Me with fractions. 9 8/13 + 9/16 = ? 7 8/12 - 8 5/7 = ?

Hello there. Lets start solving your problems.

For the first one, its 9 8/13 + 9/16 so
= 125/13 + 9/16
= 2117/208
= 10 37/208 is the answer. (In decimal form its 10.17788)

For the second one its 7 8/12 - 8 5/7 so
= 7 2/3 - 8 5/7
= 23/3 - 8 5/7
= 23/3 - 61/7
= -22/21
= 1 1/21 is the answer. (In decimal form its 1.047619)

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18

- "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."