Exam 6: Meanings for Fractions

To change 3 $\frac { 1 } { 4 }$ to a fraction, a common rule is to calculate 3 × 4, add 1, and write that answer over 4: 3 $\frac { 1 } { 4 }$ = $\frac { ( 3 \times 4 ) + 1 } { 4 }$ = $\frac { 13 } { 4 }$ . Use a number line (and words as you need them) to explain why that rule makes sense. $To change 3 \frac { 1 } { 4 } to a fraction, a common rule is to calculate 3 × 4, add 1, and write that answer over 4: 3 \frac { 1 } { 4 } = \frac { ( 3 \times 4 ) + 1 } { 4 } = \frac { 13 } { 4 } . Use a number line (and words as you need them) to explain why that rule makes sense.$

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Question 1

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Cut each unit into four equal pieces. Then the 3 = $\frac { ( 3 \times 4 ) } { 4 }$ , plus the $\frac { 1 } { 4 }$ , give 3 $\frac { 1 } { 4 }$ = $\frac { ( 3 \times 4 ) + 1 } { 4 }$ .

As a decimal, 0.525% is:

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Question 2

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Which value is larger, 17/40 pound or 29/64 pound? Explain your thinking, showing your understanding of fractions and benchmarks, without using decimals or common denominators.

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Question 3

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Using a benchmark of 1/2 pound, 17/40 is 3/40 under 1/2 and 29/64 is 3/64 under 1/2. Since fortieths are larger than sixty-fourths, 3/40 > 3/64, so 17/40 will be more under 1/2 than 29/64 will be. Therefore, 29/64 pounds is larger.

Which is larger, 7/9 or 9/11? Provide a justification for your choice, which does not refer to decimals.

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Question 4

Put these amounts in order, from smallest to largest: $8.5 \% \quad 1.7 \quad \frac{15}{11} \quad \frac{14}{8} \quad 110 \%$

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Question 5

$\frac { 4 } { 5 } - \frac { 5 } { 8 }$ Is NOT equivalent to:

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Question 6

What is the fraction equivalent of each decimal amount? A) 0.651 B) 0.44444 …

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Question 7

Given a number line and only the points for the indicated fractions, accurately locate and label the point for the number in each part. If your markings do not make your reasoning clear, add an explanation. $Given a number line and only the points for the indicated fractions, accurately locate and label the point for the number in each part. If your markings do not make your reasoning clear, add an explanation. A) 0 B) 2/3$ A) 0 B) 2/3

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Question 8

Which pair of numbers is relatively prime?

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Question 9

Give three decimals between 0.301 and 0.302. If it is not possible, explain why not.

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Question 10

Given a number line and only the points for the indicated fractions, accurately locate and label the point for the number in each part. If your markings do not make your reasoning clear, add an explanation. $Given a number line and only the points for the indicated fractions, accurately locate and label the point for the number in each part. If your markings do not make your reasoning clear, add an explanation. A) 2 B) 2 \frac { 1 } { 2 }$ A) 2 B) $2 \frac { 1 } { 2 }$

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Question 11

Pat and Dana like to argue with each other about mathematics problems. They discuss the figure below. Pat: "The shaded region is one-and-a-half times as much as the unshaded region." Dana: "Wait! I think that the unshaded region is 2/3 of the shaded region." Who is correct? Why?

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Question 12

20% of 150 is 1/3 of:

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Question 13

Mark 3/5 on this number line as A. Mark 5/3 on the number line as B.

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Question 14

Correct the following statement so that it is true in some nontrivial way: If D = $0.7\overline{42}$ , then 100D = 74.200.

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Question 15

Which is the greater value, 9/16 of a cup or 15/28 of a cup? Explain showing your grasp of fractions and benchmarks, without using decimals or complicated common denominators.

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Question 16

If the hearts shown represent only 2/5 of the chocolate hearts you gave away on Valentine's Day, how many chocolate hearts did you give away in all?

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Question 17

Put these fractions in order from smallest to largest. $\frac { 200 } { 303 }$ $\frac { 6 } { 9 }$ $\frac { 9 } { 12 }$ $\frac { 203 } { 300 }$

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Question 18

Sketch a line segment that is 12.5% longer than 8 inches. How long is the line segment you sketched?

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Question 19

Name three ways of thinking about the symbol $\frac { 7 } { 8 }$

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Question 20

Showing 1 - 20 of 85

Exam 6: Meanings for Fractions

As a decimal, 0.525% is:

Which value is larger, 17/40 pound or 29/64 pound? Explain your thinking, showing your understanding of fractions and benchmarks, without using decimals or common denominators.

Which is larger, 7/9 or 9/11? Provide a justification for your choice, which does not refer to decimals.

Put these amounts in order, from smallest to largest: 8.5%1.71511148110% 8.5 \% \quad 1.7 \quad \frac{15}{11} \quad \frac{14}{8} \quad 110 \% 8.5%1.71115​814​110%

45−58\frac { 4 } { 5 } - \frac { 5 } { 8 }54​−85​ Is NOT equivalent to:

What is the fraction equivalent of each decimal amount? A) 0.651 B) 0.44444 …

Given a number line and only the points for the indicated fractions, accurately locate and label the point for the number in each part. If your markings do not make your reasoning clear, add an explanation. A) 0 B) 2/3

Which pair of numbers is relatively prime?

Give three decimals between 0.301 and 0.302. If it is not possible, explain why not.

Given a number line and only the points for the indicated fractions, accurately locate and label the point for the number in each part. If your markings do not make your reasoning clear, add an explanation. A) 2 B) 2122 \frac { 1 } { 2 }221​

Pat and Dana like to argue with each other about mathematics problems. They discuss the figure below. Pat: "The shaded region is one-and-a-half times as much as the unshaded region." Dana: "Wait! I think that the unshaded region is 2/3 of the shaded region." Who is correct? Why?

20% of 150 is 1/3 of:

Mark 3/5 on this number line as A. Mark 5/3 on the number line as B.

Correct the following statement so that it is true in some nontrivial way: If D = 0.742‾0.7\overline{42}0.742 , then 100D = 74.200.

Which is the greater value, 9/16 of a cup or 15/28 of a cup? Explain showing your grasp of fractions and benchmarks, without using decimals or complicated common denominators.

If the hearts shown represent only 2/5 of the chocolate hearts you gave away on Valentine's Day, how many chocolate hearts did you give away in all?

Put these fractions in order from smallest to largest. 200303\frac { 200 } { 303 }303200​ 69\frac { 6 } { 9 }96​ 912\frac { 9 } { 12 }129​ 203300\frac { 203 } { 300 }300203​

Sketch a line segment that is 12.5% longer than 8 inches. How long is the line segment you sketched?

Name three ways of thinking about the symbol 78\frac { 7 } { 8 }87​

Reasoning About Quantities

Numeration Systems

Understanding Whole Number Operations

Some Conventional Ways of Computing

Using Numbers in Sensible Ways

Computing With 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

Put these amounts in order, from smallest to largest: $8.5 \% \quad 1.7 \quad \frac{15}{11} \quad \frac{14}{8} \quad 110 \%$

$\frac { 4 } { 5 } - \frac { 5 } { 8 }$ Is NOT equivalent to:

Correct the following statement so that it is true in some nontrivial way: If D = $0.7\overline{42}$ , then 100D = 74.200.

Put these fractions in order from smallest to largest. $\frac { 200 } { 303 }$ $\frac { 6 } { 9 }$ $\frac { 9 } { 12 }$ $\frac { 203 } { 300 }$

Name three ways of thinking about the symbol $\frac { 7 } { 8 }$