Question 1

One meaning of 16/19 ÷ 25/17 is, "How many 25/17 of 1 are in 16/19 of 25/17?"

Accepted Answer

A) True 
 B)False  False

Question 2

Using a rectangular region as the unit, illustrate each of the following. 
A) $2 / 3 + 4 / 5$
B) $7 / 5 + 3 / 2$
C) $10 / 8 - 1 / 2$

Accepted Answer

A) The expected way is to start with 2/3 of a rectangular region shaded. Cut it with marks perpendicular to the marks for thirds to give slivers that are fifths (and small boxes that are fifteenths), turning the 2/3 into 10/15. Notice that, in order to add another 4/5, we need 12/15, yet there are only 5/15 left in the first box. A duplicate of the first box needs to be made, so the other 7/15 can be shaded. An additional 4/5 would entail four slivers or 12 small boxes. Since there are only five small boxes left, seven small boxes, or 7/15, of another whole is needed.
B) This is similar to part A, except that each addend is more than one whole. There are 2 9/10 when all the work is done.
C) The easiest way is to recognize that 10/8 = 5/4 = 1 1/4, but that may not be regarded as fair. Show 10/8 with parallel cutting marks and shading on the two rectangular regions. That should show that 1/2 is 4/8, which can then be crossed out from the 10/8.

Question 3

Following is an example of a child's work. You are to study the work and then judge the student's understanding.
?
Rona was asked to subtract $2 \frac { 5 } { 8 }$ 
 from $4 \frac { 1 } { 8 }$ 
. Her work is shown below. 
$\begin{array} { r } 
\text { Rona's work:}&4 \frac { 1 } { 8 } = 3 \frac { 11 } { 8 } \\
&\underline{- 2 \frac { 5 } { 8 } = - 2 \frac { 5 } { 8 } }\
&\quad\quad\quad\quad 1 \frac { 6 } { 8 }
\end{array}$ ? 
A) Is Rona's work correct or incorrect?
B) If the work is incorrect, please explain why.

Accepted Answer

A) Incorrect
B) In changing a 1 from the 4 into eighths, Rona did the usual base-ten place value, borrowing 10 rather than the correct 8/8 + 1/8.

Question 4

Division involving only positive numbers always gives a smaller answer than the number being divided.

Accepted Answer

A) True 
 B)False

Question 5

Which point of A-E would BEST locate the point for n ÷ 0.89 on the number line (n is positive)?

Accepted Answer

The answer of Which point of A-E would BEST locate...

Question 6

How many portions of 2/3 a pound can be obtained from 30 pounds?

Accepted Answer

A)  20 
B)  45 
C)  60 
D)  90 
A)  20 
B)  45 
C)  60 
D)  90

Question 7

Karen and Sara go for a bike ride. Karen biked for $3 \frac { 1 } { 3 }$Hours, which was 2/3 as many hours as Sara biked. How many hours did Sara bike?

Accepted Answer

A)  2 $\frac { 2 } { 9 }$ 
B)  2 $\frac { 2 } { 3 }$ 
C)  4 
D)  5 
A)  2 $\frac { 2 } { 9 }$ 
B)  2 $\frac { 2 } { 3 }$ 
C)  4 
D)  5

Question 8

What calculation would solve this story problem?
George had 4/5 of a pie. He ate 2/3 of what he had. What part of a whole pie did he eat?

Accepted Answer

A)  4/5 + 2/3 
B)  4/5 - 2/3 
C)  2/3 × 4/5 
D)  4/5 ÷ 2/3 
A)  4/5 + 2/3 
B)  4/5 - 2/3 
C)  2/3 × 4/5 
D)  4/5 ÷ 2/3

Question 9

The stagecoach robbers have a 12-mile head start on the sheriff's posse. But the sheriff's posse has faster horses, so the posse catches up by 3/4 of a mile every hour. How many hours will it take the posse to catch the robbers? Show your work.

Accepted Answer

The answer of The stagecoach robbers have a 12-mile head...

Question 10

Which location on the number line indicated by the letter P, Q, R, S T, U, or W represents each of the following?   
A) 1/2 × 2
B) 5/8 of 1/2
C) 3/4 of 2/3
D) 1 ÷ 2/3
E) 1/4 ÷ 1/3

Accepted Answer

A) U 
B) Q

Question 11

Finish the following story problem so that your question could be answered by the calculation 18 ÷1/2.
You buy 18 muffins for an after-school faculty meeting …

Accepted Answer

The answer of Finish the following story problem so that...

Question 12

If two numbers are multiplied, their product is greater than (or equal to) each number.

Accepted Answer

A) True 
 B)False

Question 13

After the family had gone 140 miles, the children asked, "Are we getting close?" The driver said, "We've gone only 2/7 of the way." How far did the family still have to go?

Accepted Answer

A)  40 miles 
B)  80 miles 
C)  350 miles 
D)  490 miles 
A)  40 miles 
B)  80 miles 
C)  350 miles 
D)  490 miles

Question 14

One meaning of 45/59 ÷ 35/17 is, "How many 35/17of 1 are in 45/59 of 1?"

Accepted Answer

A) True 
 B)False

Question 15

One day, Joe's old car used 5/8 of a quart of oil. The next day, it used only 2/3 as much oil. How many quarts of oil did the car use on the second day? Which computation will answer the question?

Accepted Answer

A)  5/8 + 2/3 
B)  2/3 × 5/8 
C)  5/8 ÷ 2/3 
D)  2/3 ÷ 5/8 
A)  5/8 + 2/3 
B)  2/3 × 5/8 
C)  5/8 ÷ 2/3 
D)  2/3 ÷ 5/8

Question 16

Three-fourths of seven ones is the same amount as seven 3/4 of one.

Accepted Answer

A) True 
 B)False

Question 17

Is one meaning of 1/4 × 1/3 the following: How many 1s is 1/4 of 1/3 of 1? If it is one meaning, how much of a 1 or how many 1s?

Accepted Answer

The answer of Is one meaning of 1/4 × 1/3...

Question 18

A) On the number line below, show approximately where 4/7 + 1/2 would be using number sense. Label it
B) On the same number line, show approximately where 4/7 - 1/2 would be, using number sense. Label it b.

Accepted Answer

The answer of A) On the number line below, show...

Question 19

Make up a story problem that could be solved by calculating 123 - $48 \frac { 1 } { 3 }$

Accepted Answer

There are various possibilitie

Question 20

Donny is asked to solve the following problem: If cheese is $1.89 per pound, how much does 0.67 pounds cost? Which computation will answer the question?

Accepted Answer

A)  1.89 + 0.67 
B)  1.89 - 0.67 
C)  0.67 - 1.89 
D)  0.67 × 1.89 
E)  1.89 ÷ 0.67
F)0.67 ÷ 1.89 
A)  1.89 + 0.67 
B)  1.89 - 0.67 
C)  0.67 - 1.89 
D)  0.67 × 1.89 
E)  1.89 ÷ 0.67
F)0.67 ÷ 1.89

Exam 7: Computing With Fractions

One meaning of 16/19 ÷ 25/17 is, "How many 25/17 of 1 are in 16/19 of 25/17?"

Using a rectangular region as the unit, illustrate each of the following. A) 2/3+4/52 / 3 + 4 / 52/3+4/5 B) 7/5+3/27 / 5 + 3 / 27/5+3/2 C) 10/8−1/210 / 8 - 1 / 210/8−1/2

Division involving only positive numbers always gives a smaller answer than the number being divided.

Which point of A-E would BEST locate the point for n ÷ 0.89 on the number line (n is positive)?

How many portions of 2/3 a pound can be obtained from 30 pounds?

Karen and Sara go for a bike ride. Karen biked for 3133 \frac { 1 } { 3 }331​ Hours, which was 2/3 as many hours as Sara biked. How many hours did Sara bike?

What calculation would solve this story problem? George had 4/5 of a pie. He ate 2/3 of what he had. What part of a whole pie did he eat?

The stagecoach robbers have a 12-mile head start on the sheriff's posse. But the sheriff's posse has faster horses, so the posse catches up by 3/4 of a mile every hour. How many hours will it take the posse to catch the robbers? Show your work.

Which location on the number line indicated by the letter P, Q, R, S T, U, or W represents each of the following? A) 1/2 × 2 B) 5/8 of 1/2 C) 3/4 of 2/3 D) 1 ÷ 2/3 E) 1/4 ÷ 1/3

Finish the following story problem so that your question could be answered by the calculation 18 ÷1/2. You buy 18 muffins for an after-school faculty meeting …

If two numbers are multiplied, their product is greater than (or equal to) each number.

After the family had gone 140 miles, the children asked, "Are we getting close?" The driver said, "We've gone only 2/7 of the way." How far did the family still have to go?

One meaning of 45/59 ÷ 35/17 is, "How many 35/17of 1 are in 45/59 of 1?"

One day, Joe's old car used 5/8 of a quart of oil. The next day, it used only 2/3 as much oil. How many quarts of oil did the car use on the second day? Which computation will answer the question?

Three-fourths of seven ones is the same amount as seven 3/4 of one.

Is one meaning of 1/4 × 1/3 the following: How many 1s is 1/4 of 1/3 of 1? If it is one meaning, how much of a 1 or how many 1s?

A) On the number line below, show approximately where 4/7 + 1/2 would be using number sense. Label it B) On the same number line, show approximately where 4/7 - 1/2 would be, using number sense. Label it b.

Make up a story problem that could be solved by calculating 123 - 481348 \frac { 1 } { 3 }4831​

Donny is asked to solve the following problem: If cheese is $1.89 per pound, how much does 0.67 pounds cost? Which computation will answer the question?

Reasoning About Quantities

Numeration Systems

Understanding Whole Number Operations

Some Conventional Ways of Computing

Using Numbers in Sensible Ways

Meanings for Fractions

Multiplicative Comparisons and Multiplicative Reasoning

Ratios, Rates, Proportions, and Percents

Integers and Other Number Systems

Number Theory

What Is Algebra

A Quantitative Approach to Algebra and Graphing

Understanding Change: Relationships Among Time, Distance, and Rate

Further Topics in Algebra and Change

Polygons

Polyhedra

Symmetry

Tessellations

Similarity

Curves, Constructions, and Curved Surfaces

Transformation Geometry

Measurement Basics

Area, Surface Area, and Volume

Counting Units Fast: Measurement Formulas

Special Topics in Measurement

Quantifying Uncertainty

Determining More Complicated Probabilities

Introduction to Statistics and Sampling

Representing and Interpreting Data With One Variable

Dealing With Multiple Data Sets or With Multiple Variables

Variability in Samples

Special Topics in Probability

Filters

Using a rectangular region as the unit, illustrate each of the following. A) $2 / 3 + 4 / 5$ B) $7 / 5 + 3 / 2$ C) $10 / 8 - 1 / 2$

Karen and Sara go for a bike ride. Karen biked for $3 \frac { 1 } { 3 }$ Hours, which was 2/3 as many hours as Sara biked. How many hours did Sara bike?

Make up a story problem that could be solved by calculating 123 - $48 \frac { 1 } { 3 }$