Operations on Rational Numbers

Mathematics — First Preparatory

Worked examples

Comparison aspect	Main idea	Keywords
Example 1	Find 1/2 + 1/3	Find
Solution	The common denominator is 6 so the sum is 3/6 + 2/6 = 5/6	commondenominator
Example 2	Find (−3/4) + (5/8)	Find
Solution	Make the denominators 8: −6/8 + 5/8 = −1/8	Makedenominators
Example 3	Find (2/3) × (−9/10)	Find
Solution	(2 × −9)/(3 × 10) = −18/30 which simplifies to −3/5 after dividing by 6. We can also cancel before multiplying: 2 and 10 share a factor of 2 and 3 and 9 share a factor of 3	simplifiesafterdividingcancel
Example 4	Find (3/4) ÷ (−6/5)	Find
Solution	Multiply by the reciprocal: 3/4 × (−5/6) = −15/24 = −5/8	Multiplyreciprocal
Example 5 (the hardest)	Find 2 1/2 − (−1 3/4) as a mixed number	Findmixednumber
Solution	2 1/2 = 5/2 and 1 3/4 = 7/4. So 5/2 + 7/4 = 10/4 + 7/4 = 17/4 = 4 1/4

Operations on Rational Numbers · 5 / 7