Class 7 | Ganita Prakash | Chapter 8
๐ Working with Fractions
Multiplication ยท Division ยท Reciprocals ยท Problems
โ๏ธ 8.1 โ Multiplication of Fractions
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Multiplying Fractions:
Examples:
a/b ร c/d = (aรc)/(bรd)
Examples:
- 2/3 ร 4/5 = (2ร4)/(3ร5) = 8/15
- 3/4 ร 8/9 = 24/36 = 2/3 (simplify!)
- 1/2 ร 1/2 = 1/4 (half of a half = quarter!)
Fraction ร Whole number:
2/3 ร 6 = 2/3 ร 6/1 = 12/3 = 4
Or shortcut: 2/3 ร 6 = 2 ร (6รท3) = 2 ร 2 = 4
Simplify BEFORE multiplying (cancel common factors!):
3/4 ร 8/9 โ cancel: 3 and 9 (รท3), 4 and 8 (รท4) โ 1/1 ร 2/3 = 2/3
2/3 ร 6 = 2/3 ร 6/1 = 12/3 = 4
Or shortcut: 2/3 ร 6 = 2 ร (6รท3) = 2 ร 2 = 4
Simplify BEFORE multiplying (cancel common factors!):
3/4 ร 8/9 โ cancel: 3 and 9 (รท3), 4 and 8 (รท4) โ 1/1 ร 2/3 = 2/3
๐ Pizza thinking!
1/2 of 3/4 pizza = 3/8 pizza
"Of" means MULTIPLY: 1/2 ร 3/4 = 3/8
1/2 of 3/4 pizza = 3/8 pizza
"Of" means MULTIPLY: 1/2 ร 3/4 = 3/8
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โ 8.2 โ Division of Fractions
Dividing by a fraction = Multiplying by its reciprocal!
a/b รท c/d = a/b ร d/c
(Flip the second fraction, then multiply!)
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Examples:
2/3 รท 4/5 = 2/3 ร 5/4 = 10/12 = 5/6
5 รท 1/2 = 5 ร 2 = 10
(How many halves in 5 wholes? 10 halves!)
1/2 รท 4 = 1/2 ร 1/4 = 1/8
2/3 รท 4/5 = 2/3 ร 5/4 = 10/12 = 5/6
5 รท 1/2 = 5 ร 2 = 10
(How many halves in 5 wholes? 10 halves!)
1/2 รท 4 = 1/2 ร 1/4 = 1/8
๐ Reciprocal = Flip the fraction!
Reciprocal of 3/4 = 4/3
Reciprocal of 5 = 1/5
Reciprocal of 1/7 = 7
Any number ร its reciprocal = 1 โ
(3/4 ร 4/3 = 12/12 = 1 โ )
Reciprocal of 3/4 = 4/3
Reciprocal of 5 = 1/5
Reciprocal of 1/7 = 7
Any number ร its reciprocal = 1 โ
(3/4 ร 4/3 = 12/12 = 1 โ )
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๐งฉ 8.3 โ Problems with Fractions
Common Problem Types:
๐ Part of a whole:
3/4 of 24 apples = 3/4 ร 24 = 18 apples
๐ถ Fraction of distance:
Walked 2/5 of 15 km = 2/5 ร 15 = 6 km
๐ฐ Fraction of money:
Spent 3/8 of โน400 = 3/8 ร 400 = โน150
๐ Part of a whole:
3/4 of 24 apples = 3/4 ร 24 = 18 apples
๐ถ Fraction of distance:
Walked 2/5 of 15 km = 2/5 ร 15 = 6 km
๐ฐ Fraction of money:
Spent 3/8 of โน400 = 3/8 ร 400 = โน150
Read: identify what fraction of what
"Of" = multiply; "divided equally" = divide
Write the fraction equation
Simplify before multiplying
Check: answer should make sense!
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โก Quick Tips & Tricks
๐ง Mental Math Shortcuts!
- Half of a fraction: multiply by 1/2 โ divide numerator by 2
- Double a fraction: multiply by 2 โ multiply numerator by 2
- To compare fractions: cross-multiply! a/b vs c/d โ compare ad vs bc
- Mixed number to improper: 2 3/4 โ (2ร4+3)/4 = 11/4
- Improper to mixed: 11/4 โ 2 remainder 3 โ 2 3/4
Adding/Subtracting Fractions โ common denominator first!
1/3 + 1/4 โ LCD = 12 โ 4/12 + 3/12 = 7/12
3/5 โ 1/3 โ LCD = 15 โ 9/15 โ 5/15 = 4/15
1/3 + 1/4 โ LCD = 12 โ 4/12 + 3/12 = 7/12
3/5 โ 1/3 โ LCD = 15 โ 9/15 โ 5/15 = 4/15
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๐ Quick Cheatsheet
Multiply: topรtop
bottomรbottom
a/b ร c/d = ac/bd
bottomรbottom
a/b ร c/d = ac/bd
Divide = Flip &
Multiply!
รท c/d = ร d/c
Multiply!
รท c/d = ร d/c
Reciprocal = flip
3/4 โ 4/3
n ร 1/n = 1
3/4 โ 4/3
n ร 1/n = 1
"of" = ร
Simplify first!
Then multiply
Simplify first!
Then multiply
| Operation | Rule | Example |
|---|---|---|
| Multiply | Numerator ร numerator, denominator ร denominator | 2/3 ร 3/4 = 6/12 = 1/2 |
| Divide | Multiply by reciprocal of divisor | 2/3 รท 4/5 = 2/3 ร 5/4 = 5/6 |
| Simplify | Divide top & bottom by HCF | 6/9 โ 6รท3/9รท3 = 2/3 |
| "of" | Always multiply! | 1/2 of 20 = 10 |
๐ Chapter 8 Complete! ๐
Made with โค๏ธ by @edugrown
Made with โค๏ธ by @edugrown