# Julia’s frogs are 2 5 of the amount of Rimma’s frogs. If Rimma gives 1 2 of her frogs to Julia, what will be the ratio of Julia’s frogs to Rimma’s frogs?

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## Rimma = x

Julia = 2/5 x

Rimma gives away 1/2 of her frogs.
Now Rimma has 1/2x and Julia has 2/5x + 1/2x=4/10x +5/10x =9/10x

Ratios are fractions so put Julia's on top of Rimma's and simplify.

(9/10 x) / (1/2x)

The x's will cancel. Invert the second fraction and multiply.
(9/10)*(2/1) = 18/10= 9/5

Ratio of Julia's frogs to Rimma's frogs is 9:5.

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## To solve this problem, we need to follow these steps:

Step 1: Determine the number of Julia's frogs compared to Rimma's frogs.
- From the given information, we know that Julia's frogs are 2/5 of the amount of Rimma's frogs.

Step 2: Calculate the number of Rimma's frogs.
- If we assume the number of Rimma's frogs as "x," then Julia's frogs would be (2/5)*x.

Step 3: Calculate the number of Rimma's frogs after giving away 1/2 of them to Julia.
- Rimma gives away (1/2)*x frogs to Julia, so the remaining number of Rimma's frogs is (x - (1/2)*x) = (1/2)*x.

Step 4: Calculate the new number of Julia's frogs after receiving 1/2 of Rimma's frogs.
- Julia receives (1/2)*x frogs from Rimma, so the new number of Julia's frogs is (2/5)*x + (1/2)*x.

Step 5: Calculate the ratio of Julia's frogs to Rimma's frogs.
- The ratio is given by the expression: (number of Julia's frogs) / (number of Rimma's frogs).

Now, let's simplify the expressions:

Step 2 (rewritten): Julia's frogs = (2/5)*x.
Step 3 (rewritten): Rimma's frogs = (1/2)*x.
Step 4 (rewritten): New Julia's frogs = (2/5)*x + (1/2)*x = (4/10 + 5/10)*x = (9/10)*x.

Finally, we can calculate the ratio in Step 5:
Ratio = (number of Julia's frogs) / (number of Rimma's frogs)
= [(9/10)*x] / [(1/2)*x]
= (9/10) / (1/2)
= (9/10) * (2/1)
= 18/10
= 9/5

Hence, the ratio of Julia's frogs to Rimma's frogs is 9:5.

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