Question

1. the number \\(\frac{5}{3}\\) is a ______ because 5 and 3 ar
2. the set of ______ consists of the counting n
3. the sum of \\((a + b) + c\\) is equal to the sum of \\(a + (b + c)\\) as ex by the ______
4. if you evaluate \\(n \times (y + z)\\) by writing it as \\((n \times y) + (n \times z)\\), y the ______

add and subtract fractions and decimals
add or subtract.

1. \\(2\frac{1}{3} + 6\frac{3}{5}\\)
2. \\(9\frac{1}{10}\\) (cut off)
3. \\(19.86 + 7.091\\)
4. \\(57\\) (cut off)

multiply and divide fractions and decimals
multiply or divide.

1. \\(4.08 \times 29.7\\)
2. \\(1\\) (cut off)
3. \\(\frac{15}{16} \times 9\frac{1}{5}\\)
4. \\(4\\) (cut off)

1. byron has \\(1\frac{7}{10}\\) kilograms of black pepper. he uses \\(\frac{7}{8}\\) of the and splits it between 7 pepper shakers. how much pepp in each shaker?

\\(\circleda\\) \\(\frac{119}{80}\\) kg
\\(\circledb\\) \\(\frac{1}{8}\\) kg
\\(\circledc\\) \\(1.4125\\) kg
\\(\circledd\\) \\(\frac{17}{80}\\) kg

Explanation:

Problem 7: \( 2\frac{1}{3} + 6\frac{3}{5} \)

Step 1: Convert mixed numbers to improper fractions

\( 2\frac{1}{3}=\frac{2\times3 + 1}{3}=\frac{7}{3} \)
\( 6\frac{3}{5}=\frac{6\times5+3}{5}=\frac{33}{5} \)

Step 2: Find a common denominator (15) and add

\( \frac{7}{3}+\frac{33}{5}=\frac{7\times5}{3\times5}+\frac{33\times3}{5\times3}=\frac{35}{15}+\frac{99}{15}=\frac{35 + 99}{15}=\frac{134}{15} \)

Step 3: Convert back to mixed number

\( \frac{134}{15}=8\frac{14}{15} \)

Step 1: Align decimal points and add

\(

$$\begin{align*} 19.860\\ +7.091\\ \hline 26.951 \end{align*}$$

\)

Step 1: Multiply as whole numbers

\( 408\times297 = 408\times(300 - 3)=408\times300-408\times3=122400 - 1224 = 121176 \)

Step 2: Count decimal places (3 places: 4.08 has 2, 29.7 has 1; 2 + 1 = 3)

\( 121176\div1000 = 121.176 \)

Answer:

\( 8\frac{14}{15} \)

Problem 9: \( 19.86 + 7.091 \)