What is the answer to 4 3/7+2 2/5+3 2/3?

 Q. What is the answer to 4 3/7+2 2/5+3 2/3?👇👇

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To solve the addition of mixed numbers $4\frac{3}{7}+2\frac{2}{5}+3\frac{2}{3}$, follow these steps:

1. Convert the mixed numbers to improper fractions:

   $$\mathrm{<span\; style="font-size:\; x-large;">4</span>}\frac{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}{\mathrm{<span\; style="font-size:\; x-large;">7</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">4</span>}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">7</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}}{\mathrm{<span\; style="font-size:\; x-large;">7</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">28</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}}{\mathrm{<span\; style="font-size:\; x-large;">7</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">31</span>}}{\mathrm{<span\; style="font-size:\; x-large;">7</span>}}$$
   $$\mathrm{<span\; style="font-size:\; x-large;">2</span>}\frac{\mathrm{<span\; style="font-size:\; x-large;">2</span>}}{\mathrm{<span\; style="font-size:\; x-large;">5</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">2</span>}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">5</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">2</span>}}{\mathrm{<span\; style="font-size:\; x-large;">5</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">10</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">2</span>}}{\mathrm{<span\; style="font-size:\; x-large;">5</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">12</span>}}{\mathrm{<span\; style="font-size:\; x-large;">5</span>}}$$
   $$\mathrm{<span\; style="font-size:\; x-large;">3</span>}\frac{\mathrm{<span\; style="font-size:\; x-large;">2</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">2</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">9</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">2</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">11</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}$$

2. Find the least common denominator (LCD):

   The denominators are 7, 5, and 3. The LCD of these numbers is the least common multiple (LCM) of 7, 5, and 3.

   $$\text{<span style="font-size: x-large;">LCM</span>}<span\; style="font-size:\; x-large;">(</span>\mathrm{<span\; style="font-size:\; x-large;">7</span>}<span\; style="font-size:\; x-large;">,</span>\mathrm{<span\; style="font-size:\; x-large;">5</span>}<span\; style="font-size:\; x-large;">,</span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">)</span><span\; style="font-size:\; x-large;">=</span>\mathrm{<span\; style="font-size:\; x-large;">105</span>}$$

1. Find the least common denominator (LCD):

   The denominators are 7, 5, and 3. The LCD of these numbers is the least common multiple (LCM) of 7, 5, and 3.

   $$\text{<span style="font-size: x-large;">LCM</span>}<span\; style="font-size:\; x-large;">(</span>\mathrm{<span\; style="font-size:\; x-large;">7</span>}<span\; style="font-size:\; x-large;">,</span>\mathrm{<span\; style="font-size:\; x-large;">5</span>}<span\; style="font-size:\; x-large;">,</span>\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">)</span><span\; style="font-size:\; x-large;">=</span>\mathrm{<span\; style="font-size:\; x-large;">105</span>}$$

2. Convert each fraction to have the common denominator (105):

   $$\frac{\mathrm{<span\; style="font-size:\; x-large;">31</span>}}{\mathrm{<span\; style="font-size:\; x-large;">7</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">31</span>}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">15</span>}}{\mathrm{<span\; style="font-size:\; x-large;">7</span>}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">15</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">465</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}$$
   $$\frac{\mathrm{<span\; style="font-size:\; x-large;">12</span>}}{\mathrm{<span\; style="font-size:\; x-large;">5</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">12</span>}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">21</span>}}{\mathrm{<span\; style="font-size:\; x-large;">5</span>}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">21</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">252</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}$$
   $$\frac{\mathrm{<span\; style="font-size:\; x-large;">11</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">11</span>}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">35</span>}}{\mathrm{<span\; style="font-size:\; x-large;">3</span>}<span\; style="font-size:\; x-large;">\times </span>\mathrm{<span\; style="font-size:\; x-large;">35</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">385</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}$$

3. Add the fractions:

   $$\frac{\mathrm{<span\; style="font-size:\; x-large;">465</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}<span\; style="font-size:\; x-large;">+</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">252</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}<span\; style="font-size:\; x-large;">+</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">385</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">465</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">252</span>}<span\; style="font-size:\; x-large;">+</span>\mathrm{<span\; style="font-size:\; x-large;">385</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}<span\; style="font-size:\; x-large;">=</span>\frac{\mathrm{<span\; style="font-size:\; x-large;">1102</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}$$

4. Convert the improper fraction back to a mixed number:

   $$\frac{\mathrm{<span\; style="font-size:\; x-large;">1102</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}<span\; style="font-size:\; x-large;">=</span>\mathrm{<span\; style="font-size:\; x-large;">10</span>}\frac{\mathrm{<span\; style="font-size:\; x-large;">52</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}$$

So, the sum of $4\frac{3}{7}+2\frac{2}{5}+3\frac{2}{3}$ is:

$$\mathrm{<span\; style="font-size:\; x-large;">10</span>}\frac{\mathrm{<span\; style="font-size:\; x-large;">52</span>}}{\mathrm{<span\; style="font-size:\; x-large;">105</span>}}$$