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
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:
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
amount of lemonade 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.
Party A has votes
Party B has votes
Party C has votes
Party D has votes
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?
The eldest son received dollars.
The middle son received dollars.
The youngest son received dollars.
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.