Question 1

Divide: $\frac { 1 } { 3 } \div \frac { 1 } { 15 }$

Accepted Answer

A)  $\frac { 1 } { 45 }$ 
B)  $5$ 
C)  $0$ 
D)  Undefined 
E)  $\frac { 1 } { 90 }$ 
A)  $\frac { 1 } { 45 }$ 
B)  $5$ 
C)  $0$ 
D)  Undefined 
E)  $\frac { 1 } { 90 }$

Question 2

Simplify: $\left( \frac { 5 } { 6 } \right) ^ { 2 } - \frac { 7 } { 20 }$

Accepted Answer

A)  $\frac { 497 } { 1440 }$ 
B)  $\frac { 31 } { 180 }$ 
C)  $\frac { 31 } { 90 }$ 
D)  $1 \frac { 31 } { 180 }$ 
E)  $1 \frac { 31 } { 90 }$ 
A)  $\frac { 497 } { 1440 }$ 
B)  $\frac { 31 } { 180 }$ 
C)  $\frac { 31 } { 90 }$ 
D)  $1 \frac { 31 } { 180 }$ 
E)  $1 \frac { 31 } { 90 }$

Question 3

Subtract: $\begin{array} { r } 
\frac { 5 } { 13 } \
\
- \quad \frac { 1 } { 13 } \
\hline
\end{array}$

Accepted Answer

A)  $1 \frac { 2 } { 13 }$ 
B)  $1 \frac { 4 } { 13 }$ 
C)  $\frac { 4 } { 13 }$ 
D)  $\frac { 2 } { 13 }$ 
E)  $2 \frac { 4 } { 13 }$ 
A)  $1 \frac { 2 } { 13 }$ 
B)  $1 \frac { 4 } { 13 }$ 
C)  $\frac { 4 } { 13 }$ 
D)  $\frac { 2 } { 13 }$ 
E)  $2 \frac { 4 } { 13 }$

Question 4

Find the total of $\frac { 1 } { 6 }$ , $\frac { 5 } { 6 }$ , and $\frac { 1 } { 3 }$ .

Accepted Answer

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

Question 5

Find the least common multiple (LCM) of the numbers 8, 10.

Accepted Answer

A)  80 
B)  2 
C)  40 
D)  1 
E)  8 
A)  80 
B)  2 
C)  40 
D)  1 
E)  8

Question 6

Simplify: $3 \cdot \left( \frac { 1 } { 2 } \right) ^ { 3 } \cdot \left( \frac { 1 } { 3 } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 1 } { 48 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $27$ 
E)  $\frac { 1 } { 24 }$ 
A)  $\frac { 1 } { 8 }$ 
B)  $\frac { 1 } { 48 }$ 
C)  $\frac { 9 } { 2 }$ 
D)  $27$ 
E)  $\frac { 1 } { 24 }$

Question 7

Write the fraction in simplest form. $\frac { 8 } { 21 }$

Accepted Answer

A)  $\frac { 16 } { 21 }$ 
B)  $\frac { 4 } { 21 }$ 
C)  $\frac { 8 } { 21 }$ 
D)  $1$ 
E)  $0$ 
A)  $\frac { 16 } { 21 }$ 
B)  $\frac { 4 } { 21 }$ 
C)  $\frac { 8 } { 21 }$ 
D)  $1$ 
E)  $0$

Question 8

A patient with high blood pressure who weighs 168 pounds is put on a diet to lose 21 pounds in three months. The patient loses $10 \frac { 1 } { 8 }$ pounds the first month and $9 \frac { 5 } { 8 }$ pounds the second month. How much weight must be lost the third month for the goal to be achieved?

Accepted Answer

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

Question 9

A 15-mile "Race for the Cure" event has three checkpoints. The first checkpoint is $1 \frac { 1 } { 4 }$ miles from the starting point. The second checkpoint is $4 \frac { 1 } { 4 }$ miles from the first checkpoint. How many miles is the second checkpoint from the finish line?

Accepted Answer

A)    miles 
B)    miles 
C)    miles 
D)    miles 
E)    miles 
A)    miles 
B)    miles 
C)    miles 
D)    miles 
E)    miles

Question 10

Write the mixed number $6 \frac { 3 } { 8 }$ as an improper fraction.

Accepted Answer

A)  $\frac { 45 } { 16 }$ 
B)  $\frac { 51 } { 16 }$ 
C)  $\frac { 51 } { 8 }$ 
D)  $6$ 
E)  $\frac { 3 } { 8 }$ 
A)  $\frac { 45 } { 16 }$ 
B)  $\frac { 51 } { 16 }$ 
C)  $\frac { 51 } { 8 }$ 
D)  $6$ 
E)  $\frac { 3 } { 8 }$

Question 11

Divide: $15 \div \frac { 3 } { 4 }$

Accepted Answer

A)  $11 \frac { 1 } { 2 }$ 
B)  $11 \frac { 1 } { 4 }$ 
C)  $16 \frac { 1 } { 3 }$ 
D)  $20$ 
E)  $1 \frac { 1 } { 3 }$ 
A)  $11 \frac { 1 } { 2 }$ 
B)  $11 \frac { 1 } { 4 }$ 
C)  $16 \frac { 1 } { 3 }$ 
D)  $20$ 
E)  $1 \frac { 1 } { 3 }$

Question 12

Multiply: $3 \times \frac { 5 } { 9 }$

Accepted Answer

A)  $1 \frac { 2 } { 3 }$ 
B)  $1 \frac { 5 } { 27 }$ 
C)  $\frac { 5 } { 27 }$ 
D)  $3 \frac { 5 } { 9 }$ 
E)  $3 \frac { 2 } { 3 }$ 
A)  $1 \frac { 2 } { 3 }$ 
B)  $1 \frac { 5 } { 27 }$ 
C)  $\frac { 5 } { 27 }$ 
D)  $3 \frac { 5 } { 9 }$ 
E)  $3 \frac { 2 } { 3 }$

Question 13

Identify the following fraction as a proper fraction, an improper fraction, or a mixed number. $\frac { 15 } { 14 }$

Accepted Answer

A)  Proper fraction 
B)  Mixed number 
C)  Improper fraction 
A)  Proper fraction 
B)  Mixed number 
C)  Improper fraction

Question 14

Add: $7 \frac { 3 } { 10 } + 2 \frac { 2 } { 3 }$

Accepted Answer

A)  $10 \frac { 87 } { 100 }$ 
B)  $10 \frac { 29 } { 30 }$ 
C)  $9 \frac { 29 } { 30 }$ 
D)  $9 \frac { 87 } { 100 }$ 
E)  $10 \frac { 29 } { 270 }$ 
A)  $10 \frac { 87 } { 100 }$ 
B)  $10 \frac { 29 } { 30 }$ 
C)  $9 \frac { 29 } { 30 }$ 
D)  $9 \frac { 87 } { 100 }$ 
E)  $10 \frac { 29 } { 270 }$

Question 15

Simplify: $\left( \frac { 1 } { 3 } \right) ^ { 4 } \cdot \left( \frac { 8 } { 11 } \right) ^ { 2 }$

Accepted Answer

A)  $\frac { 64 } { 1089 }$ 
B)  $\frac { 64 } { 3267 }$ 
C)  $\frac { 64 } { 9801 }$ 
D)  $\frac { 64 } { 363 }$ 
E)  $\frac { 64 } { 891 }$ 
A)  $\frac { 64 } { 1089 }$ 
B)  $\frac { 64 } { 3267 }$ 
C)  $\frac { 64 } { 9801 }$ 
D)  $\frac { 64 } { 363 }$ 
E)  $\frac { 64 } { 891 }$

Question 16

Write the fraction in simplest form. $\frac { 69 } { 3 }$

Accepted Answer

A)  $69$ 
B)  $\frac { 1 } { 23 }$ 
C)  $3$ 
D)  $\frac { 1 } { 3 }$ 
E)  $23$ 
A)  $69$ 
B)  $\frac { 1 } { 23 }$ 
C)  $3$ 
D)  $\frac { 1 } { 3 }$ 
E)  $23$

Question 17

Find the least common multiple (LCM) of the numbers 12, 10, 16.

Accepted Answer

A)  240 
B)  2 
C)  1920 
D)  1 
E)  12 
A)  240 
B)  2 
C)  1920 
D)  1 
E)  12

Question 18

A patient with type 2 diabetes weighs 315 pounds and is advised to follow a prescribed nutrition plan in order to lose weight. During the first month of the diet, weekly losses were recorded as follows: $5 \frac { 1 } { 4 }$ pounds, $5 \frac { 3 } { 4 }$ pounds, 3 pounds, and $4 \frac { 1 } { 2 }$ pounds. What is the patient's weight at the end of the month?

Accepted Answer

A)  $296 \frac { 1 } { 2 }$ pounds 
B)  $297 \frac { 1 } { 2 }$ pounds 
C)  $295 \frac { 1 } { 2 }$ pounds 
D)  $298 \frac { 1 } { 2 }$ pounds 
E)  $294 \frac { 1 } { 2 }$ pounds 
A)  $296 \frac { 1 } { 2 }$ pounds 
B)  $297 \frac { 1 } { 2 }$ pounds 
C)  $295 \frac { 1 } { 2 }$ pounds 
D)  $298 \frac { 1 } { 2 }$ pounds 
E)  $294 \frac { 1 } { 2 }$ pounds

Question 19

Find the greatest common factor (GCF) of the numbers 9, 12, 15.

Accepted Answer

A)  3 
B)  9 
C)  12 
D)  15 
E)  108 
A)  3 
B)  9 
C)  12 
D)  15 
E)  108

Question 20

Add: $\frac { 4 } { 7 } + \frac { 9 } { 14 } + \frac { 11 } { 28 }$

Accepted Answer

A)  $2 \frac { 17 } { 28 }$ 
B)  $1 \frac { 17 } { 14 }$ 
C)  $1 \frac { 17 } { 28 }$ 
D)  $\frac { 17 } { 28 }$ 
E)  $\frac { 17 } { 14 }$ 
A)  $2 \frac { 17 } { 28 }$ 
B)  $1 \frac { 17 } { 14 }$ 
C)  $1 \frac { 17 } { 28 }$ 
D)  $\frac { 17 } { 28 }$ 
E)  $\frac { 17 } { 14 }$

Divide: $\frac { 1 } { 3 } \div \frac { 1 } { 15 }$

Simplify: $\left( \frac { 5 } { 6 } \right) ^ { 2 } - \frac { 7 } { 20 }$

Subtract: -

Find the total of $\frac { 1 } { 6 }$ , $\frac { 5 } { 6 }$ , and $\frac { 1 } { 3 }$ .

Find the least common multiple (LCM) of the numbers 8, 10.

Simplify: $3 \cdot \left( \frac { 1 } { 2 } \right) ^ { 3 } \cdot \left( \frac { 1 } { 3 } \right) ^ { 2 }$

Write the fraction in simplest form. $\frac { 8 } { 21 }$

A patient with high blood pressure who weighs 168 pounds is put on a diet to lose 21 pounds in three months. The patient loses $10 \frac { 1 } { 8 }$ pounds the first month and $9 \frac { 5 } { 8 }$ pounds the second month. How much weight must be lost the third month for the goal to be achieved?

A 15-mile "Race for the Cure" event has three checkpoints. The first checkpoint is $1 \frac { 1 } { 4 }$ miles from the starting point. The second checkpoint is $4 \frac { 1 } { 4 }$ miles from the first checkpoint. How many miles is the second checkpoint from the finish line?

Write the mixed number $6 \frac { 3 } { 8 }$ as an improper fraction.

Divide: $15 \div \frac { 3 } { 4 }$

Multiply: $3 \times \frac { 5 } { 9 }$

Identify the following fraction as a proper fraction, an improper fraction, or a mixed number. $\frac { 15 } { 14 }$

Add: $7 \frac { 3 } { 10 } + 2 \frac { 2 } { 3 }$

Simplify: $\left( \frac { 1 } { 3 } \right) ^ { 4 } \cdot \left( \frac { 8 } { 11 } \right) ^ { 2 }$

Write the fraction in simplest form. $\frac { 69 } { 3 }$

Find the least common multiple (LCM) of the numbers 12, 10, 16.

Find the greatest common factor (GCF) of the numbers 9, 12, 15.

Add: $\frac { 4 } { 7 } + \frac { 9 } { 14 } + \frac { 11 } { 28 }$

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Exam 2: Fractions

Divide: 13÷115\frac { 1 } { 3 } \div \frac { 1 } { 15 }31​÷151​

Simplify: (56)2−720\left( \frac { 5 } { 6 } \right) ^ { 2 } - \frac { 7 } { 20 }(65​)2−207​

Subtract: -

Find the total of 16\frac { 1 } { 6 }61​ , 56\frac { 5 } { 6 }65​ , and 13\frac { 1 } { 3 }31​ .

Find the least common multiple (LCM) of the numbers 8, 10.

Simplify: 3⋅(12)3⋅(13)23 \cdot \left( \frac { 1 } { 2 } \right) ^ { 3 } \cdot \left( \frac { 1 } { 3 } \right) ^ { 2 }3⋅(21​)3⋅(31​)2

Write the fraction in simplest form. 821\frac { 8 } { 21 }218​

A 15-mile "Race for the Cure" event has three checkpoints. The first checkpoint is 1141 \frac { 1 } { 4 }141​ miles from the starting point. The second checkpoint is 4144 \frac { 1 } { 4 }441​ miles from the first checkpoint. How many miles is the second checkpoint from the finish line?

Write the mixed number 6386 \frac { 3 } { 8 }683​ as an improper fraction.

Divide: 15÷3415 \div \frac { 3 } { 4 }15÷43​

Multiply: 3×593 \times \frac { 5 } { 9 }3×95​

Identify the following fraction as a proper fraction, an improper fraction, or a mixed number. 1514\frac { 15 } { 14 }1415​

Add: 7310+2237 \frac { 3 } { 10 } + 2 \frac { 2 } { 3 }7103​+232​

Simplify: (13)4⋅(811)2\left( \frac { 1 } { 3 } \right) ^ { 4 } \cdot \left( \frac { 8 } { 11 } \right) ^ { 2 }(31​)4⋅(118​)2

Write the fraction in simplest form. 693\frac { 69 } { 3 }369​

Find the least common multiple (LCM) of the numbers 12, 10, 16.

Find the greatest common factor (GCF) of the numbers 9, 12, 15.

Add: 47+914+1128\frac { 4 } { 7 } + \frac { 9 } { 14 } + \frac { 11 } { 28 }74​+149​+2811​

Whole Numbers

Decimals

Ratio and Proportion

Percents

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Statistics and Probability

Us Units of Measurement

Metric System Measurement

Rational Numbers

Introduction to Algebra

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Divide: $\frac { 1 } { 3 } \div \frac { 1 } { 15 }$

Simplify: $\left( \frac { 5 } { 6 } \right) ^ { 2 } - \frac { 7 } { 20 }$

Find the total of $\frac { 1 } { 6 }$ , $\frac { 5 } { 6 }$ , and $\frac { 1 } { 3 }$ .

Simplify: $3 \cdot \left( \frac { 1 } { 2 } \right) ^ { 3 } \cdot \left( \frac { 1 } { 3 } \right) ^ { 2 }$

Write the fraction in simplest form. $\frac { 8 } { 21 }$

A 15-mile "Race for the Cure" event has three checkpoints. The first checkpoint is $1 \frac { 1 } { 4 }$ miles from the starting point. The second checkpoint is $4 \frac { 1 } { 4 }$ miles from the first checkpoint. How many miles is the second checkpoint from the finish line?

Write the mixed number $6 \frac { 3 } { 8 }$ as an improper fraction.

Divide: $15 \div \frac { 3 } { 4 }$

Multiply: $3 \times \frac { 5 } { 9 }$

Identify the following fraction as a proper fraction, an improper fraction, or a mixed number. $\frac { 15 } { 14 }$

Add: $7 \frac { 3 } { 10 } + 2 \frac { 2 } { 3 }$

Simplify: $\left( \frac { 1 } { 3 } \right) ^ { 4 } \cdot \left( \frac { 8 } { 11 } \right) ^ { 2 }$

Write the fraction in simplest form. $\frac { 69 } { 3 }$

Add: $\frac { 4 } { 7 } + \frac { 9 } { 14 } + \frac { 11 } { 28 }$