Chapter 1: Q19. (page 20)

Evaluate the following expression and name the property used in each step:
$3 \frac{2}{3} + 4 + 5 \frac{1}{3}$

Short Answer

Expert verified

The value of the expression is: $3 \frac{2}{3} + 4 + 5 \frac{1}{3} = 13$ .

Step by step solution

Step 1. Given information.

The given expression is:

$3 \frac{2}{3} + 4 + 5 \frac{1}{3}$

Step 2. Write the concept.

The substitution property for multiplication, addition, and subtraction is:

$\begin{matrix} a \cdot b = c \\ a \div b = c \\ a \pm b = c \end{matrix}$

The Associative property is:

$a + (b + c) = (a + b) + c$

Also, to add or subtract the fraction, the denominator must be the same.

Step 3. Write mixed fraction to fraction.

$\begin{matrix} 3 \frac{2}{3} = \frac{11}{3} \\ 5 \frac{1}{3} = \frac{16}{3} \end{matrix}$

Step 4. Evaluate the expression.

The expression $3 \frac{2}{3} + 4 + 5 \frac{1}{3}$ can be written as in below:

$3 \frac{2}{3} + 4 + 5 \frac{1}{3} = \frac{11}{3} + 4 + \frac{16}{3}$

Then,

$\begin{array}{l} \frac{11}{3} + 4 + \frac{16}{3} = (\frac{11}{3} + \frac{16}{3}) + 4 (Associative Property) \\ = (\frac{27}{3}) + 4 (Substitution Property) \end{array}$

Since, $(\frac{27}{3}) + 4 = \frac{27}{3} + \frac{4}{1}$ . So,

$\begin{array}{l} \frac{11}{3} + 4 + \frac{16}{3} = \frac{27 \times 1}{3 \times 1} + \frac{4 \times 3}{1 \times 3} \\ = \frac{27}{3} + \frac{12}{3} (Substitution Property) \\ = \frac{39}{3} (Substitution Property) \\ = \frac{3 \times 13}{3} \\ = 13 \end{array}$

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Evaluate the following expression and name the property used in each step:
$3 \frac{2}{3} + 4 + 5 \frac{1}{3}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Write mixed fraction to fraction.

Step 4. Evaluate the expression.

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Evaluate the following expression and name the property used in each step:323+4+513

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Write the concept.

Step 3. Write mixed fraction to fraction.

Step 4. Evaluate the expression.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Evaluate the following expression and name the property used in each step:
$3 \frac{2}{3} + 4 + 5 \frac{1}{3}$