Class 6 ยท Maths ยท Ganita Prakash
Chapter 7 ๐
Chapter 7 ๐
Fractions
Quick, colourful revision notes โ easy to read before your test!
Chapter Contents
7.1 โ 7.2 Fractional Units
A fractional unit (unit fraction) is what you get when 1 whole is divided into equal parts, e.g. ยฝ, โ
, ยผ...
A fraction a/b has a numerator (a, parts we have) and a denominator (b, total equal parts).
A fraction a/b has a numerator (a, parts we have) and a denominator (b, total equal parts).
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Fig 1: Unit fractions โ more slices means each slice is smaller!
A common trap: 1/9 is smaller than 1/5 โ sharing among more people means a smaller share each, even though 9 > 5!
7.3 โ 7.4 Fractions on the Number Line
Any fraction can be marked as a length on the number line by dividing each unit gap into equal parts.
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Fig 2: Thirds marked on the number line from 0 to 2
There are infinitely many fractions between 0 and 1 โ you can always divide into smaller and smaller equal parts!
7.5 Mixed Fractions
A mixed number = a whole number part + a fraction part less than 1 (e.g. 2โ
).
A fraction where numerator > denominator (like 8/3) is greater than 1 whole.
A fraction where numerator > denominator (like 8/3) is greater than 1 whole.
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Fig 3: Converting an improper fraction into a mixed number
To convert back: 2โ
= (2 ร 3 + 2)/3 = 8/3. Multiply whole ร denominator, add the numerator, keep the same denominator.
7.6 Equivalent Fractions
Equivalent fractions represent the same amount, even though they look different โ e.g. ยฝ = 2/4 = 3/6 = 4/8.
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Fig 4: A fraction wall โ all these bars are the exact same total length!
Multiply (or divide) both the numerator and denominator by the same number to get an equivalent fraction โ the value never changes.
7.7 Comparing Fractions
Step 1: Convert both fractions to equivalent fractions with the same denominator (use a common multiple).
Step 2: Compare just the numerators โ bigger numerator means bigger fraction!
Step 2: Compare just the numerators โ bigger numerator means bigger fraction!
Compare 4/5 and 7/9 using 45 as common denominator: 4/5 = 36/45, and 7/9 = 35/45. Since 36 > 35, 4/5 > 7/9.
7.8 Addition & Subtraction of Fractions
Same denominator: just add/subtract the numerators, keep the denominator the same.
Different denominators: first convert to equivalent fractions with the same denominator, then add/subtract.
Different denominators: first convert to equivalent fractions with the same denominator, then add/subtract.
ยฝ + ยผ: rewrite ยฝ as 2/4, then 2/4 + 1/4 = ยพ.
๐ฏ Quick Summary
- Fractional unit = 1 whole split into equal parts; more parts = smaller each share.
- Fractions can be marked as exact lengths on the number line.
- Mixed number = whole part + fraction part; convert using รdenominator +numerator.
- Equivalent fractions: multiply/divide numerator & denominator by the same number.
- To compare or add/subtract fractions with different denominators, first make denominators equal.
โ๏ธ Notes by @edugrown โ happy revising! ๐