Fractions
A fraction describes a part of a whole or of a group. This Class 6 Ganita Prakash chapter explains what the numerator and denominator mean, sorts fractions into proper, improper and mixed, and shows how to find equivalent fractions, compare them, and add or subtract fractions with the same denominator.
Learning objectives
- Read a fraction as a part of a whole.
- Classify fractions as proper, improper or mixed.
- Find equivalent fractions and compare fractions.
- Add and subtract like fractions.
Key concepts
What a fraction means
A fraction such as ¾ has a denominator (bottom number) telling how many equal parts the whole is divided into, and a numerator (top number) telling how many of those parts are taken. So ¾ means 3 of 4 equal parts. Fractions can also be shown as points on a number line between 0 and 1.
Types of fractions
A proper fraction has a numerator smaller than its denominator (like ⅖), so it is less than one. An improper fraction has a numerator equal to or larger than its denominator (like 7/4), so it is one or more. A mixed number combines a whole number and a proper fraction, like 1¾, which equals 7/4.
Equivalent fractions
Different fractions can name the same value; ½, 2/4 and 3/6 are all equivalent. We get an equivalent fraction by multiplying or dividing both the numerator and denominator by the same number. Dividing by the largest common factor gives the simplest form.
Comparing, adding and subtracting like fractions
Fractions with the same denominator are called like fractions; the one with the larger numerator is greater. To add or subtract like fractions, keep the denominator and add or subtract only the numerators, so 2/5 + 1/5 = 3/5.
Important formulas
Equivalent fraction
multiply or divide top and bottom by the same number
Adding like fractions
a/d + b/d = (a + b)/d
Mixed to improper
whole × denominator + numerator, over denominator
Key definitions
- Numerator
- The top number of a fraction; the parts taken.
- Denominator
- The bottom number; the total equal parts in the whole.
- Proper fraction
- A fraction less than one, with numerator below denominator.
- Equivalent fractions
- Different fractions that represent the same value.
Solved examples
Q1. Is 5/8 a proper or improper fraction?
Solution: Proper — the numerator 5 is less than the denominator 8.
Q2. Write a fraction equivalent to ½ with denominator 6.
Solution: Multiply top and bottom by 3: ½ = 3/6.
Q3. Add 3/7 + 2/7.
Solution: Same denominator, so add numerators: (3 + 2)/7 = 5/7.
Common mistakes to avoid
- Adding denominators as well as numerators when adding like fractions.
- Thinking a larger denominator always means a larger fraction.
- Changing only the numerator when making an equivalent fraction.
- Confusing a proper fraction with an improper one.
Fractions — MCQ Quiz
10 questions with instant feedback. Use number keys 1–4 to answer.
In the fraction 3/8, the number 8 is the:
Practice questions
Short answer
What do the numerator and denominator of a fraction tell us?
The denominator is the number of equal parts in the whole; the numerator is how many parts are taken.
How do you add two like fractions?
Keep the common denominator and add the numerators.
Give a fraction equivalent to ⅓.
2/6 (multiply top and bottom by 2).
Long answer
Describe proper, improper and mixed fractions with an example of each.
A proper fraction has its numerator smaller than its denominator, so it is less than one — for example ⅗. An improper fraction has its numerator equal to or greater than its denominator, so it is one or more — for example 9/4. A mixed number is written as a whole number together with a proper fraction, such as 2¼, which can be changed to the improper fraction 9/4 by computing 2 × 4 + 1 = 9 over 4. These three forms are simply different ways of writing fractional amounts.
Explain how equivalent fractions are formed and used to compare ½ and ⅗.
An equivalent fraction names the same value and is formed by multiplying (or dividing) the numerator and denominator by the same number. To compare ½ and ⅗, rewrite them with a common denominator of 10: ½ = 5/10 and ⅗ = 6/10. Now both have the same denominator, so we compare numerators — 6/10 is greater than 5/10, which means ⅗ is greater than ½.
HOTS (Higher Order Thinking)
Without drawing, which is larger, 3/4 or 5/8? Explain.
Write 3/4 as 6/8. Comparing 6/8 and 5/8 with the same denominator, 6/8 is larger, so 3/4 is greater than 5/8.
A pizza is cut into 8 equal slices and 3 are eaten. What fraction is left, in simplest form?
5 of 8 slices remain, which is 5/8 — already in simplest form.
Quick revision
Revision notes
- Fraction = numerator (parts taken) over denominator (equal parts).
- Proper < 1; improper ≥ 1; mixed = whole + proper.
- Equivalent fractions: multiply/divide top and bottom by the same number.
- Like fractions: add/subtract numerators, keep the denominator.
Key takeaways
- A fraction is a part of a whole or of a group.
- Equivalent fractions name the same value.
- Like fractions are added by adding numerators only.
Frequently asked questions
What is a proper fraction?
A fraction whose numerator is smaller than its denominator, so its value is less than one.
How do I make an equivalent fraction?
Multiply or divide both the numerator and denominator by the same number.
How do I add fractions with the same denominator?
Add the numerators and keep the denominator unchanged.