Answer :
Sure! Let's solve the problems step-by-step:
We need to replace each square ([tex]$\square$[/tex]) with the correct number that makes each equation true.
### (a) [tex]\(\frac{2}{7}=\frac{8}{\square}\)[/tex]
1. Let's denote the unknown number with [tex]\( x \)[/tex].
2. According to the given fraction equality:
[tex]\[
\frac{2}{7} = \frac{8}{x}
\][/tex]
3. Cross-multiplying will help us find [tex]\( x \)[/tex]:
[tex]\[
2 \cdot x = 7 \cdot 8
\][/tex]
[tex]\[
2x = 56
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{56}{2} = 28
\][/tex]
So, [tex]\(\square = 28\)[/tex].
### (b) [tex]\(\frac{5}{8}=\frac{10}{\square}\)[/tex]
1. Let's denote the unknown number with [tex]\( x \)[/tex].
2. According to the given fraction equality:
[tex]\[
\frac{5}{8} = \frac{10}{x}
\][/tex]
3. Cross-multiplying will help us find [tex]\( x \)[/tex]:
[tex]\[
5 \cdot x = 8 \cdot 10
\][/tex]
[tex]\[
5x = 80
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{80}{5} = 16
\][/tex]
So, [tex]\(\square = 16\)[/tex].
### (c) [tex]\(\frac{3}{5}=\frac{\square}{20}\)[/tex]
1. Let's denote the unknown number with [tex]\( x \)[/tex].
2. According to the given fraction equality:
[tex]\[
\frac{3}{5} = \frac{x}{20}
\][/tex]
3. Cross-multiplying will help us find [tex]\( x \)[/tex]:
[tex]\[
3 \cdot 20 = 5 \cdot x
\][/tex]
[tex]\[
60 = 5x
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{60}{5} = 12
\][/tex]
So, [tex]\(\square = 12\)[/tex].
### (d) [tex]\(\frac{45}{60}=\frac{15}{\square}\)[/tex]
1. Let's denote the unknown number with [tex]\( x \)[/tex].
2. According to the given fraction equality:
[tex]\[
\frac{45}{60} = \frac{15}{x}
\][/tex]
3. Cross-multiplying will help us find [tex]\( x \)[/tex]:
[tex]\[
45 \cdot x = 60 \cdot 15
\][/tex]
[tex]\[
45x = 900
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{900}{45} = 20
\][/tex]
So, [tex]\(\square = 20\)[/tex].
### (e) [tex]\(\frac{18}{24}=\frac{\square}{4}\)[/tex]
1. Let's denote the unknown number with [tex]\( x \)[/tex].
2. According to the given fraction equality:
[tex]\[
\frac{18}{24} = \frac{x}{4}
\][/tex]
3. Cross-multiplying will help us find [tex]\( x \)[/tex]:
[tex]\[
18 \cdot 4 = 24 \cdot x
\][/tex]
[tex]\[
72 = 24x
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{72}{24} = 3
\][/tex]
So, [tex]\(\square = 3\)[/tex].
Thus, the final solutions are:
(a) 28,
(b) 16,
(c) 12,
(d) 20,
(e) 3.
We need to replace each square ([tex]$\square$[/tex]) with the correct number that makes each equation true.
### (a) [tex]\(\frac{2}{7}=\frac{8}{\square}\)[/tex]
1. Let's denote the unknown number with [tex]\( x \)[/tex].
2. According to the given fraction equality:
[tex]\[
\frac{2}{7} = \frac{8}{x}
\][/tex]
3. Cross-multiplying will help us find [tex]\( x \)[/tex]:
[tex]\[
2 \cdot x = 7 \cdot 8
\][/tex]
[tex]\[
2x = 56
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{56}{2} = 28
\][/tex]
So, [tex]\(\square = 28\)[/tex].
### (b) [tex]\(\frac{5}{8}=\frac{10}{\square}\)[/tex]
1. Let's denote the unknown number with [tex]\( x \)[/tex].
2. According to the given fraction equality:
[tex]\[
\frac{5}{8} = \frac{10}{x}
\][/tex]
3. Cross-multiplying will help us find [tex]\( x \)[/tex]:
[tex]\[
5 \cdot x = 8 \cdot 10
\][/tex]
[tex]\[
5x = 80
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{80}{5} = 16
\][/tex]
So, [tex]\(\square = 16\)[/tex].
### (c) [tex]\(\frac{3}{5}=\frac{\square}{20}\)[/tex]
1. Let's denote the unknown number with [tex]\( x \)[/tex].
2. According to the given fraction equality:
[tex]\[
\frac{3}{5} = \frac{x}{20}
\][/tex]
3. Cross-multiplying will help us find [tex]\( x \)[/tex]:
[tex]\[
3 \cdot 20 = 5 \cdot x
\][/tex]
[tex]\[
60 = 5x
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{60}{5} = 12
\][/tex]
So, [tex]\(\square = 12\)[/tex].
### (d) [tex]\(\frac{45}{60}=\frac{15}{\square}\)[/tex]
1. Let's denote the unknown number with [tex]\( x \)[/tex].
2. According to the given fraction equality:
[tex]\[
\frac{45}{60} = \frac{15}{x}
\][/tex]
3. Cross-multiplying will help us find [tex]\( x \)[/tex]:
[tex]\[
45 \cdot x = 60 \cdot 15
\][/tex]
[tex]\[
45x = 900
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{900}{45} = 20
\][/tex]
So, [tex]\(\square = 20\)[/tex].
### (e) [tex]\(\frac{18}{24}=\frac{\square}{4}\)[/tex]
1. Let's denote the unknown number with [tex]\( x \)[/tex].
2. According to the given fraction equality:
[tex]\[
\frac{18}{24} = \frac{x}{4}
\][/tex]
3. Cross-multiplying will help us find [tex]\( x \)[/tex]:
[tex]\[
18 \cdot 4 = 24 \cdot x
\][/tex]
[tex]\[
72 = 24x
\][/tex]
4. Solving for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{72}{24} = 3
\][/tex]
So, [tex]\(\square = 3\)[/tex].
Thus, the final solutions are:
(a) 28,
(b) 16,
(c) 12,
(d) 20,
(e) 3.
