10
Reducing fractions
Textbook, pp. 34–37
GoalLearn to reduce a fraction and to reach an irreducible fraction.
New words
reducing a fraction · kasrni qisqartirishirreducible fraction · qisqarmas kasrcommon divisor · umumiy bo‘luvchiGCD · EKUB
Explanation
Dividing the numerator and denominator by a common divisor is called reducing the fraction. Reducing does not change its value, because this follows from the basic property. When the numerator and denominator become coprime, the fraction is irreducible. To reduce fully in one step, divide by the GCD of numerator and denominator. For example GCD(36, 48) = 12, so 36/48 = 3/4. We always write the final answer as an irreducible fraction.
Worked examples
36/48: GCD(36, 48) = 12, 36 : 12 = 3, 48 : 12 = 4, answer 3/4.
With prime factors: 30/42 = (2 · 3 · 5)/(2 · 3 · 7) = 5/7.
Class activity
“Reducing chain”: pupils reduce the fraction on their card and find the partner who holds the answer. For example the card 12/16 finds the card 3/4. When all pairs are right the chain closes.
Practice
1
Reduce 24/36.
2/3
2
Reduce 42/105.
2/5
3
Of 24 pupils in a class, 18 read books. What part of the class is this? Write an irreducible fraction.
3/4
4
Is 9/16 irreducible? Why?
Yes: 9 = 3² and 16 = 2⁴ share no prime factor, so GCD = 1.