Simple Fractions - Examples, Exercises and Solutions

Practice FractionsPractice A fraction as a divisorPractice How do you simplify fractions?Practice Simplification and Expansion of Simple FractionsPractice Common denominatorPractice Part of a quantityPractice Placing Fractions on the Number LinePractice NumeratorPractice DenominatorPractice Remainder of a fractionPractice Remainders

Types of Fractions

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

Simple Fraction

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. 

Improper Fraction

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.

Mixed 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.

Decimal Fraction

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

Types of Fractions
Detailed explanation

Practice Simple Fractions

Question 1

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

\( 5:6= \)

Question 2

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

\( 1:2= \)

Question 3

Match the following description with the corresponding fraction:

10 tickets are distributed equally among 9 couples.

Question 4

Choose the fraction that corresponds to the following description:

11 shirts are shared equally between 8 players.

Question 5

Match the following description with the corresponding fraction:

3 apples are distributed equally among two children.

Examples with solutions for Simple Fractions

Exercise #1

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

5:6= 5:6=

Video Solution

Step-by-Step Solution

Note that the numerator is smaller than the denominator:

5 < 6

As a result, we can write it thusly:

\frac{5}{6} < 1

Therefore, the quotient in the division exercise is indeed less than 1.

Answer

Less than 1

Exercise #2

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

1:2= 1:2=

Video Solution

Step-by-Step Solution

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.

Answer

Yes

Exercise #3

Match the following description with the corresponding fraction:

10 tickets are distributed equally among 9 couples.

Step-by-Step Solution

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!

Answer

109 \frac{10}{9}

Exercise #4

Choose the fraction that corresponds to the following description:

11 shirts are shared equally between 8 players.

Step-by-Step Solution

To find the fraction that corresponds to the description of 11 shirts being shared equally among 8 players, we perform the following steps:

  • Step 1: Identify the total number of shirts. Here, this number is 11.
  • Step 2: Identify the total number of players. Here, this number is 8.
  • Step 3: Set up the fraction 118\frac{11}{8} where 11 is the number of shirts and 8 is the number of players.

This fraction 118\frac{11}{8} represents how shirts are distributed among players, meaning each player receives 118 \frac{11}{8} of a shirt.

Therefore, the correct answer to the problem is 118 \frac{11}{8} , which corresponds to choice 3.

Answer

118 \frac{11}{8}

Exercise #5

Match the following description with the corresponding fraction:

3 apples are distributed equally among two children.

Step-by-Step Solution

Let's solve the problem step by step:

We are given 3 apples that need to be distributed equally among 2 children. This requires calculating how many apples each child receives, expressed as a fraction.

  • Step 1: Identify how to divide the apples. We want each child to receive an equal share of the 3 apples. This implies a division problem: 3÷23 \div 2.
  • Step 2: Set up the division as a fraction. When you divide 3 apples among 2 children equally, you are determining 32\frac{3}{2}.
  • Step 3: Express the result as a fraction. Each child receives 32\frac{3}{2} apples.

Thus, when 3 apples are divided equally among 2 children, the result is represented by the fraction 32 \frac{3}{2} .

This matches with the correct choice provided, which is choice 4: 32 \frac{3}{2} .

Therefore, the solution to the problem is 32 \frac{3}{2} .

Answer

32 \frac{3}{2}

Question 1

Solve the following equation:

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

Exercise #6

Solve the following equation:

34−16= ? \frac{3}{4}-\frac{1}{6}=\text{ ?}

Video Solution

Step-by-Step Solution

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

However, we don't have to multiply the denominators by each other as there is a lowest common denominator: 12.

3×33×4 \frac{3\times3}{3\times4}

1×26×2 \frac{1\times2}{6\times2}

912−212=9−212=712 \frac{9}{12}-\frac{2}{12}=\frac{9-2}{12}=\frac{7}{12}

Answer

712 \frac{7}{12}