Fractions and decimals are the foundation for almost everything that comes after them in maths - percentages, ratios, algebra, and even basic science calculations. If Grade 6 is where you are meeting these properly for the first time, getting them solid now saves you years of confusion later.
Why fractions feel hard (and why they are not)
Fractions feel confusing because they behave differently from whole numbers in ways that seem wrong at first:
- Multiplying makes things smaller (half of half is a quarter)
- Dividing makes things bigger (dividing by half gives you double)
- Adding requires extra steps (finding a common denominator)
- A number can look different but be the same thing (1/2 = 2/4 = 3/6)
None of these are hard once you understand why. The problem is usually that students memorize procedures ("flip and multiply") without understanding what the fraction represents.
The mental model that makes everything click
Think of a fraction as a division that has not been done yet. 3/4 means "3 divided by 4" or equivalently "3 out of 4 equal parts."
Once you see it this way:
- Equivalent fractions: 1/2 = 2/4 because dividing 1 by 2 gives the same result as dividing 2 by 4
- Adding fractions: You need common denominators because you cannot add "parts of different sizes" - like adding 1 apple and 2 oranges does not give you 3 of either
- Multiplying fractions: "3/4 of 2/5" means "take two-fifths and then take three-quarters of that piece"
Like and unlike fractions
Like fractions have the same denominator (the bottom number). Adding them is simple: add the numerators, keep the denominator.
- 2/7 + 3/7 = 5/7
Unlike fractions have different denominators. You must convert them to like fractions first by finding the LCM of the denominators.
- 1/3 + 1/4 = 4/12 + 3/12 = 7/12
The LCM step is where most errors happen. Practice finding LCM quickly - it speeds up every fraction operation.
Converting between fractions and decimals
Fraction to decimal: Divide the numerator by the denominator.
- 3/4 = 3 divided by 4 = 0.75
- 1/3 = 1 divided by 3 = 0.333... (repeating)
Decimal to fraction: Read the decimal as a fraction of a power of 10.
- 0.25 = 25/100 = 1/4 (simplify by dividing both by 25)
- 0.6 = 6/10 = 3/5
Common equivalents worth memorizing:
- 1/2 = 0.5
- 1/4 = 0.25, 3/4 = 0.75
- 1/5 = 0.2, 2/5 = 0.4, 3/5 = 0.6, 4/5 = 0.8
- 1/8 = 0.125
Operations with decimals
Addition/Subtraction: Line up the decimal points. Add zeros if needed to make the same number of decimal places.
- 3.4 + 2.56 = 3.40 + 2.56 = 5.96
Multiplication: Multiply as if there are no decimals, then count the total decimal places in both numbers and put the point that many places from the right.
- 2.5 x 1.2: multiply 25 x 12 = 300, total decimal places = 2, so answer = 3.00 = 3
Division: Move the decimal point in the divisor to make it a whole number, move the point in the dividend the same number of places.
- 4.5 divided by 1.5: becomes 45 divided by 15 = 3
Word problems: the translation step
Most fraction word problems fail at translation, not calculation. Practice converting English to maths:
- "One-third of the students" = (1/3) x total students
- "How much is left" = 1 - (what was used)
- "Shared equally among 4" = divided by 4
- "3/5 of a number is 30" = (3/5) x number = 30, so number = 30 x (5/3) = 50
Read the problem twice. Write down what you know and what is being asked before calculating.
Common mistakes to watch for
- Adding numerators AND denominators: 1/3 + 1/4 is NOT 2/7
- Forgetting to simplify: Always check if the answer can be reduced
- Decimal point errors in multiplication: Count decimal places carefully
- Confusing "of" with "divided by": "1/3 of 12" means multiply (= 4), not divide
Practice strategy
Do 5-10 problems daily rather than 50 in one sitting. Mix the types:
- 2 conversion problems (fraction to decimal or vice versa)
- 2 operation problems (add, subtract, multiply, or divide)
- 1 word problem
This takes 15-20 minutes and builds skill faster than a weekend marathon session.
Where Fuuvix helps
Fuuvix covers fractions and decimals with visual learning cards that explain the why behind each operation - not just the procedure. Each concept is broken into digestible cards with key points and practice questions. The chapter quiz tests whether you can actually apply the concepts (not just repeat a formula), and mastery tracking shows which operations need more practice. The first chapter is free to try.
Practise this free on Fuuvix
Fuuvix has Classes 4 to 8 Science and Maths as short visual topic cards with a try-it quiz on every topic, plus olympiad-style practice sets with explanations. The first chapter of every subject is free, no account needed: browse all subjects.