Question

Change 7/4 and 9/10 to equivalent fractions given the LCD = 20

Answer 1

We have the fraction

`(7)/(4)`

We want to rewrite it as

`(x)/(20)`

Where x is a number that we don't know, but it will turn the fraction equivalent, then we can say that

`(7)/(4)=(x)/(20)`

We can do a cross multiplication and solve it for x

`\begin{gathered} 4x=7\cdot20 \\ \\ x=(7\cdot20)/(4) \end{gathered}`

Then in fact, to discover the new numerator we must do

`\text{ new numerator = }\frac{\text{ old numerator x LCD}}{\text{ old denominator}}`

Let's do it then!

`\begin{gathered} \text{ new numerator =}(7\cdot20)/(4) \\ \\ \text{ new numerator }=35 \end{gathered}`

Then

`(7)/(4)=(35)/(20)`

The equivalent fraction is 35/20

Now for the second question, we can use the logic

`\begin{gathered} \text{ new numerator = }\frac{\text{ 9 x 20}}{10} \\ \\ \text{new numerator = {}18} \end{gathered}`

The equivalent fraction is

`(9)/(10)=(18)/(20)`

Final answers:

`\begin{gathered} (7)/(4)=(35)/(20) \\ \\ (9)/(10)=(18)/(20) \end{gathered}`