Worksheet - Rational Numbers

Rational numbers are numbers that can be expressed as a fraction or a ratio of two integers. They include both positive and negative numbers, as well as zero. In this worksheet, we will be working with rational numbers and performing operations on them.

Problem:
Evaluate the expression (2/7 * 3/49) * (-7/15).

Solution:
To solve this problem, we will follow the order of operations, which states that we need to perform multiplication and division before addition and subtraction.

Step 1: Multiply the numerators and denominators
To multiply fractions, we simply multiply the numerators together and the denominators together. In this case, we have:
(2/7 * 3/49) = (2 * 3) / (7 * 49) = 6 / 343

Step 2: Multiply the resulting fraction by the next fraction
Next, we need to multiply the resulting fraction from step 1 by the fraction (-7/15):
(6/343) * (-7/15) = (6 * -7) / (343 * 15) = -42 / 5145

Step 3: Simplify the fraction, if possible
If the resulting fraction can be simplified, we should simplify it. In this case, -42 and 5145 have a common factor of 3, so we can simplify the fraction:
-42 / 5145 = (-14 * 3) / (1715 * 3) = -14 / 1715

Final Answer:
Therefore, the value of the expression (2/7 * 3/49) * (-7/15) is -14/1715.

Summary:
In this worksheet, we evaluated the expression (2/7 * 3/49) * (-7/15) by following the order of operations. We multiplied the numerators and denominators, then multiplied the resulting fraction by the next fraction, and finally simplified the fraction if possible. The final answer is -14/1715.

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