Fractions Made Simple: Proper, Improper, Mixed & Conversions

A fraction shows a part of a whole. A proper fraction has a smaller numerator than denominator (3/4). An improper fraction has a numerator equal to or bigger than the denominator (7/4). A mixed fraction is a whole number plus a proper fraction (1¾).

Parts of a Fraction

In 3/4: 3 is the numerator (how many parts we have), and 4 is the denominator (how many equal parts the whole is cut into). Think of a roti cut into 4 equal pieces — eating 3 means eating 3/4 of the roti.

Types of Fractions

Type	Meaning	Examples
Proper	Numerator < denominator (value less than 1)	2/5, 7/9
Improper	Numerator ≥ denominator (value 1 or more)	9/4, 5/5
Mixed	Whole number + proper fraction	2¼, 3⅔
Unit	Numerator is 1	1/2, 1/7
Like	Same denominators	2/9, 5/9
Unlike	Different denominators	1/3, 3/4
Equivalent	Different-looking but equal	1/2 = 2/4 = 5/10

Converting Between Improper and Mixed Fractions

Improper → Mixed: divide the numerator by the denominator. The quotient becomes the whole number and the remainder becomes the new numerator.
17/5: 17 ÷ 5 = 3, remainder 2 → 3⅖

Mixed → Improper: multiply the whole number by the denominator, add the numerator, keep the same denominator.
4 3/7: (4 × 7) + 3 = 31 → 31/7

Simplifying Fractions

Divide the numerator and denominator by their HCF. 18/24: HCF = 6, so 18/24 = 3/4. (Need a refresher? See LCM and HCF methods.)

Adding and Subtracting Fractions

Like fractions: add/subtract the numerators, keep the denominator. 2/9 + 5/9 = 7/9

Unlike fractions: make the denominators equal using the LCM first.
2/3 + 3/4 → LCM of 3 and 4 is 12 → 8/12 + 9/12 = 17/12 = 1 5/12

Subtracting: 5/6 − 1/4 → LCM is 12 → 10/12 − 3/12 = 7/12

With mixed fractions, convert to improper first: 3¼ − 1⅔ = 13/4 − 5/3 = 39/12 − 20/12 = 19/12 = 1 7/12

Multiplying and Dividing Fractions

Multiply: numerator × numerator, denominator × denominator — cancel common factors first.
3/5 × 10/9 → cancel 5 with 10, and 3 with 9 → (1 × 2)/(1 × 3) = 2/3

Mixed numbers: 2½ × 1⅕ = 5/2 × 6/5 = 30/10 = 3

Divide (Keep, Change, Flip): keep the first fraction, change ÷ to ×, flip the second.
4/7 ÷ 2/3 = 4/7 × 3/2 = 12/14 = 6/7

Comparing Fractions: The Cross-Multiplication Trick

Which is bigger, 5/8 or 3/5? Cross-multiply: 5 × 5 = 25, and 3 × 8 = 24. Since 25 > 24, 5/8 is bigger.

A Real-Life Word Problem

Riya ate 1/3 of a pizza and her brother ate 1/4. What fraction is left?
Eaten: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Left: 1 − 7/12 = 5/12

Quick Summary Table

Operation	Rule
Add / subtract	Make the denominators equal (LCM), then add or subtract the numerators
Multiply	Numerator × numerator, denominator × denominator (cancel first)
Divide	Multiply by the reciprocal of the second fraction
Mixed numbers	Convert to improper fractions before any operation
Final answer	Simplify, and convert back to a mixed number if needed

Tips for Parents

• Use food — rotis, chocolate bars and pizza slices make fractions real.
• Fold paper into halves, quarters and eighths to show equivalent fractions.
• Ask kitchen questions: "The recipe needs ¾ cup but we're making double. How much now?"

Frequently Asked Questions

What is the difference between proper and improper fractions?
In a proper fraction the numerator is smaller than the denominator, so its value is less than 1. In an improper fraction the numerator is equal to or bigger than the denominator, so its value is 1 or more.

How do you convert 17/5 into a mixed fraction?
Divide 17 by 5 to get 3 with remainder 2. So 17/5 = 3 2/5.

Why do we need the LCM to add fractions?
You can only add parts of the same size. The LCM turns both fractions into same-sized parts (a common denominator).