Chapters

Exercise 1
Exercise 2
Exercise 3
Exercise 4
Exercise 5
Exercise 6
Exercise 7
Exercise 8
Exercise 9
Exercise 10
Exercise 11
Exercise 12
Exercise 13
Exercise 14
Exercise 15
Exercise 16
Exercise 1 Solution
Exercise 2 Solution
Exercise 3 Solution
Exercise 4 Solution
Exercise 5 Solution
Exercise 6 Solution
Exercise 7 Solution
Exercise 8 Solution
Exercise 9 Solution
Exercise 10 Solution
Exercise 11 Solution
Exercise 12 Solution
Exercise 13 Solution
Exercise 14 Solution
Exercise 15 Solution
Exercise 16 Solution

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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

Exercise 2

To prepare a cake, you need:

$\text{[math]}$ of a package of $\text{[math]}$ g of sugar

$\text{[math]}$ of a $\text{[math]}$ kg package of flour

$\text{[math]}$ of a bar of butter of weighing $\text{[math]}$ g

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

Exercise 3

A well contains $\text{[math]}$ liters of water. If $\text{[math]}$ of its original content is consumed, how many liters of water are left in the well?

Exercise 4

A piece of cloth measuring $\text{[math]}$ m in length is cut to $\text{[math]}$ 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

$\text{[math]}$ bottles of juice each measuring $\text{[math]}$ of a liter

$\text{[math]}$ bottles of lemonade each measuring $\text{[math]}$ 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 $\text{[math]}$ liters?

Exercise 7

A cable measuring $\text{[math]}$ m is cut into two pieces. One piece of the cable is $\text{[math]}$ of the original length. What is the length of each piece of cable?

Exercise 8

A box contains $\text{[math]}$ chocolates. Eva ate $\text{[math]}$ of the chocolates and Ana ate $\text{[math]}$ of the chocolates.

a. How many chocolates did Eva eat?

b. How many chocolates did Ana eat?

c. What fraction of the $\text{[math]}$ chocolates have been eaten so far?

Exercise 9

Adriana has walked $\text{[math]}$ m on her way to school. This distance is $\text{[math]}$ 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 $\text{[math]}$ km. At a particular moment, Car A has traveled $\text{[math]}$ of the trip, while car B has traveled $\text{[math]}$ 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 $\text{[math]}$ of the votes went to Party A, $\text{[math]}$ went to Party B, $\text{[math]}$ went to Party C and the remainder went to Party D. The total number of votes was $\text{[math]}$ .

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 $\text{[math]}$ of the total amount of voters who are registered.

Exercise 12

Helen went to the women's boutique starting out with $\text{[math]}$ dollars. She spent $\text{[math]}$ of that amount on new clothes. How much money does Helen have left?

Exercise 13

A few years ago Peter was $\text{[math]}$ , which represents $\text{[math]}$ of the amount of his current age. How old is Peter now?

Exercise 14

A father has divided up $\text{[math]}$ dollars among his 3 sons. The eldest son received $\text{[math]}$ of the whole amount, while the middle son received $\text{[math]}$ 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: $\text{[math]}$ th for electricity, $\text{[math]}$ th for water, $\text{[math]}$ th for garbage collection, $\text{[math]}$ 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 $\text{[math]}$ dollars to go shopping with. Thursday she spent $\text{[math]}$ of that amount and Saturday she spent $\text{[math]}$ 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

$\text{[math]}$

b. half of a third

$\text{[math]}$

c. a third of a half

$\text{[math]}$

d. half of a quarter

$\text{[math]}$

Exercise 2 Solution

To prepare a cake, you need:

$\text{[math]}$ of a package of $\text{[math]}$ g of sugar

$\text{[math]}$ of a $\text{[math]}$ kg package of flour

$\text{[math]}$ of a bar of butter of $\text{[math]}$

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

$\text{[math]}$ of $\text{[math]}$ g is $\text{[math]}$ g of sugar

$\text{[math]}$ of $\text{[math]}$ g is $\text{[math]}$ g of flour

$\text{[math]}$ of $\text{[math]}$ g is $\text{[math]}$ g of butter

Exercise 3 Solution

A well contains $\text{[math]}$ liters of water. If $\text{[math]}$ of its original content is consumed, how many liters of water are left in the well?

$\text{[math]}$ is the fractional amount left in the well.

$\text{[math]}$ liters is the amount of water left in the well.

Exercise 4 Solution

A piece of cloth measuring $\text{[math]}$ m in length is cut to $\text{[math]}$ of its original length. What is the length of the piece that has been removed?

$\text{[math]}$ is the fractional amount of the piece that was removed.

$\text{[math]}$ 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

$\text{[math]}$ bottles of juice each measuring $\text{[math]}$ of a liter

$\text{[math]}$ bottles of lemonade each measuring $\text{[math]}$ 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: $\text{[math]}$ liters

amount of juice drank: $\text{[math]}$ liters

amount of lemonade drank: $\text{[math]}$ liters

total amount of liquids drank: $\text{[math]}$ liters

$\text{[math]}$ liters

Exercise 6 Solution

How many thirds of a liter are there in $\text{[math]}$ liters?

There are three $\text{[math]}$ liters in $\text{[math]}$ liter.

There are $\text{[math]}$ thirds $\text{[math]}$ 's of a liter in $\text{[math]}$ liters.

Exercise 7 Solution

A cable measuring $\text{[math]}$ m is cut into two pieces. One piece of the cable is $\text{[math]}$ of the original length. What is the length of each piece of cable?

The fractional length of the second piece of cable: $\text{[math]}$ .

The 2 pieces are $\text{[math]}$ th and $\text{[math]}$ th of the original length.

The length of the first piece: $\text{[math]}$ m.

The length of the second piece: $\text{[math]}$ m.

Exercise 8 Solution

A box contains $\text{[math]}$ chocolates. Eva ate $\text{[math]}$ of the chocolates and Ana ate $\text{[math]}$ of the chocolates.

a. How many chocolates did Eva eat?

Eva ate $\text{[math]}$ chocolates.

b. How many did Ana eat?.

Ana ate $\text{[math]}$ chocolates

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

$\text{[math]}$

Exercise 9 Solution

Adriana has walked $\text{[math]}$ m on her way to school. This distance is $\text{[math]}$ th of the total distance from her house to the school. What is the total distance from her house to the school?

$\text{[math]}$ of the total distance plus $\text{[math]}$ of the total distance will be the actual total distance.

$\text{[math]}$ is $\text{[math]}$ of $\text{[math]}$

Find $\text{[math]}$ of the distance $\text{[math]}$ m.

$\text{[math]}$ of $\text{[math]}$ m is $\text{[math]}$ m

The total distance is $\text{[math]}$ m.

Exercise 10 Solution

Two cars A and B make the same journey of $\text{[math]}$ km. At a particular moment, Car A has traveled $\text{[math]}$ of the trip, while Car B has traveled $\text{[math]}$ 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 $\text{[math]}$ of the total trip and car B has traveled $\text{[math]}$ of the total trip.

Car A: $\text{[math]}$ of the trip

Car B: $\text{[math]}$ of the trip

$\text{[math]}$ 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: $\text{[math]}$ km

Car B: $\text{[math]}$ km

Exercise 11 Solution

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

Calculate:

a. The number of votes obtained by each party.

Party A has $\text{[math]}$ votes

Party B has $\text{[math]}$ votes

Party C has $\text{[math]}$ votes

Party D has $\text{[math]}$ votes

b. The number of registered voters who did not cast a ballot if the number of voters who did was $\text{[math]}$ of the total amount of voters who are registered.

$\text{[math]}$ of the total amount of registered voters is $\text{[math]}$ voters,

so $\text{[math]}$ of the total amount of people who voted, $\text{[math]}$ , will be $\text{[math]}$ of the total amount of registered voters.

$\text{[math]}$ is $\text{[math]}$ of the registered voters,

so $\text{[math]}$ is the total amount of registered voters.

Exercise 12 Solution

Helen went to the women's boutique starting out with $\text{[math]}$ dollars. She spent $\text{[math]}$ of that amount. How much money does she have left?

$\text{[math]}$

$\text{[math]}$ dollars

Exercise 13 Solution

A few years ago Peter was 24, which represents $\text{[math]}$ of his current age. How old is Peter now?

$\text{[math]}$ of Peter's current age plus $\text{[math]}$ of Peter's current age will be Peter's actual current age.

$\text{[math]}$ is $\text{[math]}$ of $\text{[math]}$

$\text{[math]}$ of $\text{[math]}$ is $\text{[math]}$

present age is $\text{[math]}$

Exercise 14 Solution

a. How much money did each sibling receive?

The eldest son received $\text{[math]}$ dollars.

The middle son received $\text{[math]}$ dollars.

The youngest son received $\text{[math]}$ dollars.

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

The youngest son received $\text{[math]}$ of the original amount.

Exercise 15 Solution

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

Budget without cleaning expenses: $\text{[math]}$

$\text{[math]}$

Cleaning expenses: $\text{[math]}$

b. Order the expenses from least to greatest.

$\text{[math]}$

garbage $\text{[math]}$ maintenance $\text{[math]}$ cleaning $\text{[math]}$ water $\text{[math]}$ electricity

Exercise 16 Solution

Alicia had $\text{[math]}$ dollars to go shopping. Thursday she spent $\text{[math]}$ th of that amount and Saturday she spent $\text{[math]}$ th of what she had left.

a. How much money did she spend each day?

Thursday Alicia spent $\text{[math]}$ dollars.

She has $\text{[math]}$ dollars left for more shopping.

Saturday Alicia spent $\text{[math]}$ dollars.

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

She has $\text{[math]}$ dollars left.

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

Fraction Word Problems

Exercise 1

Exercise 2

Exercise 3

Exercise 4

Exercise 5

Exercise 6

Exercise 7

Exercise 8

Exercise 9

Exercise 10

Exercise 11

Exercise 12

Exercise 13

Exercise 14

Exercise 15

Exercise 16

Exercise 1 Solution

Exercise 2 Solution

Exercise 3 Solution

Exercise 4 Solution

Exercise 5 Solution

Exercise 6 Solution

Exercise 7 Solution

Exercise 8 Solution

Exercise 9 Solution

Exercise 10 Solution

Exercise 11 Solution

Exercise 12 Solution

Exercise 13 Solution

Exercise 14 Solution

Exercise 15 Solution

Exercise 16 Solution

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