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10
16
10
16=
5
8
x 2
x 2
-3
16=
7
16
5
8-
3
16=1
1 1
1
6
4
6=
2
3
x 2
x 2
34
6
2
6+
3
1
6+
2
3
6
1
6-
2
3=3 2
RECAPWe looked at these two types of calculations yesterday.
In this first example, once we have found the equivalent fraction we can subtract easily.
1
6-
4
6=3 2
In this example, once we find the equivalent fraction we can see that we cannot simply subtract the parts (1/6 – 4/6) in the mixed numbers.
As the numbers are close together, we can count on along a number line to find the difference.
1
8
6
8=
3
4
x 2
x 2
-6
8=
1
8-
3
4=9
9
Let’s look at this example.
We can see that we cannot subtract 6/8 easily once we have made the denominators the same.
We wouldn’t use ‘counting on’ because the numbers (over 9 and less than one) are not close together.
Today, we are going to use a number line and count backwards to take away for calculations like this.
1
8
6
8=
3
4
x 2
x 2
-6
8=
1
8-
3
4=9
9
1
899
7
88
6
88
5
88
4
88
3
88
1
8-1
8-1
8-1
8-1
8-1
8-
Once the denominators are the same, we can count backwards along the number line subtracting steps of 1/8 six times.
This has be shown visually using the rectangles below.
3
88
1
6-
9
12=12
Now try this calculation counting back on a number line!
Remember to make the denominators the same.
9
12
2
12
2
12=
1
6
x 2
x 2
- =
1
6-
9
12=12
2
121212
1
12-
1
12-
1
12-
1
12-
1
12-1
12-
The calculation has been represented visually using the rectangles.
We have subtracted nine steps of 1/12 to calculate our answer.
12
1
12-
1
12-1
12-
1
121211
11
12
10
121111
9
12
8
121111
7
12
6
121111
5
12
5
1211
9
12
2
12
2
12=
1
6
x 2
x 2
- =
1
6-
9
12=12
2
121212
2
12-7
12-
That took quite a long time! Is there a way we could make this easier?
We could look to partition the 9/12. Subtract 2/12 and then a further 7/12.
12
1
121211
11
12
10
121111
9
12
8
121111
7
12
6
121111
5
12
5
1211
1
10-
4
5=16
1
101616
Now try to use the partitioning strategy to make the counting back on the number line easier with this example.
Careful when counting back here. Its easy to make a mistake with the wholes. You must also check the parts carefully.
1) Make the denominators the same.
2) Rewrite using the equivalent fraction.
3) Count back along the number line. You could subtract unit fractions but try to partition to make this more efficient.
1
10
8
10
8
10=
4
5
x 2
x 2
- =
1
10-
4
5=16
1
101616
1
10-7
10-
The equivalent fraction was found. When subtracting, 8/10 was partitioned. 1/10 was subtracted first to bridge 16 and then a further 7/10 was subtracted.
16
153
10
3
1015
1) Make the denominators the same.
2) Rewrite using the equivalent fraction.
3) Count back along the number line. You could subtract unit fractions but try to partition to make this more efficient.
Careful when counting back here. Its easy to make a mistake with the wholes. You must also check the parts carefully.
1
3-
8
9=16
3
916
Think about examples like this. Subtract the wholes first and then the parts.
Now have a go at this question.
1) Make the denominators the same.
2) Rewrite using the equivalent fraction.
3) Count back along the number line. You could subtract unit fractions but try to partition to make this more efficient.
3
Careful when counting back here. Its easy to make a mistake with the wholes. You must also check the parts carefully.
8
9
3
9
3
9=
1
3
x 3
x 3
- =
1
3-
8
9=16
3
916
- 33
9-
Subtract the wholes first and then the parts.
3 was subtracted first.
Then 8/9 was partitioned. 3/9 was subtracted to bridge 13. A further 5/9 was then subtracted.
16
124
9
4
912
1) Make the denominators the same.
2) Rewrite using the equivalent fraction.
3) Count back along the number line. You could subtract unit fractions but try to partition to make this more efficient.
3
3
3
91313
5
9-
Careful when counting back here. Its easy to make a mistake with the wholes. You must also check the parts carefully.
Mr Cullen was running in a race which was km (kilometres) long. He had already completed km. How far did he have left?
3
1212
5
65
1) Make the denominators the same.
2) Rewrite using the equivalent fraction.
3) Count back along the number line. You could subtract unit fractions but try to partition to make this more efficient.
Careful when counting back here. Its easy to make a mistake with the wholes. You must also check the parts carefully.
Mr Cullen was running in a race which was km (kilometres) long. He had already completed km. How far did he have left?
3
1212
5
65
1) Make the denominators the same.
2) Rewrite using the equivalent fraction.
3) Count back along the number line. You could subtract unit fractions but try to partition to make this more efficient.
3
12-
5
6=12 5
10
12=
5
6
x 2
x 2
3
12-
10
12=12 5
3
1212
- 53
12-
65
12
3
1277
7
12-
Careful when counting back here. Its easy to make a mistake with the wholes. You must also check the parts carefully.
ACTIVITY
L.O. To subtract fractions
2
8
1
4
7
87 - = 2
8=
1
4
x 2
x 2
7
5
8-
2
8-
2
8
7
87 - =
Use jottings to count back on a number line to answer these calculations.
2
12
3
412 - =
3
9
1
3
8
99 - = 3
9=
1
3
x 3
x 3
9
3
9
8
99 - =
1
3
14
1510 - =
Complete the yellow boxes.
4
16
1
49 - = 4
16=
1
4
x 4
x 4
9
4
16- - 2
9 - =
Use jottings to count back on a number line to answer these calculations.
7
2
24
16
11
16
11
16
4
167
2
78 - =
- 4
413
14
4
3012 - =5
8
10
3
2011 - =3
3
4
Complete the yellow boxes.
L.O. To develop fraction skills
Fill in the missing fractions on these number lines.
2
7
3
10-
4
10
- -B) Draw / complete the number lines shown. Count back on the number lines, writing your answer in the yellow boxes.
7
10
3
9-
5
9
7
8-
7
8
8
12-
11
12
6
7
3
7
1
5- -
4
5
1
4- -
3
4
3
4
4
6- -
4
6
1
1
4
61
EXTENSION
L.O. To solve fraction problems (extension)
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