Question

3 2/3+2.3 repeating

Answer 1

Answer:

6.

Step-by-step explanation:

2.3 repeating = 2 1/3

So 3 2/3 + 2 1/3

= 5 + 1

= 6.

Answer 2

Answer: 6

Step-by-step explanation:

$3\frac{2}{3}+2.3^-$

Let's begin by converting the repeating decimal to a fraction and then to a mixed number.

Take the number:

$2.3^-$

Let x (our result) be equal to that number.

$x=2.3^-$

Multiply by 1 followed by as many zeros as repeating decimals; in this case 1. Therefore, 10.

$10x=2.3^-*10$

This basically moves the decimal point one number to the right and since we have infinite 3's, we simply move 1 three and add another.

$10x=23.3^-$

Subtract this and the original equation ($x=2.3^-$)

$10x=23.3^-\\-x=2.3^-$

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10 - 1 = 9 and we have the same infinite repeating number 3, therefore they cancel out, leaving 23-2 = 21

$9x=21$

Divide by 9

$x=\frac{21}{9}$

Simplify by 3.

21/3=7

9/3=3

$x=\frac{7}{3}$

Now, convert to a mixed number. To do this, divide.

7/3=2

6

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1

The 2 is the whole number, 1 is the numerator and 3 the denominator.

$2\frac{1}{3}$

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Now we can solve this;

$3\frac{2}{3}+2\frac{1}{3}$

Add the whole numbers and the fractions separately.

$(3+2)+(\frac{2}{3}+\frac{1}{3})$

$5\frac{3}{3}$

3 and 3 can be simplied.

3/3=1

3/3=1

$5\frac{1}{1}$

The result is 1, add this to the 5.

$5+1=6$