#1 is easy. Take the first 2 numbers first. 63 and 129. If we multiply 63 by 2 we get 126. Therefore the largest number the GCD can be of those 2 numbers is 129-126 = 3. 3 works for both and also for 87. Therefore, the answer is 3. (I am assuming you know how to find the GCD of 2 numbers and how to quickly see how to divide by 3)
2. 15 x 578 is the same thing as adding 1/2 back to the number and mulitplying by 10. So the answer is 10(239 + 578)=8170. *NOTE: Some people prefer double and half, so you would have 30 x 239. I think the first way is easier though.
3. I don't know if this is the easier way, but I would notice that it is 4 x 3 1/5 x 3 1/5. This becomes 4 x 3.2 x 3.2 = 4 * 10.24 = 40.96. Don't know any other way. Anyone else? Did it ask for a mixed number?
4. 31111 x 1333 / 22222. Well in fractions this is 31111 x 4/3 divided by 2/9. Or simplifying will give 31111 x (4/3) x (9/2) which simplifies to 31111 x (6) or approximately 1866. NOTE: You should be able to tell that there will be 4 digits fairly easily.
i don't think there's an easy shortcut to this...it's just a personal preference thing...whether to convert it to a decimal or leave it as a fraction and multiply doesn't matter...just pick the way that's faster for you...
