Sure, let's solve the problem step by step:
Given the values:
[tex]\[ x = \frac{3}{7} \][/tex]
[tex]\[ y = \frac{1}{3} \][/tex]
[tex]\[ z = 3 \frac{6}{7} \][/tex]
First, let's convert the mixed number [tex]\( z \)[/tex] into an improper fraction.
The mixed number [tex]\( 3 \frac{6}{7} \)[/tex] can be converted as follows:
[tex]\[ z = 3 \frac{6}{7} = 3 + \frac{6}{7} \][/tex]
Next, we convert [tex]\( 3 \)[/tex] into a fraction with the same denominator as [tex]\( \frac{6}{7} \)[/tex]:
[tex]\[ 3 = \frac{21}{7} \][/tex]
Now, let's add these fractions:
[tex]\[ z = \frac{21}{7} + \frac{6}{7} = \frac{21 + 6}{7} = \frac{27}{7} \][/tex]
Therefore, [tex]\( z \)[/tex] in improper fraction form is:
[tex]\[ z = \frac{27}{7} \][/tex]
Now, we need to calculate [tex]\( z + x \times y \)[/tex]. First, let's find [tex]\( x \times y \)[/tex]:
[tex]\[ x \times y = \frac{3}{7} \times \frac{1}{3} \][/tex]
[tex]\[ x \times y = \frac{3 \times 1}{7 \times 3} = \frac{3}{21} = \frac{1}{7} \][/tex]
Next, we add this product to [tex]\( z \)[/tex]:
[tex]\[ z + x \times y = z + \frac{1}{7} \][/tex]
Since [tex]\( z \)[/tex] is [tex]\( \frac{27}{7} \)[/tex] and [tex]\( x \times y \)[/tex] is [tex]\( \frac{1}{7} \)[/tex], we can write:
[tex]\[ z + x \times y = \frac{27}{7} + \frac{1}{7} \][/tex]
To add these fractions, we sum their numerators:
[tex]\[ z + x \times y = \frac{27 + 1}{7} = \frac{28}{7} \][/tex]
Finally, simplify the fraction:
[tex]\[ \frac{28}{7} = 4 \][/tex]
Thus, the value of [tex]\( z + x \times y \)[/tex] is:
[tex]\[ \boxed{4} \][/tex]
