Chapter 1: Q33. (page 15)

Name the property illustrated by each equation.
$(1 \frac{2}{7}) (\frac{7}{9}) = 1$

Short Answer

Expert verified

Name of the property illustrated isMultiplicative Inverse.

Step by step solution

- Write properties of real numbers

For any real numbers $a, b,$ and $c :$
Property	Addition	Multiplication
Commutative	$a + b = b + a$	$a \cdot b = b \cdot a$
Associative	$(a + b) + c = a + (b + c)$	$(a \cdot b) \cdot c = a \cdot (b \cdot c)$
Identity	$a + 0 = a = 0 + a$	$a \cdot 1 = a = 1 \cdot a$
Inverse	$a + (- a) = 0 = (- a) + a$	If $a \neq 0$ , then $a \cdot \frac{1}{a} = 1 = \frac{1}{a} \cdot a$
Distributive	$a (b + c) = a b + a c and (b + c) a = b a + c a$

- Substitution in given values

First simplify mixed fraction

$\begin{matrix} 1 \frac{2}{7} = 1 + \frac{2}{7} \\ = \frac{7}{7} + \frac{2}{7} \\ = \frac{7 + 2}{7} \\ = \frac{9}{7} \end{matrix}$

Substitute a for $\frac{9}{7}$

As $\frac{7}{9}$ can be written as $\frac{1}{\frac{9}{7}}$ which further can be written as $\frac{1}{a}$

Now given equation becomes $a \cdot \frac{1}{a} = 1$

- Identify the property

From the table of properties of real numbers, $a \cdot \frac{1}{a} = 1$ is the property of inverse in multiplication

Thus, multiplicative inverse is illustrated by given equation.

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Name the property illustrated by each equation.
$(1 \frac{2}{7}) (\frac{7}{9}) = 1$

Short Answer

Step by step solution

- Write properties of real numbers

- Substitution in given values

- Identify the property

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Name the property illustrated by each equation.12779=1

Short Answer

Step by step solution

- Write properties of real numbers

- Substitution in given values

- Identify the property

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

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Theoretical and Mathematical Physics

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Statistics

Study anywhere. Anytime. Across all devices.

Name the property illustrated by each equation.
$(1 \frac{2}{7}) (\frac{7}{9}) = 1$