Pin by Zapzapmath on Printable Math Sheets | Proportions worksheet ... - Free Printable

I'll solve each proportion equation step by step, working through them carefully.

Let me solve all 12 problems:

a) 40/24 = 20/a
Cross multiply: 40 × a = 24 × 20
40a = 480
a = 480 ÷ 40
a = 12

b) 33/a = 11/16
Cross multiply: 33 × 16 = a × 11
528 = 11a
a = 528 11
a = 48

c) 20/b = 40/26
Cross multiply: 20 × 26 = b × 40
520 = 40b
b = 520 ÷ 40
b = 13

d) 10/8 = b/24
Cross multiply: 10 × 24 = 8 × b
240 = 8b
b = 240 ÷ 8
b = 30

e) 35/a = 7/2
Cross multiply: 35 × 2 = a × 7
70 = 7a
a = 70 7
a = 10

f) 44/c = 22/94
Cross multiply: 44 × 94 = c × 22
4136 = 22c
c = 4136 ÷ 22
c = 188

g) x/6 = 22/44
Cross multiply: x × 44 = 6 × 22
44x = 132
x = 132 44
x = 3

h) y/10 = 36/20
Cross multiply: y × 20 = 10 × 36
20y = 360
y = 360 ÷ 20
y = 18

i) 15/45 = 9/y
Cross multiply: 15 × y = 45 × 9
15y = 405
y = 405 ÷ 15
y = 27

j) 40/25 = b/20
Cross multiply: 40 × 20 = 25 × b
800 = 25b
b = 800 25
b = 32

k) z/5 = 20/25
Cross multiply: z × 25 = 5 × 20
25z = 100
z = 100 ÷ 25
z = 4

l) 14/20 = 28/y
Cross multiply: 14 × y = 20 × 28
14y = 560
y = 560 ÷ 14
y = 40

Let me verify my calculations one more time to make sure they're all correct:

a) 40/24 = 20/12 → 40×12 = 480, 24×20 = 480 ✓
b) 33/48 = 11/16 → 33×16 = 528, 48×11 = 528 ✓
c) 20/13 = 40/26 → 20×26 = 520, 13×40 = 520 ✓
d) 10/8 = 30/24 → 10×24 = 240, 8×30 = 240 ✓
e) 35/10 = 7/2 → 35×2 = 70, 10×7 = 70 ✓
f) 44/188 = 22/94 → 44×94 = 4136, 188×22 = 4136 ✓
g) 3/6 = 22/44 → 3×44 = 132, 6×22 = 132 ✓
h) 18/10 = 36/20 → 18×20 = 360, 10×36 = 360 ✓
i) 15/45 = 9/27 → 15×27 = 405, 45×9 = 405 ✓
j) 40/25 = 32/20 → 40×20 = 800, 25×32 = 800 ✓
k) 4/5 = 20/25 → 4×25 = 100, 5×20 = 100 ✓
l) 14/20 = 28/40 → 14×40 = 560, 20×28 = 560 ✓

All answers check out!

Final Answer:
a = 12
b = 48
b = 13
b = 30
a = 10
c = 188
x = 3
y = 18
y = 27
b = 32
z = 4
y = 40