Welcome to the fascinating world of fractions! If you have ever found mathematical problems involving these small parts of a whole challenging, you have come to the right place. On this page dedicated to fraction problems, we will explore countless situations where these numerical pieces become the key to solving puzzles and real-world situations.
Our team of mathematics enthusiasts will guide you through practical and challenging problems, demystifying the world of fractions and showing you how to apply these skills in your daily life.
So, if you're ready to dive into the exciting universe of fractions and unlock their power to solve problems, this page is for you. Get ready to explore the magic behind fractional numbers and take your mathematical skills to the next level!
Let's start solving fraction problems together!
Fractions and The Units They Represent
Calculate what fraction of the unit these represent:
a Half of a half.
b Half of a third.
c A third of a half.
d Half of a fourth.
e A fourth of a half.
a Half of a half.
Half of a number 
is written as
Since the number is a half, then we obtain
b Half of a third.
Half of a number is written as
Since the number is a third, then we obtain
c A third of a half.
A third of a number is written as
Since the number is a half, then we obtain
d Half of a fourth.
Half of a number is written as
Since the number is a fourth, then we obtain
e A fourth of a half.
A fourth of a number is written as
Since the number is a half, then we obtain
Daily Life Problems Using Fractions
To prepare a cake, you need: 
of a package of 
of sugar, 
of a package of flour weighing 
and 
of a stick of butter weighing 
. Find, in pounds, the quantities needed to prepare the cake.
We write in pounds each of the quantities needed to prepare the cake.
of a package of of sugar
of a package of flour weighing
of a stick of butter weighing 
From a piece of fabric measuring 
, is cut. How many feet does the remaining piece measure?
We calculate how many feet equals
.
We subtract it from the .
.
A box contains 
chocolates. Eva ate 
of the chocolates and Ana 
.
a How many chocolates did Eva eat and how many did Ana eat?
b What fraction of chocolates did they eat together?
a How many chocolates did Eva eat and how many did Ana eat?
We multiply by the corresponding fraction for Eva and Ana.
Eva ate 
and Ana 
.
b What fraction of chocolates did they eat together?
A few years ago Peter was 
years old, which represents 
of his current age. How old is Peter?
We represent it graphically.
equals two of the three parts of his age, so we calculate how much one part is worth (24÷2) and multiply the result by the total number of parts, which is 
.
Therefore, Peter is 
years old.
of a neighborhood community's income is used for fuel, 
is used for electricity, 
for garbage collection, 
for building maintenance and the rest is used for cleaning.
a What fraction of income is used for cleaning?
b According to the fraction of income used, order the listed items from least to greatest.
a What fraction of income is used for cleaning?
To solve this, we must add the fractions of each of the other items and subtract this result from 
. Thus
Subtracting our previous result from we obtain
Therefore, 
of the income was used for cleaning.
b According to the fraction of income used, order the listed items from least to greatest
Taking the fractions with the same denominator
In local elections held in a town, 
of the votes went to party 
, 
to party 
, 
to 
and the rest to party 
. The total number of votes was 
. Calculate:
a The number of votes obtained by each party.
b The number of abstentions knowing that the number of voters represents 
of the electoral census.
a The number of votes obtained by each party.
Party A: 
Party B: 
Party C: 
Party D: 
b The number of abstentions knowing that the number of voters represents 
of the electoral census.
Note that the total voters is 
, that is, it is , therefore, the fraction of abstentions is
Thus, the number of abstentions using the rule of three is given by
The line is divided into 
equal parts. To know the amount that each part represents, we take into account that the first 
parts (the votes) add up to , therefore one part will be 
multiplied by which equals . And the other three parts (the abstentions) are obtained by multiplying by .
George earns $
per month and allocates the following fractions of his salary to the following categories: for rent, for food, 
for gas, 
for household services and clothing, and for personal expenses. If George saves the remainder:
a What fraction does George save?
b How much does this fraction correspond to in money?
a What fraction does George save?
To solve this, we must add each fraction and subtract the result from . Thus
Subtracting our previous result from we obtain
Therefore, George saves 
of his monthly income.
b How much does this fraction correspond to in money?
To know how much this fraction corresponds to in money, we multiply it by the total income
Thus, George saves approximately $
per month.
The history subject will be graded according to the following criteria: exam, participation, assignments, project, punctuality and the rest in attendance. What fraction does attendance represent of the total grade?
To solve this, we must add each fraction and subtract the result from . Thus
Subtracting our previous result from we obtain
Therefore, 
corresponds to attendance.
A farmer plants his acre plot every year with the following proportions: wheat, beans, 
barley, and the rest with corn. What fraction of the land should be planted with corn?
To solve this, we must add the fractions and subtract the result from . Thus
Subtracting our previous result from we obtain
Therefore, 
of the land will be planted with corn.
Phoebe plans to read a 
page book she bought last week. Since she has different activities during the week, she plans to read an average of 
pages every day from Monday to Friday, and on Saturday and Sunday, 
pages each day.
a What fraction of the total represents the pages that Fabiola can read each day of the week?
b How long will it take her to read the book?
a What fraction of the total represents the pages that Phoebe can read each day of the week?
Let 
be the fraction of pages that Phoebe can read Monday through Friday. Thus, we have the following relationship:
We solve for
Therefore, each day from Monday to Friday, Phoebe reads 
of the total pages in the book.
Similarly for Saturday and Sunday, we have the relationship
Solving
Thus, both Saturday and Sunday, Phoebe reads 
of the total pages in the book.
b How long will it take her to read the book?
Since each day from Monday to Friday, Phoebe reads pages, then in these days she will read 
pages. Similarly, on Saturday and Sunday, Phoebe reads pages. Thus, each week she will read 
pages. Therefore, it will take her 
weeks to read the book.
Fractions and Gallons
A tank contains 
gallons of water. of its contents are consumed. How many gallons of water remain?
The total water content is 
and we consume 
, therefore what remains is:
A family has consumed on a summer day: Two bottles of a gallon and a half of water, four cans of gallon of juice and five lemonades of gallon. How many gallons of liquid have they drunk? Express the result as a mixed number.
First we convert the gallon and a half to a fraction.
We multiply each number of items by its corresponding fraction. We find a common denominator and add
We divide the numerator by the denominator 
, the quotient 
is the whole number of the mixed number, the remainder 
is the numerator of the fraction and the denominator is the same as the improper fraction 
:
How many thirds of a gallon are there in 
gallons?
We divide the total gallons by one third
We can also solve it using graphics.
In gallon there are three thirds, so in gallons there will be: 
thirds.
A gallon of gasoline is sold for $
. If a car's tank is filled with $
. How many gallons does this amount represent?
We will convert the $ to gallons with the equivalence of gallon costs $. Note that
Thus,
That is, for $ we would get 
of gasoline.
A plant in a pot is watered every 
days with gallons of water. The plant consumes 
of the water it receives and the rest is drained through the pot's drainage. If the plant is watered for days. How much water was consumed and how much was drained by the plant?
To solve this, we observe that in the period of days, the plant was watered 
times. If each time the plant received gallons of water, then in this period, the plant received 
gallons of water.
We multiply this amount by 
to know the amount of water that was consumed by the plant. Thus,
Thus, the plant consumed 
gallons of water.
Similarly, we multiply the 
gallons by 
which is the amount of water that the plant drains. Then,
That is, the plant drained gallons of water in this time period.
Fractions and Distances
A cable 
long is cut into two pieces. One piece has 
of the cable. How many feet does each piece measure?
We calculate how many feet 
equals and subtract it from 
.
Subtracting from
Ana has traveled 
, which is of the way from her house to the institute. What distance is there from her house to the institute?
We represent it graphically.
equals three parts of the way, so we calculate how much one part is worth 
and multiply the result by the total number of parts 
:
Two automobiles and make the same 
journey. Automobile has traveled 
of the journey when has traveled 
of the same. Which one is ahead? How many miles has each one traveled?
We reduce to a common denominator to compare the fractions
is ahead.
Now let's analyze the distance traveled by each one:
Automobile 
Automobile 
A tailor has 
yards and needs 
yards of fabric to make pants. How much fabric does he need to buy to make the pants?
To solve this problem, we need to subtract from the fraction 
, which is the fabric needed, the fraction 
, which is the fabric the tailor has. The result will be the amount needed. Thus,
Therefore, the tailor needs to buy 
of fabric.
A tractor works 
miles of land in of an hour. How many miles of land will it work in 
hours?
We calculate how many 
of an hour there are in 
hours. To do this, we calculate
Finally, we multiply 
by 
and simplify
Therefore, the tractor will work 
miles in this time.
Fractions and Money
Elena goes shopping with $180. She spends of that amount. How much does she have left?
We calculate how much equals and subtract it from $180.
.
A father distributes $1800 among his children. He gives the oldest 
of that amount, the middle child and the youngest the rest. How much did each one receive? What fraction of the money did the third one receive?
Oldest: 
.
Middle: 
.
Youngest: First let's calculate the fraction of money corresponding to the youngest
.
Now let's calculate the amount
.
A person has a debt of $200 and paid of it. How much is left to pay?
To solve this problem, we first calculate the amount paid and then subtract it from $200 to know the amount remaining to pay.
What was paid is 
.
What remains to be paid is 
.
Two friends, Louis and John, went shopping and together they spent a total of $450. If Louis spent of what John spent, how much did each one spend?
Let 
be the amount spent by Louis and 
be the amount spent by John. Thus, we have the following relationships
.
We substitute the first condition into the second equation
.
Therefore, John paid $300 and Louis paid
Alicia has $300 for shopping. On Thursday she spent of that amount and on Saturday of what she had left. How much did she spend each day and how much does she have left at the end?
Thursday: 
Saturday: First let's calculate what she had left after Thursday
Now we need to calculate the fraction she spent from this amount
Remaining: Let's subtract from $180 the amount she spent on Saturday
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