Evaluate The Expression If $x = \frac{1}{10}$ And $y = \frac{1}{6}$.$x + Y$x + Y = \square$ (Type An Integer Or A Fraction. Simplify Your Answer.)

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Introduction

In mathematics, evaluating expressions with given variables is a fundamental concept that helps us understand the relationship between different values. In this article, we will evaluate the expression x+yx + y given that x=110x = \frac{1}{10} and y=16y = \frac{1}{6}.

Understanding the Variables

Before we proceed with the evaluation, let's understand the given variables.

  • x: The value of xx is given as 110\frac{1}{10}.
  • y: The value of yy is given as 16\frac{1}{6}.

Evaluating the Expression

Now that we have understood the variables, let's evaluate the expression x+yx + y.

To add fractions, we need to have the same denominator. In this case, the least common multiple (LCM) of 10 and 6 is 30. We can rewrite the fractions with the denominator 30.

  • x: 110=330\frac{1}{10} = \frac{3}{30}
  • y: 16=530\frac{1}{6} = \frac{5}{30}

Now that we have the same denominator, we can add the fractions.

x+y=330+530=830x + y = \frac{3}{30} + \frac{5}{30} = \frac{8}{30}

Simplifying the Fraction

The fraction 830\frac{8}{30} can be simplified by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.

830=415\frac{8}{30} = \frac{4}{15}

Conclusion

In conclusion, the value of x+yx + y given that x=110x = \frac{1}{10} and y=16y = \frac{1}{6} is 415\frac{4}{15}.

Final Answer

The final answer is 415\boxed{\frac{4}{15}}.

Related Topics

References

Further Reading

FAQs

  • Q: What is the value of x+yx + y given that x=110x = \frac{1}{10} and y=16y = \frac{1}{6}? A: The value of x+yx + y is 415\frac{4}{15}.
  • Q: How do I add fractions with different denominators? A: To add fractions with different denominators, you need to have the same denominator. You can do this by finding the least common multiple (LCM) of the denominators and rewriting the fractions with the LCM as the denominator.
  • Q: How do I simplify a fraction? A: To simplify a fraction, you need to divide both the numerator and the denominator by their greatest common divisor (GCD).

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Introduction

In our previous article, we evaluated the expression x+yx + y given that x=110x = \frac{1}{10} and y=16y = \frac{1}{6}. In this article, we will answer some frequently asked questions related to evaluating expressions with given variables.

Q&A

Q: What is the value of x−yx - y given that x=110x = \frac{1}{10} and y=16y = \frac{1}{6}?

A: To find the value of x−yx - y, we need to subtract the value of yy from the value of xx. We can do this by rewriting the fractions with the same denominator.

  • x: 110=330\frac{1}{10} = \frac{3}{30}
  • y: 16=530\frac{1}{6} = \frac{5}{30}

Now that we have the same denominator, we can subtract the fractions.

x−y=330−530=−230x - y = \frac{3}{30} - \frac{5}{30} = \frac{-2}{30}

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.

−230=−115\frac{-2}{30} = \frac{-1}{15}

Q: How do I evaluate the expression x⋅yx \cdot y given that x=110x = \frac{1}{10} and y=16y = \frac{1}{6}?

A: To evaluate the expression x⋅yx \cdot y, we need to multiply the values of xx and yy. We can do this by multiplying the numerators and the denominators separately.

x⋅y=110⋅16=1⋅110⋅6=160x \cdot y = \frac{1}{10} \cdot \frac{1}{6} = \frac{1 \cdot 1}{10 \cdot 6} = \frac{1}{60}

Q: What is the value of x+y+zx + y + z given that x=110x = \frac{1}{10}, y=16y = \frac{1}{6}, and z=14z = \frac{1}{4}?

A: To find the value of x+y+zx + y + z, we need to add the values of xx, yy, and zz. We can do this by rewriting the fractions with the same denominator.

  • x: 110=330\frac{1}{10} = \frac{3}{30}
  • y: 16=530\frac{1}{6} = \frac{5}{30}
  • z: 14=7.530\frac{1}{4} = \frac{7.5}{30}

Now that we have the same denominator, we can add the fractions.

x+y+z=330+530+7.530=15.530x + y + z = \frac{3}{30} + \frac{5}{30} + \frac{7.5}{30} = \frac{15.5}{30}

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 1.5.

15.530=10.3320\frac{15.5}{30} = \frac{10.33}{20}

Q: How do I evaluate the expression xy\frac{x}{y} given that x=110x = \frac{1}{10} and y=16y = \frac{1}{6}?

A: To evaluate the expression xy\frac{x}{y}, we need to divide the value of xx by the value of yy. We can do this by dividing the numerators and the denominators separately.

xy=11016=110⋅61=610\frac{x}{y} = \frac{\frac{1}{10}}{\frac{1}{6}} = \frac{1}{10} \cdot \frac{6}{1} = \frac{6}{10}

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 2.

610=35\frac{6}{10} = \frac{3}{5}

Conclusion

In conclusion, we have answered some frequently asked questions related to evaluating expressions with given variables. We have also provided examples and step-by-step solutions to help you understand the concepts better.

Final Answer

The final answer is 35\boxed{\frac{3}{5}}.

Related Topics

References

Further Reading

FAQs

  • Q: What is the value of x−yx - y given that x=110x = \frac{1}{10} and y=16y = \frac{1}{6}? A: The value of x−yx - y is −115\frac{-1}{15}.
  • Q: How do I evaluate the expression x⋅yx \cdot y given that x=110x = \frac{1}{10} and y=16y = \frac{1}{6}? A: The value of x⋅yx \cdot y is 160\frac{1}{60}.
  • Q: What is the value of x+y+zx + y + z given that x=110x = \frac{1}{10}, y=16y = \frac{1}{6}, and z=14z = \frac{1}{4}? A: The value of x+y+zx + y + z is 10.3320\frac{10.33}{20}.
  • Q: How do I evaluate the expression xy\frac{x}{y} given that x=110x = \frac{1}{10} and y=16y = \frac{1}{6}? A: The value of xy\frac{x}{y} is 35\frac{3}{5}.