How many times does 1/2 go into 2/3?

How many times does 1/2 go into 2/3?👇👇

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Mathe full solution Here 👇👇👇👇

To determine how many times $\frac{1}{2}$ goes into $\frac{2}{3}$, we need to perform the division of $\frac{2}{3}$ by $\frac{1}{2}$. This can be expressed mathematically as:

$$\frac{\frac{\mathrm{<span\; style="font-size:\; x-large;">2</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}\frac{\mathrm{<span\; style="font-size:\; x-large;">1</span>}}{\mathrm{<span\; style="font-size:\; x-large;">2</span>}}}{}$$

When dividing by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{1}{2}$ is $2$. So, we rewrite the division as a multiplication:

$$\frac{\mathrm{<span\; style="font-size:\; x-large;">2</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">2</span>}$$

Now, we perform the multiplication:

$$\frac{\mathrm{<span\; style="font-size:\; x-large;">2</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">2</span>}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">2</span>}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">2</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">4</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}$$

Thus, $\frac{1}{2}$ goes into $\frac{2}{3}$ a total of $\frac{4}{3}$ times.

To express this result more clearly:

$$\frac{\mathrm{<span\; style="font-size:\; x-large;">4</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}<span\; style="font-size:\; x-large;">=</span>\mathrm{<span\; style="font-size:\; x-large;">1</span>}\frac{\mathrm{<span\; style="font-size:\; x-large;">1</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}$$

So, $\frac{1}{2}$ goes into $\frac{2}{3}$ exactly $1\frac{1}{3}$ times.