1. Bella's recipe for a batch of cookies calls for 4 1/2 cups of flour. if she wants to make 2/5 of a batch of cookies how much flour should she use?
2/5 * (4 1/2)
= 2/5 * 9/2
= 9/5
= 1 1/5 cups flour
2. A submarine is at an elevation of - 9 4/7 meters. It then descends another 63 1/3 meters. What is the submarines new elevation?
(-9 4/7) - (63 1/3)
= (-9 12/21) - (63 7/21)
= -72 19/21 meters
3. Ann rides her bike at a pace of 10 1/6 miles per hour. If she rode her bike for 2 1/4 hours, how many miles did she ride?
(10 1/6) / (2 1/4)
= (61/6) / (9/4)
= 61/6 * 4/9
=122/27
= 4 4/27 miles
4. Evaluate (3 1/2) /(-1 1/4)
= (7/2) / (-5/4)
= (7/2) * (-4/5)
= -14/5
= -2 1/7
5. Maria is running on a track that is 3/7 of a mile long. So far she has run 1/5 of the way around the track. How far has she run so far?
(3/7) *(1/5)
= 3/35 of mile?
6. Max is training for a marathon. He ran 11.9 miles away from his home. then he ran 6.8 towards his home. Finally, he ran 2.4 miles away form his home. How far is Max from his home?
11.9 - 6.8 = 5.1
5.1 + 2.4 = 7.5 miles away
#1. 9/5 is correct, but 9/5 = 1 4/5
#2. ok
#3. distance = speed * time
(10 1/6) * (2 1/4) = 61/6 * 9/4 = 183/8
#4. ok
#5. ok
#6. ok
To solve each of these problems, you can follow these steps:
1. For the first problem, to find how much flour Bella should use for 2/5 of a batch of cookies, you can multiply the amount of flour needed for a full batch by 2/5. So, you multiply 4 1/2 cups by 2/5 to get the answer.
2. For the second problem, to find the submarine's new elevation, you need to subtract the amount it descended from its initial elevation. So, you subtract 63 1/3 meters from -9 4/7 meters.
3. For the third problem, to find how many miles Ann rode her bike, you can divide the pace in miles per hour by the number of hours she rode. So, you divide 10 1/6 miles per hour by 2 1/4 hours.
4. For the fourth problem, to evaluate the given expression, you divide the first number by the second number. So, you divide 3 1/2 by -1 1/4.
5. For the fifth problem, to find how far Maria has run so far, you multiply the length of the track by the fraction of the distance she has covered. So, you multiply 3/7 of a mile by 1/5.
6. For the sixth problem, to find how far Max is from his home, you need to subtract the distances he ran towards his home from the distances he ran away from his home. So, you subtract 6.8 miles from 11.9 miles and then add 2.4 miles.