Let's begin by listing the first few multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 38, 40, 44. So, between 1 and 37 there are 9 such multiples: {4, 8, 12, 16, 20, 24, 28, 32, 36}. Note that 4 divided into 36 is 9.
Let's experiment by modifying the given problem a bit, for the purpose of discovering any pattern that may exist:
<span>How many multiples of 4 are there in {n; 37< n <101}? We could list and then count them: {40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100}; there are 16 such multiples in that particular interval. Try subtracting 40 from 100; we get 60. Dividing 60 by 4, we get 15, which is 1 less than 16. So it seems that if we subtract 40 from 1000 and divide the result by 4, and then add 1, we get the number of multiples of 4 between 37 and 1001:
1000 -40 ------- 960
Dividing this by 4, we get 240. Adding 1, we get 241.
Finally, subtract 9 from 241: We get 232.
There are 232 multiples of 4 between 37 and 1001.
Can you think of a more straightforward method of determining this number? </span>
53/4•2/6=1 11/12 Because you must turn 5 3/4 into an improper fraction. So 23/4•2/6. Next you are able to cross reduce because 2 goes into 2 and four so now you have 23/2•1/6 now just multiply across. 2•6=12 and 23•1=23 so now you have 23/12 which equals 1 11/12
If BD is congruent to BC, that means that the sides are equal, so their angles are too. 6x-9 = 3x+24 3x = 33 x = 33/3 x = 11 Angle BCD: 6×11-9 = 66-9 =57° Angle BDC: 3×11+24 = 33+24 = 57° Angle B: x = 180° - 2×57° x = 66°
