Question 1

Find the sum. $2 \frac { 2 } { 5 } + 1 \frac { 1 } { 10 } + 6 \frac { 1 } { 15 }$

Accepted Answer

The answer of Find the sum. \(2 \frac { 2...

Question 2

Find the sum. $7 \frac { 3 } { 11 } + 7 \frac { 2 } { 11 }$

Accepted Answer

To add the mixed numbers, first add the whole numbers: 7 + 7 = 14. Then add the fractions: $ \frac{3}{11} + \frac{2}{11} = \frac{5}{11} $. Combine them to get $ 14 \frac{5}{11} $.

Question 3

Find the difference. $261 \frac { 2 } { 11 } - 107 \frac { 1 } { 55 }$

Accepted Answer

To find the difference, convert the mixed numbers to improper fractions: $261 \frac{2}{11} = \frac{2873}{11}$ and $107 \frac{1}{55} = \frac{5906}{55}$. Find a common denominator (55), convert the fractions, and subtract: $\frac{14365}{55} - \frac{5906}{55} = \frac{8459}{55}$. Convert back to a mixed number: $154 \frac{9}{55}$.

Question 4

A businesswoman's flight leaves Atlanta at 1 P.M. and arrives in New York at 3:45 P.M. Express the duration of the flight as a mixed number.

Accepted Answer

The flight duration is 3:45 P.M. - 1:00 P.M. = 2:45 P.M. = 2 hours and 45 minutes. 45 minutes is 3/4 of an hour, so the duration of the flight is 2 3/4 hours.

Question 5

The fire escape stairway in an office building is shown in the illustration below. Each riser is $6 \frac { 1 } { 2 }$ inches high. If each floor is 105 inches high and the building is 65 stories tall, how many steps are there in the stairway?  
__________ steps

Accepted Answer

The answer of The fire escape stairway in an office...

Question 6

How many inches of molding are needed to produce the square picture frame shown?  where $a = 14 \frac { 1 } { 8 }$ .

Accepted Answer

The answer of How many inches of molding are needed...

Question 7

Find the area of the license plate.

Accepted Answer

The answer of Find the area of the license plate....

Question 8

A sandwich shop sells a $\frac { 1 } { 2 }$ pound club sandwich, made up of turkey and ham. The owner buys the turkey in $1 \frac { 1 } { 2 }$ pound packages and the ham in $2 \frac { 5 } { 8 }$ pound packages. If he mixes a package of each of the meats together, how many sandwiches can he make from the mixture? 
Give your answer as mixed number, if necessary.

Accepted Answer

The answer of A sandwich shop sells a \(\frac {...

Question 9

Find the difference. $19 \frac { 3 } { 11 } - 4 \frac { 1 } { 55 }$

Accepted Answer

Convert the mixed numbers to improper fractions, find a common denominator, subtract, and simplify to get $15 \frac { 14 } { 55 }$.

Question 10

Simplify the complex fraction. $\frac { \frac { 2 } { 7 } } { \frac { 1 } { 3 } }$

Accepted Answer

To simplify a complex fraction, multiply the numerator and denominator by the reciprocal of the denominator.$\frac { \frac { 2 } { 7 } } { \frac { 1 } { 3 } } = \frac { \frac { 2 } { 7 } } { \frac { 1 } { 3 } } \cdot \frac { 3 } { 1 } = \frac { 2 } { 7 } \cdot 3 = \frac { 6 } { 7 }$

Question 11

Find the sum. $\begin{array} { r } 
- 7 \frac { 2 } { 5 } \
\
+ \quad 13 \frac { 1 } { 11 } \
\hline
\end{array}$

Accepted Answer

Convert the mixed numbers to improper fractions, find a common denominator, perform the addition, and convert back to a mixed number.

Question 12

Find the sum. $40 \frac { 3 } { 7 } + 70 \frac { 1 } { 5 }$

Accepted Answer

To find the sum of mixed numbers, first convert them to improper fractions:$40 \frac { 3 } { 7 } = \frac { ( 40 \times 7 ) + 3 } { 7 } = \frac { 283 } { 7 }$$70 \frac { 1 } { 5 } = \frac { ( 70 \times 5 ) + 1 } { 5 } = \frac { 351 } { 5 }$Now, add the improper fractions:$\frac { 283 } { 7 } + \frac { 351 } { 5 } = \frac { ( 283 \times 5 ) + ( 351 \times 7 ) } { 35 } = \frac { 1415 + 2457 } { 35 } = \frac { 3872 } { 35 }$Convert the improper fraction back to a mixed number:$3872 \div 35 = 110 \frac { 22 } { 35 }$Therefore, the sum of $40 \frac { 3 } { 7 } + 70 \frac { 1 } { 5 }$ is $110 \frac { 22 } { 35 }$.

Question 13

Multiply. $- 12 \cdot 2 \frac { 1 } { 3 }$

Accepted Answer

The answer of Multiply. \(- 12 \cdot 2 \frac {...

Question 14

Find the sum. $\begin{array} { r } 
76 \frac { 3 } { 11 } \
\
+ \quad 276 \frac { 2 } { 7 } \
\hline
\end{array}$

Accepted Answer

The answer of Find the sum. \(\begin{array} { r }...

Question 15

Find the sum. $- 4 \frac { 3 } { 5 } + \left( - 8 \frac { 1 } { 25 } \right)$

Accepted Answer

The answer of Find the sum. \(- 4 \frac {...

Question 16

Divide. $5 \frac { 1 } { 5 } \div 4 \frac { 1 } { 4 }$

Accepted Answer

The answer of Divide. \(5 \frac { 1 } {...

Question 17

The sign marks the emergency exit on a school bus. Find the area of the sign.

Accepted Answer

The answer of The sign marks the emergency exit on...

Question 18

Divide. $- 1 \frac { 1 } { 3 } \div 2 \frac { 1 } { 4 }$

Accepted Answer

Convert the mixed numbers to fractions:$- 1 \frac { 1 } { 3 } = \frac { - 4 } { 3 }$$2 \frac { 1 } { 4 } = \frac { 9 } { 4 }$Then divide:$\frac { - 4 } { 3 } \div \frac { 9 } { 4 } = \frac { - 4 } { 3 } \cdot \frac { 4 } { 9 } = \frac { - 16 } { 27 }$

Question 19

Find the sum. $\begin{array} { r } 
5 \frac { 1 } { 7 } \
\
+ \quad 10 \frac { 2 } { 5 } \
\hline
\end{array}$

Accepted Answer

To add mixed numbers, first add the whole numbers, then add the fractions.$5 \frac { 1 } { 7 } + 10 \frac { 2 } { 5 } = 15 \frac { 1 } { 7 } + 10 \frac { 4 } { 10 } = 15 \frac { 1 } { 7 } + 10 \frac { 2 } { 5 } = 15 \frac { 5 } { 35 } + 10 \frac { 14 } { 35 } = 15 \frac { 19 } { 35 }$

Question 20

Subtract the following mixed numbers. $\begin{array} { r } 
5 \frac { 2 } { 3 } \
\
- \quad 4 \frac { 3 } { 8 } \
\hline
\end{array}$

Accepted Answer

To subtract mixed numbers, first convert them to improper fractions. Then, subtract the numerators and keep the denominator the same. Finally, convert the improper fraction back to a mixed number.$5 \frac { 2 } { 3 } = \frac { 17 } { 3 }$$4 \frac { 3 } { 8 } = \frac { 35 } { 8 }$$\frac { 17 } { 3 } - \frac { 35 } { 8 } = \frac { 136 } { 24 } - \frac { 105 } { 24 } = \frac { 31 } { 24 }$$\frac { 31 } { 24 } = 1 \frac { 7 } { 24 }$Therefore, the answer is $1 \frac { 7 } { 24 }$.

Quiz 3: Fractions and Mixed Numbers

Find the sum. $2 \frac { 2 } { 5 } + 1 \frac { 1 } { 10 } + 6 \frac { 1 } { 15 }$

Find the sum. $7 \frac { 3 } { 11 } + 7 \frac { 2 } { 11 }$

Find the difference. $261 \frac { 2 } { 11 } - 107 \frac { 1 } { 55 }$

A businesswoman's flight leaves Atlanta at 1 P.M. and arrives in New York at 3:45 P.M. Express the duration of the flight as a mixed number.

Find the area of the license plate.

Find the difference. $19 \frac { 3 } { 11 } - 4 \frac { 1 } { 55 }$

Simplify the complex fraction. $\frac { \frac { 2 } { 7 } } { \frac { 1 } { 3 } }$

Find the sum. $\begin{array} { r } - 7 \frac { 2 } { 5 } \\\\+ \quad 13 \frac { 1 } { 11 } \\\hline\end{array}$

Find the sum. $40 \frac { 3 } { 7 } + 70 \frac { 1 } { 5 }$

Multiply. $- 12 \cdot 2 \frac { 1 } { 3 }$

Find the sum. $\begin{array} { r } 76 \frac { 3 } { 11 } \\\\+ \quad 276 \frac { 2 } { 7 } \\\hline\end{array}$

Find the sum. $- 4 \frac { 3 } { 5 } + \left( - 8 \frac { 1 } { 25 } \right)$

Divide. $5 \frac { 1 } { 5 } \div 4 \frac { 1 } { 4 }$

The sign marks the emergency exit on a school bus. Find the area of the sign.

Divide. $- 1 \frac { 1 } { 3 } \div 2 \frac { 1 } { 4 }$

Find the sum. $\begin{array} { r } 5 \frac { 1 } { 7 } \\\\+ \quad 10 \frac { 2 } { 5 } \\\hline\end{array}$

Subtract the following mixed numbers. $\begin{array} { r } 5 \frac { 2 } { 3 } \\\\- \quad 4 \frac { 3 } { 8 } \\\hline\end{array}$

Quiz 3: Fractions and Mixed Numbers

Find the sum. 225+1110+61152 \frac { 2 } { 5 } + 1 \frac { 1 } { 10 } + 6 \frac { 1 } { 15 }252​+1101​+6151​

Find the sum. 7311+72117 \frac { 3 } { 11 } + 7 \frac { 2 } { 11 }7113​+7112​

Find the difference. 261211−107155261 \frac { 2 } { 11 } - 107 \frac { 1 } { 55 }261112​−107551​

A businesswoman's flight leaves Atlanta at 1 P.M. and arrives in New York at 3:45 P.M. Express the duration of the flight as a mixed number.

The fire escape stairway in an office building is shown in the illustration below. Each riser is 6126 \frac { 1 } { 2 }621​ inches high. If each floor is 105 inches high and the building is 65 stories tall, how many steps are there in the stairway? __________ steps

How many inches of molding are needed to produce the square picture frame shown? where a=1418a = 14 \frac { 1 } { 8 }a=1481​ .

Find the area of the license plate.

Find the difference. 19311−415519 \frac { 3 } { 11 } - 4 \frac { 1 } { 55 }19113​−4551​

Simplify the complex fraction. 2713\frac { \frac { 2 } { 7 } } { \frac { 1 } { 3 } }31​72​​

Find the sum. −725+13111\begin{array} { r } - 7 \frac { 2 } { 5 } \\\\+ \quad 13 \frac { 1 } { 11 } \\\hline\end{array}−752​+13111​​​

Find the sum. 4037+701540 \frac { 3 } { 7 } + 70 \frac { 1 } { 5 }4073​+7051​

Multiply. −12⋅213- 12 \cdot 2 \frac { 1 } { 3 }−12⋅231​

Find the sum. 76311+27627\begin{array} { r } 76 \frac { 3 } { 11 } \\\\+ \quad 276 \frac { 2 } { 7 } \\\hline\end{array}76113​+27672​​​

Find the sum. −435+(−8125) - 4 \frac { 3 } { 5 } + \left( - 8 \frac { 1 } { 25 } \right) −453​+(−8251​)

Divide. 515÷4145 \frac { 1 } { 5 } \div 4 \frac { 1 } { 4 }551​÷441​

The sign marks the emergency exit on a school bus. Find the area of the sign.

Divide. −113÷214- 1 \frac { 1 } { 3 } \div 2 \frac { 1 } { 4 }−131​÷241​

Find the sum. 517+1025\begin{array} { r } 5 \frac { 1 } { 7 } \\\\+ \quad 10 \frac { 2 } { 5 } \\\hline\end{array}571​+1052​​​

Subtract the following mixed numbers. 523−438\begin{array} { r } 5 \frac { 2 } { 3 } \\\\- \quad 4 \frac { 3 } { 8 } \\\hline\end{array}532​−483​​​

Find the sum. $2 \frac { 2 } { 5 } + 1 \frac { 1 } { 10 } + 6 \frac { 1 } { 15 }$

Find the sum. $7 \frac { 3 } { 11 } + 7 \frac { 2 } { 11 }$

Find the difference. $261 \frac { 2 } { 11 } - 107 \frac { 1 } { 55 }$

Find the difference. $19 \frac { 3 } { 11 } - 4 \frac { 1 } { 55 }$

Simplify the complex fraction. $\frac { \frac { 2 } { 7 } } { \frac { 1 } { 3 } }$

Find the sum. $\begin{array} { r } - 7 \frac { 2 } { 5 } \\\\+ \quad 13 \frac { 1 } { 11 } \\\hline\end{array}$

Find the sum. $40 \frac { 3 } { 7 } + 70 \frac { 1 } { 5 }$

Multiply. $- 12 \cdot 2 \frac { 1 } { 3 }$

Find the sum. $\begin{array} { r } 76 \frac { 3 } { 11 } \\\\+ \quad 276 \frac { 2 } { 7 } \\\hline\end{array}$

Find the sum. $- 4 \frac { 3 } { 5 } + \left( - 8 \frac { 1 } { 25 } \right)$

Divide. $5 \frac { 1 } { 5 } \div 4 \frac { 1 } { 4 }$

Divide. $- 1 \frac { 1 } { 3 } \div 2 \frac { 1 } { 4 }$

Find the sum. $\begin{array} { r } 5 \frac { 1 } { 7 } \\\\+ \quad 10 \frac { 2 } { 5 } \\\hline\end{array}$

Subtract the following mixed numbers. $\begin{array} { r } 5 \frac { 2 } { 3 } \\\\- \quad 4 \frac { 3 } { 8 } \\\hline\end{array}$