Deck 3: Fractions and Mixed Numbers

Question 1

Write the number as a fraction. $19$

A) $\frac { 19 } { 1 }$
B) $- \frac { 1 } { 19 }$
C) $\frac { 1 } { 19 }$
D) $- \frac { 19 } { 19 }$
E) $- \frac { 19 } { 1 }$

Answer 1

$\frac { 19 } { 1 }$

Question 2

Multiply and reduce your answer to lowest terms. $\left( - \frac { 2 } { 39 } \right) \cdot \left( - \frac { 13 } { 4 } \right)$

A) $- 6$
B) $- \frac { 1 } { 6 }$
C) $- \frac { 1 } { 26 }$
D) $\frac { 1 } { 6 }$
E) $6$

Answer 2

$\frac { 1 } { 6 }$

Question 3

Multiply and reduce your answer to lowest terms. $- \frac { 72 } { 5 } \cdot \frac { 7 } { 36 } \cdot \frac { 1 } { 14 }$

A) $- \frac { 1 } { 5 }$
B) $\frac { 1 } { 5 }$
C) $- 1$
D) $1$
E) $- \frac { 5 } { 5 }$

Answer 3

$- \frac { 1 } { 5 }$

Question 4

Multiply and reduce your answer to lowest terms. $\frac { 1 } { 9 } \cdot \frac { 3 } { 7 }$

A) $\frac { 1 } { 3 }$
B) $3$
C) $63$
D) $\frac { 1 } { 63 }$
E) $\frac { 1 } { 21 }$

Question 5

Perform the multiplication. Simplify the result when possible. $\frac { 3 } { 32 } \cdot \frac { 40 } { 3 }$

A) $\frac { 7 } { 6 }$
B) $\frac { 5 } { 4 }$
C) $\frac { 7 } { 8 }$
D) $\frac { 8 } { 7 }$
E) $\frac { 4 } { 3 }$

Question 6

Write the number as a fraction with the indicated denominator.
7 as ninths

Question 7

Simplify the fraction to lowest terms. $\frac { 36 } { 18 }$

A) $\frac { 1 } { 18 }$
B) $18$
C) $\frac { 1 } { 2 }$
D) $2$
E) $\frac { 18 } { 36 }$

Question 8

Write the equivalent of the fraction using a denominator of 26 . $\frac { 10 } { 13 }$

A) $\frac { 26 } { 13 }$
B) $\frac { 1 } { 26 }$
C) $\frac { 26 } { 20 }$
D) $\frac { 20 } { 26 }$
E) $\frac { 10 } { 26 }$

Question 9

Perform the operation. $\frac { 13 } { 9 } \left( - \frac { 54 } { 13 } \right)$

A) $13$
B) $- 6$
C) $- 13$
D) $6$
E) n one of these

Question 10

The number above the bar in a fraction is called the _____.

A) denominator
B) reciprocal
C) divisor
D) integer
E) numerator

Question 11

Write the number as a fraction. $- 27$

A) $\frac { 27 } { 1 }$
B) $- \frac { 1 } { 27 }$
C) $\frac { 1 } { 27 }$
D) $- \frac { 27 } { 27 }$
E) $- \frac { 27 } { 1 }$

Question 12

In the fraction , the numerator is __________.

Question 13

For the fraction , 5 is the __________ and 13 is the __________.

Question 14

Simplify the fraction to lowest terms. $\frac { 2 } { 3 }$

A) $0.2$
B) $\frac { 1 } { 3 }$
C) $\frac { 1 } { 2 }$
D) $\frac { 3 } { 2 }$
E) Does not simplify further.

Question 15

What is the numerator of the fraction? $\frac { 2 } { 17 }$

A) $17$
B) $2$
C) $0.118$
D) $\frac { 2 } { 17 }$
E) $\frac { 17 } { 2 }$

Question 16

Write the number as a fraction with the indicated denominator.
 3  as halves

A) $\frac { 6 } { 2 }$
B) $\frac { 1 } { 2 }$
C) $\frac { 3 } { 2 }$
D) $\frac { 2 } { 3 }$
E) $\frac { 2 } { 6 }$

Question 17

Write the equivalent of the fraction using a denominator of 21 . $\frac { 2 } { 7 }$

A) $\frac { 21 } { 7 }$
B) $\frac { 1 } { 21 }$
C) $\frac { 21 } { 6 }$
D) $\frac { 6 } { 21 }$
E) $\frac { 2 } { 21 }$

Question 18

Simplify, if possible. $\frac { 13 } { 0 }$

A) $13$
B) $0$
C) $\frac { 1 } { 13 }$
D) $1$
E) undefined

Question 19

Simplify the fraction to lowest terms. $\frac { 24 } { 60 }$

A) $\frac { 2 } { 4 }$
B) $\frac { 8 } { 20 }$
C) $\frac { 2 } { 5 }$
D) $\frac { 6 } { 15 }$
E) Does not simplify further.

Question 20

Simplify, if possible. $\frac { 24 } { 24 }$

A) $24$
B) $1$
C) $\frac { 1 } { 24 }$
D) $- 1$
E) $\frac { 24 } { 1 }$

Question 21

Complete the operation and simplify if necessary. $\frac { 14 } { 23 } - \frac { 10 } { 23 }$

A) $4$
B) $\frac { 24 } { 23 }$
C) $\frac { 4 } { 23 }$
D) $\frac { 5 } { 23 }$
E) $\frac { 4 } { 19 }$

Question 22

Rewrite $36 \div 4$ as a multiplication by the reciprocal of 4, and find the result.

A) 9
B) 8
C) 5
D) 12
E) 7

Question 23

The surface of planet Zafar covers an area of approximately 121,447,000 square miles. About of that area is covered by water. Find the number of square miles of the surface covered by water.
__________ square miles

Question 24

Perform the operation. $\frac { 2 } { 3 } - \left( - \frac { 3 } { 5 } \right)$

A) $\frac { 19 } { 15 }$
B) $\frac { 2 } { 5 }$
C) $\frac { 1 } { 15 }$
D) $\frac { 2 } { 3 }$
E) $- \frac { 1 } { 15 }$

Question 25

Find the quotient. $\frac { 1 } { 4 } \div \frac { 7 } { 5 }$

A) $\frac { 8 } { 9 }$
B) $\frac { 5 } { 28 }$
C) $\frac { 7 } { 33 }$
D) $\frac { 9 } { 31 }$
E) $\frac { 7 } { 20 }$

Question 26

Subtract as indicated, and express your answer in lowest terms. $- \frac { 2 } { 17 } - \frac { 7 } { 85 }$

A) $- \frac { 1 } { 5 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 5 }$
D) $\frac { 4 } { 5 }$
E) $- \frac { 4 } { 5 }$

Question 27

If nylon is $ 11 per square yard, how much would the fabric cost to make a triangular sail with a base of 15 feet and a height of 24 feet?

A) $220
B) $990
C) $440
D) $3,960
E) $1,980

Question 28

Find the value of the expression $\left( \frac { 1 } { 2 } \right) ^ { 3 }$ .

A) $\frac { 1 } { 8 }$
B) $\frac { 1 } { 4 }$
C) $\frac { 1 } { 32 }$
D) $\frac { 1 } { 16 }$
E) $\frac { 1 } { 64 }$

Question 29

A production process applies several layers of a clear acrylic coat to outdoor furniture to help protect it from the weather. If each protective coat is inch thick, how many applications will be needed to build up inch of clear finish?
__________ applications

Question 30

Complete the operation and simplify if necessary. $- \frac { 3 } { 21 } - \frac { 2 } { 3 }$

A) $- \frac { 17 } { 21 }$
B) $\frac { 11 } { 21 }$
C) $- \frac { 1 } { 21 }$
D) $\frac { 17 } { 21 }$
E) $- \frac { 17 } { 3 }$

Question 31

Do the addition. Simplify the result when possible. $\frac { 1 } { 7 } + \frac { 1 } { 28 }$

A) $\frac { 5 } { 4 }$
B) $\frac { 1 } { 14 }$
C) $\frac { 5 } { 28 }$
D) $\frac { 5 } { 7 }$
E) $\frac { 3 } { 28 }$

Question 32

Article V of the Constitution requires a two-thirds vote of the House of Representatives to propose a constitutional amendment. The House has 375 members. Find the number of votes needed to meet this requirement.
Number of votes = __________

Question 33

Simplify the numerical expression. $- \left( \frac { 1 } { 3 } \right) ^ { - 4 }$

A) 27
B) $- \frac { 1 } { 81 }$
C) $- 81$
D) $- \frac { 1 } { 27 }$
E) 256

Question 34

Find the reciprocal of the number. $\frac { 2 } { 7 }$

A) $\frac { 7 } { 2 }$
B) $\frac { 2 } { 7 }$
C) $- \frac { 7 } { 2 }$
D) $- \frac { 2 } { 7 }$
E) $\frac { 1 } { 2 }$

Question 35

Each lap around a stadium track is mile. How many laps would a runner have to complete to get a 42-mile workout?
__________ laps

Question 36

Find the quotient. $\frac { 7 } { 3 } \div \left( - \frac { 5 } { 2 } \right)$

A) $\frac { 19 } { 14 }$
B) $- \frac { 16 } { 20 }$
C) $- \frac { 35 } { 6 }$
D) $- \frac { 13 } { 18 }$
E) $- \frac { 14 } { 15 }$

Question 37

The probability that a couple will have n baby boys in a row is given by the formula $\left( \frac { 1 } { 2 } \right) ^ { n }$ .  Find the probability that a couple will have 5 baby boys in a row.

A) $\frac { 1 } { 20 }$
B) $\frac { 1 } { 10 }$
C) $\frac { 1 } { 32 }$
D) $\frac { 1 } { 25 }$
E) 32

Question 38

Find the quotient. $\left( - \frac { 3 } { 7 } \right) \div \left( - \frac { 5 } { 28 } \right)$

A) $\frac { 12 } { 35 }$
B) $- \frac { 12 } { 5 }$
C) $\frac { 12 } { 5 }$
D) $- \frac { 4 } { 5 }$
E) $\frac { 4 } { 5 }$

Question 39

A recipe calls for cup of flour, and the only measuring container you have holds cup. How many cups of flour would you need to add to follow the recipe?
__________ cups

Question 40

Perform the addition. Simplify the result when possible. $\frac { 6 } { 11 } + \frac { 6 } { 11 }$

A) $\frac { 12 } { 13 }$
B) $\frac { 12 } { 11 }$
C) $\frac { 12 } { 5 }$
D) $\frac { 11 } { 12 }$
E) $\frac { 12 } { 121 }$

Question 41

Each region outlined in black represents one whole. Write an improper fraction and a mixed number to represent the shaded portion.

Question 42

Graph the given numbers on a number line. $- 2 \frac { 3 } { 4 } , - \frac { 1 } { 3 } , \frac { 3 } { 2 } , 4 \frac { 1 } { 2 }$

A)
B)
C)
D)

Question 43

Write the mixed number as an improper fraction. $5 \frac { 2 } { 3 }$

A) $5$
B) $\frac { 2 } { 3 }$
C) $\frac { 3 } { 2 }$
D) $\frac { 17 } { 3 }$
E) $\frac { 13 } { 3 }$

Question 44

A mechanic likes to hang his wrenches above his tool bench in order of narrowest to widest. What is the proper order of the wrenches in the illustration? in., in., in., in.

Question 45

Place a > or __________ __________

Question 46

What is the difference in power between a and a garage door opener?
Enter your answer as a simplified fraction without the units.

Question 47

Evaluate the power and write your answer as an improper fraction. $\left( - 1 \frac { 1 } { 2 } \right) ^ { 3 }$

A) $- \frac { 27 } { 8 }$
B) $\frac { 8 } { 4 }$
C) $\frac { 27 } { 8 }$
D) $- \frac { 8 } { 4 }$
E) $\frac { 4 } { 8 }$

Question 48

Write the improper fraction as a mixed number. $\frac { 42 } { 5 }$

A) $8 \frac { 5 } { 4 }$
B) $2 \frac { 5 } { 4 }$
C) $8 \frac { 2 } { 5 }$
D) $8 \frac { 1 } { 5 }$

Question 49

Complete the operation and simplify if necessary. $\frac { 4 } { 13 } + \frac { 7 } { 26 }$

A) $\frac { 3 } { 19 }$
B) $\frac { 15 } { 26 }$
C) $\frac { 15 } { 52 }$
D) $15$
E) $\frac { 9 } { 13 }$

Question 50

The illustration below shows the length of each section of a three-part hike. What is the longest and shortest section, if $A B = \frac { 4 } { 5 }$ , $B C = \frac { 11 } { 13 }$ , $C D = \frac { 7 } { 10 }$ .

A) Longest: $\frac { 4 } { 5 }$ ; Shortest: $\frac { 7 } { 10 }$ .
B) Longest: $\frac { 4 } { 5 }$ ; Shortest: $\frac { 11 } { 13 }$ .
C) Longest: $\frac { 11 } { 13 }$ ; Shortest: $\frac { 4 } { 5 }$ .
D) Longest: $\frac { 7 } { 10 }$ ; Shortest: $\frac { 4 } { 5 }$ .
E) Longest: $\frac { 11 } { 13 }$ ; Shortest: $\frac { 7 } { 10 }$ .

Question 51

We read  as " ____ -__________."

Question 52

Use one of the symbols to make the statement true. _____

Question 53

Complete the operation and simplify if necessary. $\frac { 1 } { 4 } + \frac { 7 } { 8 }$

A) $\frac { 4 } { 7 }$
B) $\frac { 1 } { 8 }$
C) $\frac { 1 } { 4 }$
D) $\frac { 9 } { 13 }$
E) $\frac { 9 } { 8 }$

Question 54

Write the improper fraction as a mixed number or a whole number. $\frac { 150 } { 14 }$

A) $9 \frac { 5 } { 7 }$
B) $10 \frac { 7 } { 5 }$
C) $10 \frac { 5 } { 7 }$
D) $- 10 \frac { 5 } { 7 }$
E) $11 \frac { 5 } { 7 }$

Question 55

Write the improper fraction as a mixed number or a whole number. $- \frac { 61 } { 7 }$

A) $- 8 \frac { 5 } { 7 }$
B) $- 8 \frac { 6 } { 7 }$
C) $- 8 \frac { 7 } { 6 }$
D) $- 8 \frac { 7 } { 5 }$
E) $8 \frac { 5 } { 7 }$

Question 56

Insert one of the symbols , or = in the blank. $\left| - 3 \frac { 1 } { 3 } \right|$ _____ $\frac { 10 } { 3 }$

A) =
B) >
C).

Question 57

Each region outlined in black represents one whole. Write an improper fraction and a mixed number to represent the shaded portion.

Question 58

What fractions have been graphed on the number line?

Question 59

What mixed numbers have been graphed on the number line?

Question 60

Multiply the fractions below and write your answer as an improper fraction.

Question 61

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

A) $8 \frac { 17 } { 30 }$
B) $11 \frac { 23 } { 30 }$
C) $9 \frac { 17 } { 30 }$
D) $10 \frac { 17 } { 25 }$
E) $10 \frac { 23 } { 30 }$

Question 62

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

A) $14 \frac { 5 } { 66 }$
B) $14 \frac { 6 } { 11 }$
C) $14 \frac { 5 } { 11 }$
D) $7 \frac { 5 } { 11 }$
E) $14 \frac { 3 } { 11 }$

Question 63

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

A) $261 \frac { 21 } { 55 }$
B) $368 \frac { 1 } { 5 }$
C) $368 \frac { 9 } { 55 }$
D) $154 \frac { 9 } { 55 }$
E) $154 \frac { 1 } { 5 }$

Question 64

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.

A) $2 \frac { 3 } { 4 }$  hr.
B) $4 \frac { 3 } { 4 }$  hr.
C) $4 \frac { 1 } { 4 }$  hr.
D) $3 \frac { 3 } { 4 }$  hr.
E) $2 \frac { 1 } { 4 }$  hr.

Question 65

The fire escape stairway in an office building is shown in the illustration below. Each riser is 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

Question 66

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

A) $196 \frac { 1 } { 2 }$ in.
B) $56 \frac { 1 } { 2 }$ in.
C) $28 \frac { 1 } { 4 }$ in.
D) $55 \frac { 7 } { 8 }$  in.
E) $14 \frac { 1 } { 64 }$  in.

Question 67

Find the area of the license plate.

Question 68

A sandwich shop sells a pound club sandwich, made up of turkey and ham. The owner buys the turkey in pound packages and the ham in 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.

Question 69

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

A) $15 \frac { 4 } { 11 }$
B) $14 \frac { 16 } { 55 }$
C) $15 \frac { 14 } { 55 }$
D) $23 \frac { 14 } { 55 }$
E) $15 \frac { 16 } { 55 }$

Question 70

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

A) $\frac { 6 } { 7 }$
B) $1 \frac { 1 } { 6 }$
C) $\frac { 2 } { 21 }$
D) $10 \frac { 1 } { 2 }$
E) $\frac { 2 } { 3 }$

Question 71

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

A) $6 \frac { 2 } { 5 }$
B) $5 \frac { 38 } { 55 }$
C) $7 \frac { 27 } { 55 }$
D) $6 \frac { 3 } { 55 }$
E) $6 \frac { 27 } { 5 }$

Question 72

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

A) $110 \frac { 3 } { 7 }$
B) $110 \frac { 22 } { 35 }$
C) $111 \frac { 22 } { 35 }$
D) $110 \frac { 4 } { 35 }$
E) $110 \frac { 22 } { 7 }$

Question 73

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

A) $- 9 \frac { 1 } { 3 }$
B) $20$
C) $- 24 \frac { 1 } { 3 }$
D) $- 28$
E) $28$

Question 74

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

A) $352 \frac { 3 } { 11 }$
B) $352 \frac { 43 } { 77 }$
C) $353 \frac { 43 } { 77 }$
D) $352 \frac { 5 } { 77 }$
E) $352 \frac { 43 } { 11 }$

Question 75

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

A) $4 \frac { 17 } { 26 }$
B) $- 4 \frac { 16 } { 25 }$
C) $- 12 \frac { 16 } { 25 }$
D) $- 12 \frac { 14 } { 25 }$
E) $12 \frac { 16 } { 25 }$

Question 76

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

A) $\frac { 65 } { 34 }$
B) $\frac { 13 } { 10 }$
C) $\frac { 20 } { 17 }$
D) $\frac { 5 } { 4 }$
E) $\frac { 104 } { 85 }$

Question 77

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

Question 78

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

A) $- \frac { 16 } { 27 }$
B) $\frac { 1 } { 2 }$
C) $- \frac { 4 } { 9 }$
D) $- \frac { 1 } { 2 }$
E) $\frac { 16 } { 27 }$

Question 79

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

A) $15 \frac { 1 } { 7 }$
B) $15 \frac { 19 } { 35 }$
C) $16 \frac { 19 } { 35 }$
D) $15 \frac { 3 } { 35 }$
E) $15 \frac { 19 } { 7 }$

Question 80

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

A) $1 \frac { 7 } { 24 }$
B) $\frac { 7 } { 24 }$
C) $1 \frac { 1 } { 24 }$
D) $2$
E) $1 \frac { 1 } { 4 }$