There are various types of fractions that need to be known:

There are various types of fractions that need to be known:

A simple fraction is the classic among all fractions and contains only a numerator and a denominator.

**The fraction line**- symbolizes the division operation.**The numerator**– represents the part of the whole (the relevant part we are asked about in the question – the thing that needs to be divided equally among everyone).**The denominator**– represents the whole – the total – the total number of "pieces" there are.

An improper fraction is any number written like a fraction with a numerator and a denominator, but it is actually a whole number or a whole number with a fraction.

A mixed number is a fraction composed of a whole number and a fraction, hence its name – it combines both whole numbers and fractions.

A decimal fraction represents a non-whole number using a decimal point.

The decimal fraction can be without whole numbers at all or with whole number

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 1:2= \)

A fraction is essentially a part of the whole where the numerator is the part

and the denominator is the total whole.

For example - $1 \over 8$ pizza will describe one pizza slice out of $8$ pizza slices that exist in a family-sized pizza.

Another example:

If there are $3$ balls in a bag and only $2$ of them are pink, we can say that the pink balls constitute $2 \over 3$ of the balls in the bag.

A simple fraction is the classic among all fractions and contains only a numerator and a denominator.

**The fraction line** - symbolizes the division operation. **The numerator** – represents the part of the whole (the relevant part we are asked about in the question – the thing that needs to be divided equally among everyone). **The denominator** – represents the whole – the total – the total number of "pieces" there are. **For example:**

Dana had a birthday cake. Dana's mom cut the cake into $20$ equal slices.

At the birthday party, the children ate $15$ slices of cake in total, including Dana.

Present a simple fraction that represents the part of the cake that remains.

Solution:

The part of the cake that was eaten is $15$ slices out of $20$, which means there are $5$ slices left out of $20$, which is: $5 \over 20$.

If we simplify, we get $1 \over 4$.

Click here to learn more about a simple fraction

Test your knowledge

Question 1

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

Question 2

Choose the fraction that corresponds to the following description:

11 shirts are shared equally between 8 players.

Question 3

Match the following description with the corresponding fraction:

10 tickets are distributed equally among 9 couples.

An improper fraction is any number written like a fraction with a numerator and a denominator, but it is actually a whole number or a whole number with a fraction.

How can you remember this?

The word "improper" indicates that the fraction we see is not really a simple fraction but an improper one – "similar" to a simple fraction but actually it is not because it is whole or more than whole and not just a part of a whole.

**Exercise:**

In the orange cake recipe, you need one and a half cups of flour.

Describe the amount of flour in the cake using an improper fraction.

Solution:

A cup and a half is actually $1 \frac{1}{2}$. Now let's convert this mixed number to an improper fraction:

We multiply the number of wholes by the denominator.

To the result we obtained, we add the numerator – the final result will be the new numerator.

In the denominator – we don't change anything.

We get:

$3 \over 2$

Click here to learn more about improper fractions

A mixed number is a fraction composed of a whole number and a fraction, hence its name – it combines both whole numbers and fractions.

The whole number appears to the left of the fraction, followed immediately by the fraction.

Examples of mixed numbers:

$4 \frac{3}{5}$

$11 \frac{9}{10}$

$2 \frac{1}{2}$

**Advanced Exercise:**

Romi asked her mom how much longer until their vacation in Spain.

Her mom replied: exactly two weeks and three days.

Represent the time until the vacation as a mixed number.

Solution:

Note, we need to express two weeks and three days using a mixed number.

Therefore, we express the two weeks as $2$ as a whole number and the three days as $3 \over 7$, meaning three days out of a week.

(The whole number in this case represents $2$ full weeks)

We get that: $2\frac {3}{7}$ is the duration in a mixed number until the vacation in Spain.

Click here to learn more about mixed fractions

Do you know what the answer is?

Question 1

Match the following description with the corresponding fraction:

3 apples are distributed equally among two children.

Question 2

\( \frac{3}{4}-\frac{1}{6}= \)

Question 3

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 1:2= \)

A decimal fraction represents a non-whole number using a decimal point.

The decimal fraction can be without whole numbers at all or with whole numbers.

The decimal point divides the fraction as follows:

Another example:

We will check the whole numbers – the decimal fraction with the larger whole number is the greater one.

If the whole numbers are the same, we will check the digits after the decimal point.

We will go digit by digit in order (starting from the tenths, hundredths, and so on).

If they are identical, we will continue.

If they are different, we will determine which fraction is greater accordingly.

Click here to learn more about decimal fractions

Check your understanding

Question 1

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

\( 5:6= \)

Question 2

Choose the fraction that corresponds to the following description:

11 shirts are shared equally between 8 players.

Question 3

Match the following description with the corresponding fraction:

10 tickets are distributed equally among 9 couples.

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$1:2=$

Note that the numerator is smaller than the denominator:

1 < 2

As a result, we can claim that:

\frac{1}{2}<1

Therefore, the fraction in the division problem is indeed less than 1.

Yes

Without calculating, determine whether the quotient in the division exercise is less than 1 or not:

$5:6=$

Note that the numerator is smaller than the denominator:

5 < 6

As a result, we can claim that:

\frac{5}{6} < 1

Therefore, the quotient in the division problem is indeed less than 1

Yes

Match the following description with the corresponding fraction:

10 tickets are distributed equally among 9 couples.

We need to understand that every fraction is actually a division exercise,

so when we divide 10 tickets among 9 people,

we are dividing 10 by 9

that is 10:9

The division exercise can also be written as a fraction

and that's the solution!

$\frac{10}{9}$

$\frac{3}{4}-\frac{1}{6}=$

In this question, we need to find a common denominator.

However, we don't have to multiply the denominators by each other,

there is a lower common denominator: 12.

$\frac{3\times3}{3\times4}$

$\frac{1\times2}{6\times2}$

$\frac{9}{12}-\frac{2}{12}=\frac{9-2}{12}=\frac{7}{12}$

$\frac{7}{12}$

Related Subjects

- Opposite numbers
- Elimination of Parentheses in Real Numbers
- Addition and Subtraction of Real Numbers
- Multiplication and Division of Real Numbers
- Integer powering
- Positive and negative numbers and zero
- Real line or Numerical line
- Sum of Fractions
- Subtraction of Fractions
- Multiplication of Fractions
- Division of Fractions
- Comparing Fractions
- Decimal Fractions
- What is a Decimal Number?
- Reducing and Expanding Decimal Numbers
- Addition and Subtraction of Decimal Numbers
- Comparison of Decimal Numbers
- Converting Decimals to Fractions