((2)/(3)+(4)/(9)) Of (3)/(5)- 1(2)/(3)times1(1)/(4)-(1)/(3)

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Jun 07, 2024

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Evaluating the Expression: ((2)/(3)+(4)/(9)) of (3)/(5)- 1(2)/(3) times 1(1)/(4)-(1)/(3)

In this article, we will evaluate the expression ((2)/(3)+(4)/(9)) of (3)/(5)- 1(2)/(3) times 1(1)/(4)-(1)/(3). This expression involves several operations, including addition, subtraction, multiplication, and division of fractions.

Step 1: Evaluate the Expression Inside the Parentheses

First, let's evaluate the expressions inside the parentheses:

(2)/(3) + (4)/(9)

To add these fractions, we need to find a common denominator, which is 9. So, we can rewrite the fractions as:

(6)/(9) + (4)/(9)

Now, we can add them:

(10)/(9)

So, the expression inside the parentheses is (10)/(9).

Step 2: Evaluate the Expression (3)/(5) - 1(2)/(3) times 1(1)/(4)

Next, let's evaluate the expression:

(3)/(5) - 1(2)/(3) times 1(1)/(4)

First, let's multiply 1(2)/(3) and 1(1)/(4):

(2)/(3) × (1)/(4) = (2)/(12) = (1)/(6)

Now, let's subtract (1)/(6) from (3)/(5):

(3)/(5) - (1)/(6)

To subtract these fractions, we need to find a common denominator, which is 30. So, we can rewrite the fractions as:

(18)/(30) - (5)/(30)

Now, we can subtract them:

(13)/(30)

Step 3: Multiply the Results

Finally, let's multiply the results of Steps 1 and 2:

((10)/(9)) × ((13)/(30))

To multiply these fractions, we can multiply the numerators and denominators separately:

(10 × 13) / (9 × 30) = (130) / (270)

Simplifying the fraction, we get:

(13)/(27)

Therefore, the final result of the expression ((2)/(3)+(4)/(9)) of (3)/(5)- 1(2)/(3) times 1(1)/(4)-(1)/(3) is (13)/(27).