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Class 7 Working with Fractions: cheat sheet
CBSE Mathematics. Multiplying and dividing fractions and mixed numbers, reciprocals, and finding a fraction of an amount.
Key ideas
- Multiply fractions by multiplying the numerators and multiplying the denominators; cancel common factors first.
- Change mixed numbers to improper fractions before multiplying or dividing.
- “Of” means multiply: 2/3 of 60 = 2/3 × 60 = 40.
- The reciprocal of a/b is b/a; a number times its reciprocal is 1.
- To divide by a fraction, multiply by its reciprocal.
- Multiplying by a proper fraction makes a number smaller; dividing by it makes the number bigger.
Remember
| Multiplying | a/b × c/d = (a × c)/(b × d) |
| Dividing | a/b ÷ c/d = a/b × d/c |
| Mixed number | 2 1/3 = (2 × 3 + 1)/3 = 7/3 |
Watch out
- Multiplying the whole numbers and fractions of mixed numbers separately.
- Turning the first fraction upside down instead of the second when dividing.
- Taking the second fraction of the whole amount instead of what is left.
Worked example
A family earns Rs 34,740 a month. They spend 1/3 of it on rent and 1/2 of what is left on food. How much do they spend on rent, on food, and how much is left?
Working: 1/3 × 34740 = 11580; 1/2 × 23160 = 11580
Answer: rent Rs 11,580, food Rs 11,580, left Rs 11,580
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