11
Bringing fractions to a common denominator
Textbook, pp. 39–42
GoalLearn to bring fractions to a common denominator; find the least common denominator.
New words
common denominator · umumiy maxrajadditional factor · qo‘shimcha ko‘paytuvchileast common multiple · EKUKbringing (to a form) · keltirish
Explanation
Replacing fractions with different denominators by fractions with the same denominator is called bringing them to a common denominator. The most convenient common denominator is the LCM of the denominators. First find the LCM, then divide it by each denominator to get the additional factor. Multiply the numerator and the denominator of each fraction by its own additional factor. For example for 3/4 and 5/6, LCM(4, 6) = 12: 3/4 = 9/12 and 5/6 = 10/12.
Worked examples
3/4 and 5/6: LCM(4, 6) = 12. Additional factors: 12 : 4 = 3 and 12 : 6 = 2. So 3/4 = 9/12 and 5/6 = 10/12.
2/9 and 5/12: LCM(9, 12) = 36. The additional factors are 4 and 3, so 8/36 and 15/36.
Class activity
“Common-denominator meeting”: two pupils get fraction cards with different denominators. They find the LCM of the denominators and rewrite both cards. Another pair checks them.
Practice
1
Bring 1/6 and 3/8 to a common denominator.
4/24 va 9/24
2
Bring 1/2, 2/3, 3/4 to the least common denominator.
6/12, 8/12, 9/12
3
Find the least common denominator of 5/12 and 7/18.
36
4
Why is it more convenient to take the LCM rather than the product of denominators?
The LCM is a smaller number, so the calculation is easier and we may avoid reducing afterwards.