Equivalent Fractions Today we will be finding fractions with the same value cancelling fractions comparing fractions ordering fractions

finding fractions with the same value

1 2

1 2 2 4

1 2 3 6

1 2 4 8

1 3

1 3 2 6

1 3 3 9

1 3 4 12

2 3

2 3 4 6

2 3 6 9

2 3 8 12

Here is an example of a fraction chain 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100

And another 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100

And another 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100

Use the table to create a fraction chain for 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100

We use these columns to get 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 15 21 24 27 30 28 32 36 40 25 35 45 50 42 48 54 60 49 56 63 70 64 72 80 81 90 100

1 4 2 8 3 12 4 16 5 20 etcetera

Make some chains for these fractions:

Make some chains for these fractions:

Filling in the gaps 3 4 ? 20 =

3 4 15 20 = How did we do that?

× 5 3 4 15 20 = × 5

What about this one? 2 3 ? 18 =

What is the multiplier? 2 3 ? 18 = × 6

2 3 12 18 What we do to the denominator × 6 = × 6 we must do to the numerator

And what we do to the numerator 3 8 12 ? =

And what we do to the numerator × 4 3 8 12 ? =

3 8 12 32 And what we do to the numerator = × 4 we do to the denominator

Try these: 2 7 ? 21 = 1 6 ? 24 = 4 9 12 ? = 3 8 18 ? =

And the answers are: 2 7 6 21 = 1 6 4 24 = 4 9 12 27 = 3 8 18 48 =

cancelling fractions

24 36 Consider the fraction: There are any number of fractions equivalent to this…

÷ 2 ÷ 2 ÷ 3 24 36 12 18 6 9 2 3 When we get to ⅔ we stop because there is nothing else we can divide by.

24 36 2 3 Dividing in this way is called cancelling, or simplifying. We could have got from the first fraction to last one by dividing by different numbers, for example: 24 36 2 3 ÷ 12

Look for common factors – numbers that will divide into both numerator and denominator. 21 28 ? ÷ ?

The common factor is 7 – the only number that will divide 21 and 28 3 4 ÷ 7

What are the common factors of 6 and 12? ÷ ?

We could divide by 2, 3, or 6 6 12 ? ÷ ?

Whatever we do, it doesn’t matter, as long as we keep dividing until we can’t divide any more. 6 12 3 6 1 2 ÷ 2 ÷ 3 ÷ 2 ÷ 3

Try cancelling these: 12 15 ? = 8 20 ? = 15 25 ? = 18 30 ? =

Try cancelling these: 12 15 4 5 = 8 20 2 5 = 15 25 3 5 = 18 30 3 5 =

comparing fractions

Now that we can we can find equivalent fractions, we can look at comparing fractions

For example, is it possible to say which is biggest out of these pairs? 3 7 2 5 & 3 4 5 6 & 3 8 2 & 5 6 7 9 &

The only one we can say for certain is this one: 3 8 2 & Because they have the same denominator.

For example, this pair could be converted thus, and we can say: For the others, we need to create equivalent fractions with the same denominator. 3 4 5 6 & For example, this pair could be converted thus, and we can say: 9 12 10 <

And these will give us: & These: > 5 6 7 9 & 15 18 14 > These: We use 18 because it is the lowest common denominator – we could have used any other suitable denominator.

And finally these will give us: & 3 7 2 5 & These: 15 35 14 > Again, 35 is the lowest common denominator.

Replace the ? with <, >, or = Try these: 3 5 7 10 ? 5 8 3 4 ? 3 4 2 ? 2 3 10 15 ? Replace the ? with <, >, or =

And the answers are: < < > = 7 10 5 8 6 6 10 9 12 8 12 10 15

Finally, make fractions using a set of numbered cards, and order them yourself.