Sure! Let's solve each of the equations step-by-step to find the missing numerators.
### 1. Solve for [tex]\( x \)[/tex] in the equation [tex]\( \frac{5}{2} = \frac{x}{4} \)[/tex]
To find the value of [tex]\( x \)[/tex], you can cross-multiply:
[tex]\[ 5 \times 4 = 2 \times x \][/tex]
This gives us:
[tex]\[ 20 = 2x \][/tex]
Now, divide both sides by 2:
[tex]\[ x = \frac{20}{2} = 10.0 \][/tex]
So, [tex]\( x = 10.0 \)[/tex].
### 2. Solve for [tex]\( x \)[/tex] in the equation [tex]\( \frac{12}{24} = \frac{x}{6} \)[/tex]
Again, cross-multiply:
[tex]\[ 12 \times 6 = 24 \times x \][/tex]
This gives us:
[tex]\[ 72 = 24x \][/tex]
Now, divide both sides by 24:
[tex]\[ x = \frac{72}{24} = 3.0 \][/tex]
So, [tex]\( x = 3.0 \)[/tex].
### 3. Solve for [tex]\( x \)[/tex] in the equation [tex]\( \frac{7}{8} = \frac{x}{32} \)[/tex]
Cross-multiply:
[tex]\[ 7 \times 32 = 8 \times x \][/tex]
This gives us:
[tex]\[ 224 = 8x \][/tex]
Now, divide both sides by 8:
[tex]\[ x = \frac{224}{8} = 28.0 \][/tex]
So, [tex]\( x = 28.0 \)[/tex].
### 4. Solve for [tex]\( x \)[/tex] in the equation [tex]\( \frac{31}{3} = \frac{x}{6} \)[/tex]
Cross-multiply:
[tex]\[ 31 \times 6 = 3 \times x \][/tex]
This gives us:
[tex]\[ 186 = 3x \][/tex]
Now, divide both sides by 3:
[tex]\[ x = \frac{186}{3} = 62.0 \][/tex]
So, [tex]\( x = 62.0 \)[/tex].
### 5. Solve for [tex]\( x \)[/tex] in the equation [tex]\( \frac{7}{3} = \frac{x}{300} \)[/tex]
Cross-multiply:
[tex]\[ 7 \times 300 = 3 \times x \][/tex]
This gives us:
[tex]\[ 2100 = 3x \][/tex]
Now, divide both sides by 3:
[tex]\[ x = \frac{2100}{3} = 700.0 \][/tex]
So, [tex]\( x = 700.0 \)[/tex].
### Summary:
1. [tex]\( x = 10.0 \)[/tex]
2. [tex]\( x = 3.0 \)[/tex]
3. [tex]\( x = 28.0 \)[/tex]
4. [tex]\( x = 62.0 \)[/tex]
5. [tex]\( x = 700.0 \)[/tex]
These are the missing numerators for the provided equations.
