Question

2. Calculate che missing numbe
a. 2 : 5 = 20 :
b. 10 000 7 : ? 100 : 1
C. ? : 0,3 = 5 : 6
D. 5cm : 1m = ? : 400
E. 40 seconds : 2 mins = 11 : ?
F. 20g : ? Mg 40 : 1
G. ? hrs : 30 seconds : 240 : 1

Show working how you got the answer

Answer 1

Let's solve the missing numbers in each of the given proportions step by step.

### a. \( \frac{2}{5} = \frac{20}{x} \)

To find \( x \), we can cross-multiply:

\[
2 \cdot x = 5 \cdot 20
\]

Simplifying gives:

\[
2x = 100
\]

Dividing both sides by 2:

\[
x = 50
\]

### b. \( \frac{10,000}{7} = \frac{100}{x} \)

Cross-multiply:

\[
10,000 \cdot x = 7 \cdot 100
\]

This simplifies to:

\[
10,000x = 700
\]

Dividing both sides by 10,000:

\[
x = \frac{700}{10,000} = 0.07
\]

### c. \( \frac{x}{0.3} = \frac{5}{6} \)

Cross-multiply:

\[
x \cdot 6 = 5 \cdot 0.3
\]

This simplifies to:

\[
6x = 1.5
\]

Dividing both sides by 6:

\[
x = \frac{1.5}{6} = 0.25
\]

### d. \( \frac{5 \text{ cm}}{1 \text{ m}} = \frac{x}{400} \)

First, convert 1 m to cm (1 m = 100 cm):

\[
\frac{5}{100} = \frac{x}{400}
\]

Cross-multiplying gives:

\[
5 \cdot 400 = 100 \cdot x
\]

This simplifies to:

\[
2000 = 100x
\]

Dividing both sides by 100:

\[
x = 20
\]

### e. \( \frac{40 \text{ seconds}}{2 \text{ mins}} = \frac{11}{x} \)

First, convert 2 mins to seconds (2 mins = 120 seconds):

\[
\frac{40}{120} = \frac{11}{x}
\]

Cross-multiply:

\[
40x = 11 \cdot 120
\]

This simplifies to:

\[
40x = 1320
\]

Dividing by 40:

\[
x = \frac{1320}{40} = 33
\]

### f. \( \frac{20 \text{ g}}{x \text{ Mg}} = \frac{40}{1} \)

First, convert g to Mg (1 Mg = 1,000,000 g):

\[
\frac{20}{x \times 1,000,000} = 40
\]

Cross-multiply:

\[
20 = 40x \times 1,000,000
\]

This simplifies to:

\[
20 = 40,000,000x
\]

Dividing by 40,000,000:

\[
x = \frac{20}{40,000,000} = 0.0000005 \text{ Mg}
\]

### g. \( \frac{x \text{ hrs}}{30 \text{ seconds}} = \frac{240}{1} \)

First, convert hours to seconds (1 hr = 3600 seconds):

\[
\frac{x \times 3600}{30} = 240
\]

Cross-multiply:

\[
x \times 3600 = 240 \times 30
\]

This simplifies to:

\[
x \times 3600 = 7200
\]

Dividing by 3600:

\[
x = \frac{7200}{3600} = 2 \text{ hrs}
\]

### Summary of Results
- a. \( x = 50 \)
- b. \( x = 0.07 \)
- c. \( x = 0.25 \)
- d. \( x = 20 \)
- e. \( x = 33 \)
- f. \( x = 0.0000005 \text{ Mg} \)
- g. \( x = 2 \text{ hrs} \)