# Worksheet: Operations on Real Numbers

In this worksheet, we will practice solving problems involving operations and properties of operations on real numbers.

Q1:

Complete .

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Q2:

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Q3:

Given that the dimensions of a rectangle are cm and cm, find its area.

Q4:

What is the additive inverse of ?

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Q5:

Find the additive inverse of .

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Q6:

Find the multiplicative inverse of .

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Q7:

Given that is the multiplicative inverse of , find the value of .

Q8:

Given that is the multiplicative inverse of , find the value of .

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Q9:

Given that the multiplicative inverse of is , find the value of .

Q10:

Given that , find .

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Q11:

What is the additive inverse of ?

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Q12:

Find the multiplicative inverse of , giving your answer in its simplest form.

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Q13:

Find the multiplicative inverse of .

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Q14:

Complete .

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Q15:

Find the volume of the cube, given that the length of its edge is cm. • A22 cm3
• B12 cm3
• C cm3
• D cm3

Q16:

Given that the dimensions of a rectangle are cm and cm, find the length of its perimeter.

Q17:

A square has a side length of cm and an area of 63 cm2. Find the area of a square whose side length is cm.

Q18:

The radius of a sphere is given by the formula , where is the sphere’s volume. Determine the difference in radius between a sphere with volume and a sphere with .

Q19:

A rational number is a number that can be written in the form , where and are integers (whole numbers) and is not zero. If we add an irrational number to a rational number, the result is irrational. If , , , and , which of the following expressions results in a rational number?

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Q20:

A rational number is a number that can be written in the form , where and are integers (whole numbers) and is not zero. The product of an irrational number and a nonzero rational number is an irrational number. If , , , and , which of the following expressions results in a rational number?

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Q21:

If , , , and , which of the following expressions results in a rational number?

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Q22:

If , , , and , which of the following expressions results in a rational number?

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Q23:

If , , , and , which of the following expressions results in a rational number?

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Q24:

If , , , and , which of the following expressions results in a rational number?

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Q25:

If and , is it true that ?

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• Byes