Chapters

## Exercise 1

Determine the fraction that matches the description below:

a. half of a half

b. half of a third

c. a third of a half

d. half of a quarter

The best Maths tutors available
4.9 (36 reviews)
Intasar
£48
/h
1st lesson free!
4.9 (28 reviews)
Paolo
£30
/h
1st lesson free!
4.9 (23 reviews)
Shane
£25
/h
1st lesson free!
5 (16 reviews)
Jamie
£25
/h
1st lesson free!
5 (17 reviews)
Matthew
£30
/h
1st lesson free!
4.9 (12 reviews)
Petar
£40
/h
1st lesson free!
4.9 (17 reviews)
Farooq
£40
/h
1st lesson free!
4.9 (7 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!
4.9 (36 reviews)
Intasar
£48
/h
1st lesson free!
4.9 (28 reviews)
Paolo
£30
/h
1st lesson free!
4.9 (23 reviews)
Shane
£25
/h
1st lesson free!
5 (16 reviews)
Jamie
£25
/h
1st lesson free!
5 (17 reviews)
Matthew
£30
/h
1st lesson free!
4.9 (12 reviews)
Petar
£40
/h
1st lesson free!
4.9 (17 reviews)
Farooq
£40
/h
1st lesson free!
4.9 (7 reviews)
Dr. Kritaphat
£49
/h
1st lesson free!

## Exercise 2

To prepare a cake, you need:

of a package of g of sugar

of a kg package of flour

of a bar of butter of weighing g

Find the quantities that are needed to prepare the cake in grams.

## Exercise 3

A well contains liters of water. If of its original content is consumed, how many liters of water are left in the well?

## Exercise 4

A piece of cloth measuring m in length is cut to of its original length. What is the length of the piece that has been removed?

## Exercise 5

A family consumed the following amounts of liquids during their Saturday picnic:

Two bottles of water each measuring a liter and a half

bottles of juice each measuring of a liter

bottles of lemonade each measuring of a liter

How many liters of liquid did the family drink during their picnic? Express the result using a mixed number.

## Exercise 6

How many thirds of a liter are there in liters?

## Exercise 7

A cable measuring m is cut into two pieces. One piece of the cable is of the original length. What is the length of each piece of cable?

## Exercise 8

A box contains chocolates. Eva ate of the chocolates and Ana ate of the chocolates.

a. How many chocolates did Eva eat?

b. How many chocolates did Ana eat?

c. What fraction of the chocolates have been eaten so far?

## Exercise 9

Adriana has walked m on her way to school. This distance is of the total distance from her house to the school. What is the total distance from her house to the school?

## Exercise 10

Two cars A and B are making the same journey of km. At a particular moment, Car A has traveled of the trip, while car B has traveled of it.

a. If the cars continue at the same speed, which of the two will arrive at the destination first?

b. How many kilometers had each car driven at that particular moment?

## Exercise 11

After the ballots have been counted in a city's local election, it was determined that of the votes went to Party A, went to Party B, went to Party C and the remainder went to Party D. The total number of votes was .

Calculate:

a. The number of votes obtained by each party.

b. The number of registered voters who did not cast a ballot if the total amount of voters that did was of the total amount of voters who are registered.

## Exercise 12

Helen went to the women's boutique starting out with dollars. She spent of that amount on new clothes. How much money does Helen have left?

## Exercise 13

A few years ago Peter was , which represents of the amount of his current age. How old is Peter now?

## Exercise 14

A father has divided up dollars among his 3 sons. The eldest son received of the whole amount, while the middle son received and the youngest son received the remainder.

a. How much money did each sibling receive?

b. What fraction of the money did the youngest son receive?

## Exercise 15

The budget for a residential complex is distributed as follows: th for electricity, th for water, th for garbage collection, th for building maintenance and the remainder is reserved for cleaning the complex.

a. What fraction of the budget is used for cleaning?

b. Order the expenses from least to greatest.

## Exercise 16

Alicia had dollars to go shopping with. Thursday she spent of that amount and Saturday she spent of what she had left.

a. How much money did she spend each day?

b. How much money does she have left at the end?

## Exercise 1 Solution

Determine the fraction that matches the description below:

a. half a half

b. half of a third

c. a third of a half

d. half of a quarter

## Exercise 2 Solution

To prepare a cake, you need:

of a package of g of sugar

of a kg package of flour

of a bar of butter of

Find the quantities that are needed to prepare the cake in grams.

of g is g of sugar

of g is g of flour

of g is g of butter

## Exercise 3 Solution

A well contains liters of water. If of its original content is consumed, how many liters of water are left in the well?

is the fractional amount left in the well.

liters is the amount of water left in the well.

## Exercise 4 Solution

A piece of cloth measuring m in length is cut to of its original length. What is the length of the piece that has been removed?

is the fractional amount of the piece that was removed.

m is the length of the piece that was removed.

## Exercise 5 Solution

A family consumed the following amounts of liquids during their Saturday picnic:

Two bottles of water each measuring a liter and a half

bottles of juice each measuring of a liter

bottles of lemonade each measuring of a liter

How many liters of liquid did the family drink during their picnic? Express the result using a mixed number.

amount of water drank: liters

amount of juice drank: liters

total amount of liquids drank: liters

liters

## Exercise 6 Solution

How many thirds of a liter are there in liters?

There are three liters in liter.

There are thirds 's of a liter in liters.

## Exercise 7 Solution

A cable measuring m is cut into two pieces. One piece of the cable is of the original length. What is the length of each piece of cable?

The fractional length of the second piece of cable: .

The 2 pieces are th and th of the original length.

The length of the first piece: m.

The length of the second piece: m.

## Exercise 8 Solution

A box contains chocolates. Eva ate of the chocolates and Ana ate of the chocolates.

a. How many chocolates did Eva eat?

Eva ate chocolates.

b. How many did Ana eat?.

Ana ate chocolates

c. What fraction of the total amount of chocolates has been eaten between them?

## Exercise 9 Solution

Adriana has walked m on her way to school. This distance is th of the total distance from her house to the school. What is the total distance from her house to the school?

of the total distance plus of the total distance will be the actual total distance.

is of

Find of the distance m.

of m is m

The total distance is m.

## Exercise 10 Solution

Two cars A and B make the same journey of km. At a particular moment, Car A has traveled of the trip, while Car B has traveled of it.

a. If the cars continue at the same speed, which of the two will arrive at the destination first?

Car A has traveled of the total trip and car B has traveled of the total trip.

Car A: of the trip

Car B: of the trip

so Car B will make it to the end of the journey just a hair faster than Car A.

b. How many kilometers have been traveled at this particular moment by each car?

Car A: km

Car B: km

## Exercise 11 Solution

After the ballots have been counted in a city's local election, it was determined that th of the votes went to Party A, th went to Party B, th went to Party C and the remainder went to Party D. The total number of votes was .

Calculate:

a. The number of votes obtained by each party.

b. The number of registered voters who did not cast a ballot if the number of voters who did was of the total amount of voters who are registered.

of the total amount of registered voters is voters,

so of the total amount of people who voted, , will be of the total amount of registered voters.

is of the registered voters,

so is the total amount of registered voters.

## Exercise 12 Solution

Helen went to the women's boutique starting out with dollars. She spent of that amount. How much money does she have left?

dollars

## Exercise 13 Solution

A few years ago Peter was 24, which represents of his current age. How old is Peter now?

of Peter's current age plus of Peter's current age will be Peter's actual current age.

is of

of is

present age is

## Exercise 14 Solution

A father has divided up dollars among his 3 sons. The eldest son received of the whole amount, while the middle son received and the youngest son received the remainder.

a. How much money did each sibling receive?

b. What fraction of the money was the amount given to the youngest son?

The youngest son received of the original amount.

## Exercise 15 Solution

The budget for a residential complex is distributed as follows: th for electricity, th for water, th for garbage collection, th for building maintenance and the remainder is reserved for cleaning the complex.

a. What fraction of the budget is used for cleaning?

Budget without cleaning expenses:

Cleaning expenses:

b. Order the expenses from least to greatest.

garbage maintenance cleaning water electricity

## Exercise 16 Solution

Alicia had dollars to go shopping. Thursday she spent th of that amount and Saturday she spent th of what she had left.

a. How much money did she spend each day?

Thursday Alicia spent dollars.

She has dollars left for more shopping.

Saturday Alicia spent dollars.

b. How much does she have left at the end?

She has dollars left.

The platform that connects tutors and students