Mike poors 12/8 cups of orange juice into serving glasses each glass holds 3/4 cups how many glasses can he fill use a common denominator to devide

The instruction to "use a common denominator to divide" may be counter-intuitive to someone taught to "invert and multiply."

To find the number of glasses, we divide the amount of juice by the glass size. The divisor is the glass size, and we want to have a common divisor with the juice quantity.

We can remove a factor of 2 from the numerator and denominator of the juice quantity to give it a denominator of 4, in common with the glass size.

number of glasses = (quantity of juice) / (glass size)

number of glasses = (6/4 cups)/(3/4 cups)

Factoring (1/4 cups) from numerator and denominator, we have

number of glasses = 6/3

number of glasses = 2

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."