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37.
a. De helft van 6 is 3, dus 1/2 ⋅ 6 = 3
b. De helft van 1/6 is 1/12, dus 1/2 ⋅ 1/6 = 1/12

38.
a. 3/4 + 1/6 = 9/12 + 2/12 = 11/12
b. 3/4 x 1/6 = 3/24 = 1/8
c. 1/3 x 1/7 = 1/21
d. -1/4 x 2/7 = -2/28 = -1/14
e. 3/5 - 23/65 = 39/65 - 23/65 = 16/65
f. 4 2/3 x 1 1/7 = 14/3 x 8/7 = 112/21 = 16/3 = 5 1/3
g. 7/12 + 2/15 = 35/60 + 8/60 = 43/60
h. 5/1 x 2/17 = 10/17

39.
a. 9/10 - 5/8 = 72/80 - 50/80 = 22/80 = 11/40
Ze moet dus 11/40 liter water erbij doen.
b. 7/12 + 1/5 = 35/60 + 12/60 = 47/60
Dus de reclame duurt 47/60 minuut. En dat is dus 47 seconden.

40.
a. 3/5 ⋅ 5/3 = 15/15 = 1
b. 1/6 ⋅ 6/1 = 6/6 = 1
c. -2/7 ⋅ -7/2 = 14/14 = 1
d. 9/2 ⋅ 2/9 = 18/18 = 1

41.
a. 2000 / (1/4) = 2000 ⋅ 4/1 = 2000 ⋅ 4 = 8000 (dozen per uur)
b. 2000 : 1/4 = 8000

42.
a. 2/3 : 1/6 = 2/3 ⋅ 6/1 = 12/3 = 4
b. -7/11 : 3/4 = -7/11 ⋅ 4/3 = -28/33
c. -2 1/3 : 6/11 = -7/3 : 6/11 = -7/3 ⋅ 11/6 = -77/18 = -4 5/18
d. 7/8 : 3 = 7/8 : 3/1 = 7/8 ⋅ 1/3 = 7/24
e. 7 2/3 : 2 2/5 = 23/3 : 12/5 = 23/3 ⋅ 5/12 = 115/36 = 3 7/36
f. -3 1/7 : -11 = -22/7 : -11/1 = -22/7 ⋅ -1/11 = 22/77 = 2/7

43.
a. 1/6 : 2/3 = 1/6 ⋅ 3/2 = 3/12 = 1/4
b. 1/6 ⋅ 2/3 = 2/18 = 1/9
c. 1/6 + 2/3 = 1/6 + 4/6 = 5/6
d. 6/5 : 2/5 = 6/5 ⋅ 5/2 = 30/10 = 3
e. 6/5 ⋅ 2/5 = 12/25
f. 6/5 - 2/5 = 4/5
g. 15 : 1 1/4 = 15 : 5/4 = 15/1 ⋅ 4/5 = 60/5 = 12
h. 15 ⋅ 2 1/3 = 15 ⋅ 7/3 = 15/1 ⋅ 7/3 = 105/3 = 35
i. 15 + 58/7 = 105/7 + 58/7 = 163/7 = 23 2/7

44.
a. 3/7 = 3x/7x
b. 8/13 = 24y/39y
c. 2/3 = 6xy/9xy

45.
a. 1/x + 3/y = y/xy + 3x/xy = (3x + y)/xy
b. 1/2 + 2/a = a/2a + 4/2a = (a + 4)/2a
c. a/b + 1/c = ac/bc + b/bc = (ac + b)/bc
d. -3/a - 1/b = -3b/ab - a/ab = (-3b - a)/ab
e. 2/5a - 3/2b = 4b/10ab - 15a/10ab = (4b - 15a)/10ab
f. 1/5 - 1/a = a/5a - 5/5a = (a - 5)/5a

46.
a. a/p + b/q = aq/pq + bp/pq = (aq + bp)/pq
b. 3 - 2/x = 3x/x - 2/x = (3x - 2)/x
c. -2a/3b + b/2a = -4a²/6ab + 3b²/6ab = (-4a² + 3b²)/6ab
d. x/5 - 3/2y = 2xy/10y - 15/10y = (2xy - 15)/10y
e. 8/3x - 5/2y = 16y/6xy - 15x/6xy = (16y - 15x)/6xy
f. 1 - 1/x = x/x - 1/x = (x - 1)/x

47.
a. 3x/6 + 2(x + 4)/6 = (3x + 2x + 8)/6 = (5x + 8)/6
b. 3(a - 7)/15 + 10a/15 = (3a - 21 + 10a)/15 = (13a - 21)/15
c. a(5 + a)/5a + 5(6 - a)/5a = (5a + a² + 30 - 5a)/5a = (a² + 30)/5a
d. (2a - 3)/a + 8/3 = 3(2a - 3)/3a + 8a/3a = (6a - 9 + 8a)/3a = (14a - 9)/3a
e. a(b + 3)/ab + b(a - 1)/ab = (ab + 3a + ab - b)/ab = (2ab + 3a - b)/ab
f. y(x + y)/xy - x(x + y)/xy = (xy + y² - x² - xy)/xy = (y² - x²)/xy

48.
a. pr/qs
b. p/q : r/s = p/q ⋅ s/r = ps/qr
c. 3ab/6c = ab/2c
d. a/6 : 3b/c = a/6 ⋅ c/3b = ac/18b
e. 4a/6b = 2a/3b
f. a/6 : 4/b = a/6 ⋅ b/4 = ab/24

49.
a. 2/x + 4/y = 2y/xy + 4x/xy = (2y + 4x)/xy
b. 2/x ⋅ 4/y = 8/xy
c. 2/x : 4/y = 2/x ⋅ y/4 = 2y/4x = y/2x
d. 1/2a - 4/b = b/2ab - 8a/2ab = (b - 8a)/2ab
e. 1/2a : 4/b = 1/2a ⋅ b/4 = b/8a
f. -3/2x + 4/3y = -9y/6xy + 8x/6xy = (-9y + 8x)/6xy

50.
a. 3(a - 1)/15 - 5(a + 3)/15 = (3a - 3 - 5a - 15)/15 = (-2a - 18)/15
b. (a² + 3a - a - 3)/15 = (a² + 2a - 3)/15
c. (a - 1)/5 ⋅ 3/(a + 3) = (3a - 3)/(5a + 15)


51.
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