1. 12/8 +5/6

Consider the LCM of 6 and 8. This is the union, multiplied, of {2,3} and {2,2,2}. We get {2,3,2,2}. Multiplied together this is of course 24. That means, our two factors are:

x/24 + y/24

From here we reason that we should include the 3 of 24/8 and the 4 of 24/6 need be included in the translation of 12/8 and 5/6. We get 12*3/8*3 and 5*4/6*4.

We now have 36/24 and 20/24 totaling to 56/24.

Observe that 56 = 8*7 and 24 = 3*8. We reduce to 7/3. Finally we deduce that 7/3 = 2 and 1/3. This is our final answer.

2. A merry go round goes around 5 times in 15 minutes. How many times does it go around in 2 hours?

We set up an equation using proportions.

5times/15 min. = x times/120 min.

or

x times = 5times*120 min. / 15 min.

x times = 5times 8 = 40 times

x=40

The merry go round goes around 40 times in 2 hours.

3. A car travels 50 miles in 2 hours. How many miles does it travel in 1 day?

We compute a rate. The speed of the carâ€™s trajectory is 50miles/2hours = 25mph. We use distance = Rate*Time. Here time = 1 day = 24 hours. Distance = 25 mph *24 hours = 600miles.

Consider the LCM of 6 and 8. This is the union, multiplied, of {2,3} and {2,2,2}. We get {2,3,2,2}. Multiplied together this is of course 24. That means, our two factors are:

x/24 + y/24

From here we reason that we should include the 3 of 24/8 and the 4 of 24/6 need be included in the translation of 12/8 and 5/6. We get 12*3/8*3 and 5*4/6*4.

We now have 36/24 and 20/24 totaling to 56/24.

Observe that 56 = 8*7 and 24 = 3*8. We reduce to 7/3. Finally we deduce that 7/3 = 2 and 1/3. This is our final answer.

2. A merry go round goes around 5 times in 15 minutes. How many times does it go around in 2 hours?

We set up an equation using proportions.

5times/15 min. = x times/120 min.

or

x times = 5times*120 min. / 15 min.

x times = 5times 8 = 40 times

x=40

The merry go round goes around 40 times in 2 hours.

3. A car travels 50 miles in 2 hours. How many miles does it travel in 1 day?

We compute a rate. The speed of the carâ€™s trajectory is 50miles/2hours = 25mph. We use distance = Rate*Time. Here time = 1 day = 24 hours. Distance = 25 mph *24 hours = 600miles.