**Proportion and Fractions**

Proportion as Fractions

In the top set maths class, the ratio of boys to girls is 2:3.

(a) What fraction of the class are boys?

(b) What is the relationship between the number of boys and the number of girls?

Starter

This diagram shows that the ratio of the lengths of blue rods to red rods is 2:1 (i.e. that blue is of red).

What fraction of the total length of this bar does blue represent?

How could we tell that from the ratio?

Proportion and Fractions

**L.O. - To write proportions as fractions, and manipulate**

the fractional representation.

the fractional representation.

1

2

There are always two different fractional view points in a proportional relationship.

One quantity is a fraction of the other; i.e. the blue is half of the red.

Each quantity is a fraction of the total; i.e. the blue is a third of the total length.

Proportion as Fractions

In the top set maths class, the ratio of boys to girls is 2:3.

(a) What fraction of the class are boys?

(b) What is the relationship between the number of boys and the number of girls?

2

5

The number of boys is the number of girls

2

3

OR The number of girls is

1

times more than the boys.

1

2

Proportion as Fractions

What fraction

of the people were

'Other'?

What is the relationship between the people eating Pork and Beef?

Proportion as Fractions

What fraction

of the people were

'Other'?

What is the relationship between the people eating Pork and Beef?

80

2

360

9

=

OR The number of people who eat Beef is 3 x greater than the

number of people who eat Pork

The number of people who eat Pork is of the number of people who eat Beef

4

15

3

4

Main Activity 1

Complete the Proportion and Fractions RAG sheet.

Main Activity 1 Answers

Red: (1) (i) 3/7 (ii) There are 3/4 as many vowels as

consonants.

(2) (i) 8/15 (ii) There are 7/8 as many boys as girls.

(3) (i) 8/21 (ii) Charles walks 8/13 of the distance

before his friends house that he walks after.

(4) (i) 2/5 (ii) Sam has 2/3 of the money that Vishal

has.

(5) (i) 3/10 (ii) The volume of juice is 3/7 of the

volume of lemonade.

Amber: (6) (i) 3/8 (ii) The volume of yellow paint is 3/5 of

the volume of blue paint.

(7) (i) 1/6 (ii) The length of the shorter side is 5/12

of the middle side and 5/13 of the longer side.

(8) (i) 2/5 (ii) The distance driven after Shane's

break is 2/3 of the distance driven before.

(9) (i) 3/7 (ii) Usman will get 3/4 of the sweets

that Jack will get.

Green: (10) (i) 3/14 (ii) The shorter length is 3/4 of the

longer length.

(11) (i) 1/5 (ii) 7/9 of the number of people who get

the bus walk to school.

(12) (i) 5/12 (ii) The green section has 3/4 the number of questions of the amber sections and 3/5 the number of questions in the red section.

Starter

This diagram shows that the ratio of the lengths of blue rods to red rods is 1:2 (i.e. that blue is of red).

What fraction of the total length of this bar does blue represent?

1/3

How could we tell that from the ratio?

There are 1 out of 3 parts in the ratio on the blue side.

1

2

**Activities**

**Key Examples**

**Activity**

Answers

Answers

Worked

Example

Worked

Example