Fractions, Decimals & Percentages

Prove algebraically that  can be written as 

Using algebra, prove that   is equal in value to

Prove algebraically that can be written as 

Prove algebraically that the recurring decimal  can be written as 

Show that the recurring decimal 

Use algebra to show that the recurring decimal 

 is a recurring decimal.

is a whole number such that

Find, in terms of , the recurring decimal  as a fraction.
Give your fraction in its simplest form.
Show clear algebraic working.

Use algebra to show that 

At a country park there is a house, a museum and a garden.

The table shows the prices per person to visit the park.

One day, 480 people visit the park.

67 visit the garden only.
40% visit the house and the museum.
 visit the house only.
The rest visit the museum only.

In total, how much do the 480 people pay to visit the park?
You may use the Venn diagram to help you.

Write these numbers in order of size.

Start with the smallest.

Smallest...............................

Largest................................

Prove algebraically that  converts to the fraction 

Convert  to a fraction in its lowest terms.

Elsa divides a two-digit number by another two-digit number.
She gets the answer 

She says that there is only one possible pair of numbers that will give this answer.
Is she correct? Show how you decide.

Sally divided a two-digit number by another two-digit number.
Her answer was 3.18181818...... .

Find two numbers that Sally could have used.

......................... and ..........................

Write this list of numbers in order, smallest first.

,  ,    ,  

Write as a fraction in its simplest form.
You must show full working in support of your answer.

Write these numbers in order of size.
Start with the smallest number.

Prove that the recurring decimal 

Show that the recurring decimal  

Use algebra to show that the recurring decimal 

The people working for a company work in Team or in Team .

number of people in Team : number of people in Team = 3 : 4

 of Team work full time.
24% of Team work full time.

Work out what fraction of the people working for the company work full time.
Give your fraction in its simplest form.

Alex makes  cakes to sell.
He makes chocolate cakes, lemon cakes and fruit cakes where

number of chocolate cakes

:

number of lemon cakes

:

number of fruit cakes

=

Alex sells

all of the chocolate cakes

of the lemon cakes

 of the fruit cakes

The profit he makes on each cake he sells is shown in the table.

Type of cake	Profit per cake he sells
chocolate
lemon
fruit

Work out the total profit that Alex makes from the cakes he sells.

£.............................................

Use algebra to show that the recurring decimal  =

Josh buys and sells books for a living.

He buys 120 books for £4 each.

He sells   of the books for £5 each.

He sells 40% of the books for £7 each.
He sells the rest of the books for £8 each.

Calculate Josh’s percentage profit.

Ahmed, Behnaz and Carmen each have some money.
Ahmed has 20% more money than Behnaz.
Carmen has  of the amount of money that Behnaz has.

Carmen has 31.50 euros.
Work out how much money Ahmed has.

.......................euros

Work out   

Circle your answer.

Convert to a recurring decimal.

On a restaurant menu there are

22 main dishes, of which are gluten-free
7 rice dishes, which are all gluten-free
5 naan breads, of which 40% are gluten-free.

This Meal Deal is on the menu.

How many of the possible Meal Deals are totally gluten-free?

Use this fact to show that 

Using part (a) or otherwise, convert   to a fraction.

Give your answer in its simplest form.

James is taking three examination papers in Spanish.
Here are his first two results.

Paper 1:            Paper 2:   

Paper 3 is out of 95.
The marks in each of the three papers are added together.

Find the lowest mark that James needs in Paper 3 to achieve 60% of the total marks.

On a plane, of the passengers were British.
30% of the British passengers were men.
There were 36 British men on the plane.

Find the total number of passengers on the plane.

Without using a calculator, show that  o can be written as .

Explain how  can be used to find  as a decimal and write down its value.

= ................

Write  as a recurring decimal.

Convert  to a fraction.