College

Fill in the missing numbers in the given boxes.

(a) [tex]\frac{5}{6}=\frac{\square}{18}[/tex]

(b) [tex]\frac{2}{7}=\frac{10}{\square}[/tex]

(c) [tex]\frac{\square}{5}=\frac{32}{40}[/tex]

Answer :

Sure! Let's solve each part step by step:

(a) [tex]\(\frac{5}{6} = \frac{\square}{18}\)[/tex]

To find the missing number in this equivalent fraction, we'll use cross-multiplication. Cross-multiplication means multiplying across the equal sign diagonally:

[tex]\[5 \times 18 = 6 \times \text{(missing number)}\][/tex]

This simplifies to:

[tex]\[90 = 6 \times \text{(missing number)}\][/tex]

To solve for the missing number, divide both sides by 6:

[tex]\[\text{Missing number} = \frac{90}{6} = 15\][/tex]

So, [tex]\(\frac{5}{6} = \frac{15}{18}\)[/tex].

(b) [tex]\(\frac{2}{7} = \frac{10}{\square}\)[/tex]

Similarly, we'll use cross-multiplication here:

[tex]\[2 \times \text{(missing denominator)} = 7 \times 10\][/tex]

This simplifies to:

[tex]\[2 \times \text{(missing denominator)} = 70\][/tex]

To find the missing denominator, divide both sides by 2:

[tex]\[\text{Missing denominator} = \frac{70}{2} = 35\][/tex]

So, [tex]\(\frac{2}{7} = \frac{10}{35}\)[/tex].

(c) [tex]\(\frac{\square}{5} = \frac{32}{40}\)[/tex]

Again, use cross-multiplication:

[tex]\[\text{(missing numerator)} \times 40 = 5 \times 32\][/tex]

This simplifies to:

[tex]\[\text{(missing numerator)} \times 40 = 160\][/tex]

To find the missing numerator, divide both sides by 40:

[tex]\[\text{Missing numerator} = \frac{160}{40} = 4\][/tex]

So, [tex]\(\frac{4}{5} = \frac{32}{40}\)[/tex].

In summary:
- For part (a), the missing number is 15.
- For part (b), the missing denominator is 35.
- For part (c), the missing numerator is 4.