Deck 3: Fractions and Mixed Numbers

Question 1

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

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

Answer 1

$2$

Question 2

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) $\frac { 2 } { 21 }$

Answer 2

$\frac { 6 } { 21 }$

Question 3

In the fraction , the numerator is __________.

Answer 3

2

Question 4

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) $6$

Question 5

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 6

Write the number as a fraction. $19$

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

Question 7

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) $- \frac { 5 } { 5 }$

Question 8

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

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

Question 9

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 10

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 11

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 12

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

Question 13

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 14

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

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

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

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 17

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 18

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

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

Question 19

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

Question 20

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 21

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 22

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 23

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 24

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 25

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 26

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 27

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 28

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 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

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

Question 42

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 43

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) $8 \frac { 1 } { 5 }$
E) $8 \frac { 1 } { 5 }$ .

Question 44

What fractions have been graphed on the number line?
 

Question 45

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 46

We read  as " ____ -__________."

Question 47

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 48

Place a > or __________ __________

Question 49

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

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

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 52

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 53

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 54

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 55

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

Question 56

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

Question 57

What mixed numbers have been graphed on the number line?

Question 58

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 59

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

A) =
B) >
C).

Question 60

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

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

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 63

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 64

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 65

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 66

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 67

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 68

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 69

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 70

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 71

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 72

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

Question 73

Find the area of the license plate.

Question 74

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

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

Question 75

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 76

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 77

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

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

Question 78

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 79

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 80

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) $154 \frac { 1 } { 5 }$