**Fractions & Ratio**

**L.O. - Understand the the two different fractional relationships that appear in a ratio.**

Red: (1) 16 children (2) 7 adults

Amber (3) 30 children (4) 10 children.

Green (5) 12 children (24 in first nursery,

36 in the second).

**Key**

Examples

Examples

**Activities**

**Activity**

Answers

Answers

**Worked**

Example

Example

**Worked**

Example

Example

Starter

(a) What is the ratio of blue to green?

(b) What fraction of the bar is blue?

(c) What fraction of the bar is green?

Starter

(a) What is the ratio of blue to green?

3:2

(b) What fraction of the bar is blue?

3/5

(c) What fraction of the bar is green?

2/5

The first link between fractions and ratios

Ratios can be seen as comparing two parts:

"There are 3 blue parts compared to 4 blue parts, so the ratio is 3:4."

Fractions can be seen as having part of the whole:

"The blue is of the whole, and the green is of the whole".

3

7

4

7

Example pair

Teacher Example:

Two quantities are in the ratio 3:5.

(a) Draw a bar model to show this.

(b) Write down the fraction of the whole for the left quantity:

(c) Write down the fraction of the whole for the right quantity:

Pupil Example:

Two quantities are in the ratio 2:5.

(a) Draw a bar model to show this.

(b) Write down the fraction of the whole for the left quantity:

(c) Write down the fraction of the whole for the right quantity:

Example pair

Teacher Example:

Two quantities are in the ratio 3:5.

(a) Draw a bar model to show this.

(b) Write down the fraction of the whole for the left quantity:

3/8

(c) Write down the fraction of the whole for the right quantity:

5/8

Pupil Example:

Two quantities are in the ratio 2:5.

(a) Draw a bar model to show this.

(b) Write down the fraction of the whole for the left quantity:

2/7

(c) Write down the fraction of the whole for the right quantity:

5/7

Activity

For each ratio, draw a bar model and write down the fraction of the whole for each part. Think about how each question can help inform the later questions.

(a) 3:4

(b) 4:3

(c) 4:5

(d) 8:10

(e) 8:6

(f) 7:7

(g) 1:1

(h) 1:0.5

Activity

For each ratio, draw a bar model and write down the fraction of the whole for each part. Think about how each question can help inform the later questions.

(a) 3:4

(b) 4:3

(c) 4:5

(d) 8:10

(e) 8:6

(f) 7:7

(g) 1:1

(h) 1:0.5

3/7 and 4/7

4/7 and 3/7

4/9 and 5/9

8/18 and 10/18 =

4/9 and 5/9

8/14 and 6/14 =

4/7 and 7/7

7/14 and 7/14 =

1/2 and 1/2

1/2 and 1/2

2/3 and 1/3

The second link between fractions and ratios

Ratios can be seen as comparing two parts:

"There are 3 blue parts compared to 4 blue parts, so the ratio is 3:4."

Fractions can also be seen as comparing two parts:

"The blue part is the size of the green part." This might be better seen with the bars on top of each other rather than next to each other:

3

4

Example pair

Teacher Example:

Two quantities are in the ratio 3:5.

(a) Draw a bar model to show this.

(b) Write down the fraction that the smaller part is of the larger part.

Pupil Example:

Two quantities are in the ratio 2:5.

(a) Draw a bar model to show this.

(b) Write down the fraction that the smaller part is of the larger part.

Example pair

Teacher Example:

Two quantities are in the ratio 3:5.

(a) Draw a bar model to show this.

(b) Write down the fraction that the smaller part is of the larger part.

3/5

Pupil Example:

Two quantities are in the ratio 2:5.

(a) Draw a bar model to show this.

(b) Write down the fraction that the smaller part is of the larger part.

2/5

Activity

For each ratio, draw a bar model and write down the fraction that the smaller part is of the larger part.. Think about how each question can help inform the later questions.

(a) 3:4

(b) 4:3

(c) 4:5

(d) 8:10

(e) 8:6

(f) 7:7

(g) 1:1

(h) 1:0.5

Activity

For each ratio, draw a bar model and write down the fraction that the smaller part is of the larger part.. Think about how each question can help inform the later questions.

(a) 3:4

(b) 4:3

(c) 4:5

(d) 8:10

(e) 8:6

(f) 7:7

(g) 1:1

(h) 1:0.5

3/4

3/4

4/5

8/10 = 4/5

6/8 = 3/4

1 (same size)

1 (same size)

1/2

Activity

1) Write down the fraction of a whole for each part, and the fraction that the smaller part is of the larger part for each ratio.

(a) 2:3 (b) 5:6 (c) 2:9 (d) 8:3 (e) 6:1

2) If the given fraction of a shape is shaded, write down the fraction unshaded, and the ratio of shaded to unshaded:

(a) 4/11 (b) 2/11 (c) 3/10 (d) 4/15 (e) 4/12

3) If the smaller part is the given fraction of the larger part, write down the ratio of smaller to larger and the fractions of the whole for each part.

(a) 4/11 (b) 2/11 (c) 3/10 (d) 4/15 (e) 4/12

4) What fractions can you write from the ratio 3:4:5?

Activity

1) Write down the fraction of a whole for each part, and the fraction that the smaller part is of the larger part for each ratio.

(a) 2:3 (b) 5:6 (c) 2:9 (d) 8:3 (e) 6:1

2) If the given fraction of a shape is shaded, write down the fraction unshaded, and the ratio of shaded to unshaded:

(a) 4/11 (b) 2/11 (c) 3/10 (d) 4/15 (e) 4/12

3) If the smaller part is the given fraction of the larger part, write down the ratio of smaller to larger and the fractions of the whole for each part.

(a) 4/11 (b) 2/11 (c) 3/10 (d) 4/15 (e) 4/12

4) What fractions can you write from the ratio 3:4:5?

2/5, 3/5, 2/3

5/11, 6/11, 5/6

2/11, 9/11, 2/9

8/11, 3/11, 3/8

6/7, 1/7, 1/6

7/11, 4:7

9/11, 2:9

7/10, 3:7

11/15, 4:11 2/3, 1:2

4:11, 4/15, 11/15

2:11, 2/13, 11/13

3:10, 3/13, 10/13

4:15, 4/19, 15/19

1:3, 1/4, 3/4