by a whole number. We can now use the fraction rules to find the answer using our method from yesterday: keep, change, flip.
- 3/4 ÷ 5
- Change the whole number into a fraction: 3/4 ÷ 5/1
- Change the division sign into a multiplication sign: 3/4 x 5/1
- Flip the second fraction: 3/4 x 1/5
- Multiply the numerators together: 3 x 1 = 3
- Multiply the denominators together: 4 x 5 = 20
- This will give us our answer that the children each get 3/20 of the chocolate bar.
Awards we have received so far.