Chapter 1: Q28. (page 20)

Examples 2 and 3 Evaluate each expression using properties of numbers. Name the property used in each step.
28. $2 \frac{3}{4} \cdot 1 \frac{1}{8} \cdot 32$

Short Answer

Expert verified

The value of expression is 99.

Step by step solution

– Write the formulae used

Associative property of multiplication:

$(a \cdot b) \cdot c = a \cdot (b \cdot c)$

Inverse property of multiplication:

$a \cdot \frac{1}{a} = \frac{1}{a} \cdot a = 1$

Commutative property of multiplication:

$a \cdot b = b \cdot a$

– Write the given information

The expression given is

$2 \frac{3}{4} \cdot 1 \frac{1}{8} \cdot 32$

- DESCRIPTION OF STEP

To solve the given expression first simplify the mixed fraction(s) in the given expression as:

$\begin{matrix} 2 \frac{3}{4} \cdot 1 \frac{1}{8} \cdot 32 = \frac{2 \times 4 + 3}{4} \cdot \frac{1 \times 8 + 1}{8} \cdot 32 \\ = \frac{11}{4} \cdot \frac{9}{8} \cdot 32 \end{matrix}$

Now use the associative property to simplify the above expression further as:

$\begin{matrix} \frac{11}{4} \cdot \frac{9}{8} \cdot 32 = \frac{11}{4} \cdot (\frac{9}{8} \cdot 32) \\ = \frac{11}{4} \cdot (\frac{9}{8} \cdot 8 \cdot 4) \\ = \frac{11}{4} \cdot 9 \cdot 4 \\ = \frac{11}{4} \cdot 4 \cdot 9 (commutativerule) \\ = 11 \cdot 9 \\ = 99 \end{matrix}$

Thus, $2 \frac{3}{4} \cdot 1 \frac{1}{8} \cdot 32 = 99$

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Examples 2 and 3 Evaluate each expression using properties of numbers. Name the property used in each step.
28. $2 \frac{3}{4} \cdot 1 \frac{1}{8} \cdot 32$

Short Answer

Step by step solution

– Write the formulae used

– Write the given information

- DESCRIPTION OF STEP

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Examples 2 and 3 Evaluate each expression using properties of numbers. Name the property used in each step.28.234⋅118⋅32

Short Answer

Step by step solution

– Write the formulae used

– Write the given information

- DESCRIPTION OF STEP

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Calculus

Geometry

Theoretical and Mathematical Physics

Decision Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

Examples 2 and 3 Evaluate each expression using properties of numbers. Name the property used in each step.
28. $2 \frac{3}{4} \cdot 1 \frac{1}{8} \cdot 32$