Question 1

Determine whether the pair of fractions is equivalent.
-$\frac { 35 } { 60 } \text { and } \frac { 42 } { 84 }$
A)not equivalent
B)equivalent

Accepted Answer

Both fractions reduce to $\frac{7}{12}$, making them equivalent. However, my initial assessment was incorrect. Upon reevaluation, it's clear that both fractions indeed reduce to $\frac{7}{12}$, which means they are equivalent. I apologize for the confusion.

Question 2

Determine whether the pair of fractions is equivalent.
-$\frac { 1 } { 7 } \text { and } \frac { 9 } { 119 }$
A)not equivalent
B)equivalent

Accepted Answer

To determine if the fractions $\frac{1}{7}$ and $\frac{9}{119}$ are equivalent, you can simplify the second fraction or find a common denominator. Simplifying $\frac{9}{119}$, since $119 = 17 \times 7$, we get $\frac{9}{17 \times 7}$. This simplifies further to $\frac{9}{119} = \frac{1}{7}$ only if the numerator 9 could be simplified to 1 with the same factor as the denominator, which it cannot. Therefore, the fractions are not equivalent.

Question 3

Solve. Write the fractions in simplest form.
-There are 8000 runners at a marathon. If 6400 are male, what fraction of the runners are female ?
A) $\frac { 6400 } { 8000 }$
B) $\frac { 2 } { 8 }$
C) $\frac { 1 } { 5 }$
D) $\frac { 4 } { 5 }$

Accepted Answer

The number of female runners is 8000 - 6400 = 1600. The fraction of runners who are female is $\frac{1600}{8000}$, which simplifies to $\frac{1}{5}$.

Question 4

Determine whether the pair of fractions is equivalent.
-$\frac { 9 } { 21 } \text { and } \frac { 6 } { 14 }$
A)not equivalent
B)equivalent

Accepted Answer

The fractions are equivalent because they both simplify to 3/7.

Question 5

Solve. Write the fractions in simplest form.
-The following graph is called a circle graph or pie chart. Each sector (shaped like a piece of pie)shows the number of each color of marbles that Jay has: 270 are red, 252 are blue, 135 are yellow, 198 are green, and 45 are
Clear. What fraction of the marbles are red? Write the fraction in simplest form.
45 
A) $\frac { 1 } { 5 }$
B) $\frac { 270 } { 900 }$
C) $\frac { 3 } { 10 }$
D) $\frac { 3 } { 7 }$

Accepted Answer

The answer of Solve. Write the fractions in simplest form.
-The...

Question 6

Multiply. Write the answer in simplest form.
-$\frac { 1 } { 7 } \cdot \frac { 15 } { 20 }$
A) $\frac { 3 } { 28 }$
B) $\frac { 4 } { 21 }$
C) $\frac { 21 } { 22 }$
D) $\frac { 16 } { 27 }$

Accepted Answer

Multiplying the fractions $\frac{1}{7} \cdot \frac{15}{20}$ simplifies to $\frac{15}{140}$ after multiplying numerators and denominators, which further simplifies to $\frac{3}{28}$ after dividing both numerator and denominator by 5.

Question 7

Solve. Write the fractions in simplest form.
-There are 1200 employees at a company. If 900 are males, what fraction of the employees are males?
A) $\frac { 1 } { 4 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 900 } { \text { males } }$
D) $\frac { 3 } { 4 }$

Accepted Answer

The fraction of employees who are males is $ \frac{900}{1200} $, which simplifies to $ \frac{3}{4} $.

Question 8

Solve. Write the fractions in simplest form.
-There are 5280 feet in a mile. What fraction of a mile is represented by 720 feet?
A) $\frac { 1 } { 44 }$
B) $\frac { 3 } { 19 }$
C) $\frac { 3 } { 22 }$
D) $\frac { 720 } { 5280 }$

Accepted Answer

To find the fraction of a mile represented by 720 feet, divide 720 by 5280. Simplifying $\frac{720}{5280}$ gives $\frac{3}{22}$.

Question 9

Solve. Write the fractions in simplest form.
-A company employs 144,000 employees worldwide. About 36,000 employees work in the United States. What fraction of the employees work in the United States?
A) $\frac { 5 } { 2 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 36,000 } { 144,000 }$
D) $\frac { 1 } { 40 }$

Accepted Answer

To find the fraction of employees working in the United States, divide the number of U.S. employees by the total number of employees: $\frac{36,000}{144,000} = \frac{1}{4}$.

Question 10

Multiply. Write the answer in simplest form.
-$\frac { 7 } { 10 } \cdot \frac { 17 } { 11 }$
A) $\frac { 119 } { 110 }$
B) $\frac { 77 } { 170 }$
C) $\frac { 2 } { 3 }$
D) $\frac { 8 } { 7 }$

Accepted Answer

Multiplying the fractions $\frac{7}{10} \cdot \frac{17}{11}$ directly gives $\frac{7 \cdot 17}{10 \cdot 11} = \frac{119}{110}$, which cannot be simplified further.

Question 11

Solve. Write the fractions in simplest form.
-A real estate agent categorized 100 available homes by housing style. $$\begin{array}{l}
\text { Distribution of Houses by Style }\
\begin{array} { l | c } 
\text { Housing Style } & \text { Number of Homes } \
\hline \text { Two Story } & 38 \
\text { One and One-Half Story } & 12 \
\text { Raised Ranch } & 6 \
\text { Split Level } & 25 \
\text { Ranch } & 19
\end{array}
\end{array}$$ What fraction of available homes are split-level homes?
A) $\frac { 25 } { 100 }$
B) $\frac { 1 } { 3 }$
C) $\frac { 25 } { 75 }$
D) $\frac { 1 } { 4 }$

Accepted Answer

The answer of Solve. Write the fractions in simplest form.
-A...

Question 12

Multiply. Write the answer in simplest form.
-$\frac { 1 } { 3 } \cdot \frac { 4 } { 5 } \cdot \frac { 2 } { 5 }$
A) $\frac { 1 } { 6 }$
B) $\frac { 8 } { 75 }$
C) $\frac { 8 } { 13 }$
D) $\frac { 4 } { 75 }$

Accepted Answer

To multiply fractions, multiply the numerators together and the denominators together: $\frac{1}{3} \cdot \frac{4}{5} \cdot \frac{2}{5} = \frac{1 \cdot 4 \cdot 2}{3 \cdot 5 \cdot 5} = \frac{8}{75}$.

Question 13

Solve. Write the fractions in simplest form.
-There are 100 centimeters in 1 meter. What fraction of a meter is 65 centimeters?
A) $\frac { 65 } { 100 }$
B) $\frac { 13 } { 20 }$
C) $\frac { 13 } { 7 }$
D) $\frac { 1 } { 10 }$

Accepted Answer

Since there are 100 centimeters in a meter, 65 centimeters is $\frac{65}{100}$ of a meter. Simplifying this fraction by dividing both the numerator and the denominator by their greatest common divisor, 5, gives $\frac{13}{20}$.

Question 14

Multiply. Write the answer in simplest form.
-$\frac { 2 } { 5 } \cdot \frac { 8 } { 9 }$
A) $\frac { 45 } { 16 }$
B) $\frac { 5 } { 7 }$
C) $\frac { 20 } { 9 }$
D) $\frac { 16 } { 45 }$

Accepted Answer

Multiplying the fractions $\frac{2}{5} \cdot \frac{8}{9}$ gives $\frac{2 \cdot 8}{5 \cdot 9} = \frac{16}{45}$, which is in simplest form.

Question 15

Multiply. Write the answer in simplest form.
-$\frac { 3 } { 9 } \cdot \frac { 3 } { 7 }$
A) $\frac { 3 } { 8 }$
B) $\frac { 7 } { 9 }$
C) $\frac { 1 } { 7 }$
D) $\frac { 5 } { 6 }$

Accepted Answer

Multiplying the fractions $\frac{3}{9} \cdot \frac{3}{7}$ simplifies to $\frac{1}{3} \cdot \frac{3}{7}$ after reducing $\frac{3}{9}$ to $\frac{1}{3}$. Further simplification gives $\frac{1}{7}$, as the 3s cancel out.

Question 16

Multiply. Write the answer in simplest form.
-$\frac { 5 } { 1 } \cdot \frac { 18 } { 11 }$
A) $\frac { 16 } { 19 }$
B) $\frac { 23 } { 12 }$
C) $\frac { 90 } { 11 }$
D) $\frac { 55 } { 18 }$

Accepted Answer

Multiplying the fractions $\frac{5}{1} \cdot \frac{18}{11}$ gives $\frac{5 \cdot 18}{1 \cdot 11} = \frac{90}{11}$, which is in simplest form.

Question 17

Determine whether the pair of fractions is equivalent.
-$\frac { 1 } { 4 } \text { and } \frac { 9 } { 12 }$
A)equivalent
B)not equivalent

Accepted Answer

The answer of Determine whether the pair of fractions is...

Question 18

Determine whether the pair of fractions is equivalent.
-$\frac { 3 } { 8 } \text { and } \frac { 39 } { 104 }$
A)equivalent
B)not equivalent

Accepted Answer

To determine if the fractions $\frac{3}{8}$ and $\frac{39}{104}$ are equivalent, you can simplify the second fraction or find a common factor. Multiplying the numerator and denominator of $\frac{3}{8}$ by 13 gives $\frac{39}{104}$, showing that they are indeed equivalent.

Question 19

Solve. Write the fractions in simplest form.
-A company employs 675,000 employees worldwide. About 49,500 employees work in the United States. What fraction of the employees do NOT work in the United States?
A) $\frac { 49,500 } { 675,000 }$
B) $\frac { 11 } { 150 }$
C) $\frac { 625,500 } { 675,000 }$
D) $\frac { 139 } { 150 }$

Accepted Answer

To find the fraction of employees not working in the United States, subtract the number of U.S. employees from the total and divide by the total: $\frac{675,000 - 49,500}{675,000} = \frac{625,500}{675,000}$. Simplifying this fraction gives $\frac{139}{150}$.

Question 20

Determine whether the pair of fractions is equivalent.
-$\frac { 3 } { 9 } \text { and } \frac { 21 } { 63 }$
A)equivalent
B)not equivalent

Accepted Answer

Both fractions simplify to $\frac{1}{3}$, making them equivalent.

Quiz 2: Multiplying and Dividing Fractions

Determine whether the pair of fractions is equivalent. - $\frac { 35 } { 60 } \text { and } \frac { 42 } { 84 }$

Determine whether the pair of fractions is equivalent. - $\frac { 1 } { 7 } \text { and } \frac { 9 } { 119 }$

Solve. Write the fractions in simplest form. -There are 8000 runners at a marathon. If 6400 are male, what fraction of the runners are female ?

Determine whether the pair of fractions is equivalent. - $\frac { 9 } { 21 } \text { and } \frac { 6 } { 14 }$

Multiply. Write the answer in simplest form. - $\frac { 1 } { 7 } \cdot \frac { 15 } { 20 }$

Solve. Write the fractions in simplest form. -There are 1200 employees at a company. If 900 are males, what fraction of the employees are males?

Solve. Write the fractions in simplest form. -There are 5280 feet in a mile. What fraction of a mile is represented by 720 feet?

Solve. Write the fractions in simplest form. -A company employs 144,000 employees worldwide. About 36,000 employees work in the United States. What fraction of the employees work in the United States?

Multiply. Write the answer in simplest form. - $\frac { 7 } { 10 } \cdot \frac { 17 } { 11 }$

Multiply. Write the answer in simplest form. - $\frac { 1 } { 3 } \cdot \frac { 4 } { 5 } \cdot \frac { 2 } { 5 }$

Solve. Write the fractions in simplest form. -There are 100 centimeters in 1 meter. What fraction of a meter is 65 centimeters?

Multiply. Write the answer in simplest form. - $\frac { 2 } { 5 } \cdot \frac { 8 } { 9 }$

Multiply. Write the answer in simplest form. - $\frac { 3 } { 9 } \cdot \frac { 3 } { 7 }$

Multiply. Write the answer in simplest form. - $\frac { 5 } { 1 } \cdot \frac { 18 } { 11 }$

Determine whether the pair of fractions is equivalent. - $\frac { 1 } { 4 } \text { and } \frac { 9 } { 12 }$

Determine whether the pair of fractions is equivalent. - $\frac { 3 } { 8 } \text { and } \frac { 39 } { 104 }$

Solve. Write the fractions in simplest form. -A company employs 675,000 employees worldwide. About 49,500 employees work in the United States. What fraction of the employees do NOT work in the United States?

Determine whether the pair of fractions is equivalent. - $\frac { 3 } { 9 } \text { and } \frac { 21 } { 63 }$

Quiz 2: Multiplying and Dividing Fractions

Determine whether the pair of fractions is equivalent. - 3560 and 4284\frac { 35 } { 60 } \text { and } \frac { 42 } { 84 }6035​ and 8442​

Determine whether the pair of fractions is equivalent. - 17 and 9119\frac { 1 } { 7 } \text { and } \frac { 9 } { 119 }71​ and 1199​

Solve. Write the fractions in simplest form. -There are 8000 runners at a marathon. If 6400 are male, what fraction of the runners are female ?

Determine whether the pair of fractions is equivalent. - 921 and 614\frac { 9 } { 21 } \text { and } \frac { 6 } { 14 }219​ and 146​

Multiply. Write the answer in simplest form. - 17⋅1520\frac { 1 } { 7 } \cdot \frac { 15 } { 20 }71​⋅2015​

Solve. Write the fractions in simplest form. -There are 1200 employees at a company. If 900 are males, what fraction of the employees are males?

Solve. Write the fractions in simplest form. -There are 5280 feet in a mile. What fraction of a mile is represented by 720 feet?

Solve. Write the fractions in simplest form. -A company employs 144,000 employees worldwide. About 36,000 employees work in the United States. What fraction of the employees work in the United States?

Multiply. Write the answer in simplest form. - 710⋅1711\frac { 7 } { 10 } \cdot \frac { 17 } { 11 }107​⋅1117​

Multiply. Write the answer in simplest form. - 13⋅45⋅25\frac { 1 } { 3 } \cdot \frac { 4 } { 5 } \cdot \frac { 2 } { 5 }31​⋅54​⋅52​