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Common denominators and unlike fractions: first steps

الأسبوع 16 · المقامات المشتركة والكسور المختلفة: الخطوات الأولى · 3 دروس
1

Finding a common denominator with the LCM

Discover Mathematics P5: Term 2, Unit 7, Lessons 1–3
GoalRewrite two fractions with the same denominator by using the least common multiple of their denominators.
New words
denominator · the bottom number of a fraction; it says how many equal parts make one wholeequivalent fractions · fractions that name the same amount, such as 1/2 and 3/6common denominator · a denominator that both fractions can share
Explanation

We can only add, subtract or compare fractions easily when they are cut into equal-sized parts, that is, when they have the same denominator. To make an equivalent fraction, multiply the top and the bottom by the same number: 1/4 = 3/12. To find a common denominator, list multiples of each denominator (the rows of a multiplication chart) and pick the smallest number that appears in both lists. That number is the least common multiple (LCM). For 4 and 6 the lists are 4, 8, 12, 16 and 6, 12, 18, so the LCM is 12. Then 1/4 = 3/12 and 1/6 = 2/12.

The smallest shared number is 12
Multiples of 448121620
Multiples of 6612182430
Worked examples
FractionMultiply byEquivalent
1/433/12
1/622/12
Rewrite 1/4 and 1/6 with a common denominator. The LCM of 4 and 6 is 12. 1/4 = (1 × 3)/(4 × 3) = 3/12 and 1/6 = (1 × 2)/(6 × 2) = 2/12.
Rewrite 1/6 and 3/8. Multiples of 6: 6, 12, 18, 24. Multiples of 8: 8, 16, 24. The LCM is 24. 1/6 = 4/24 and 3/8 = 9/24.
Which is greater, 5/6 or 7/9? The LCM of 6 and 9 is 18. 5/6 = 15/18 and 7/9 = 14/18. Since 15/18 > 14/18, 5/6 is greater.
Class activity

Multiplication chart hunt. Draw a multiplication chart up to 12 × 12. Pick two denominators, for example 4 and 10. Colour the row of 4 in one colour and the row of 10 in another and find the first number that has both colours. That is the LCM and your common denominator. Try 3 and 8, then 6 and 9, then 5 and 6.

Practice
1
Find the LCM of 9 and 12.
2
Rewrite 2/3 and 3/4 with denominator 12.
3
Rewrite 5/6 and 3/10 with their least common denominator.
4
Which is greater, 3/8 or 5/12?
5
Order from smallest to largest: 1/2, 2/3 and 3/5.