Question 1

Make up a story problem that could be solved by $3 \frac { 1 } { 2 } - 2 \frac { 1 } { 3 }$ 
 and illustrates the comparison view of subtraction.

Accepted Answer

There are various possibilities, but in each the two quantities should be distinct. For example, one recipe calls for $3 \frac { 1 } { 2 }$ 
 cups of sugar, and another calls for $2 \frac { 1 } { 3 }$ 
 cups of sugar. How much more sugar does the first recipe call for than the second?

Question 2

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

Accepted Answer

There are various possibilities. For example, Velma had 123 feet of ribbon and used 48 $\frac { 1 } { 3 }$ 
 for package bows. How much ribbon does she have left?

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

Four identical pizzas are shared among three people. Show two ways that the pizzas could be cut.

Accepted Answer

The answer of Four identical pizzas are shared among three...

Question 5

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

The answer of Using a rectangular region as the unit,...

Question 6

Explain a strategy you could use to mentally compute the exact answer to the following.
A) $2 \frac { 3 } { 8 } + 5 \frac { 1 } { 4 } + 3 \frac { 7 } { 8 } + 2$

B) $2 \frac { 4 } { 5 } + 3 \frac { 1 } { 6 } + 5 \frac { 2 } { 3 } - 1.8$

C) $3 \frac { 1 } { 2 } - 2 \frac { 3 } { 8 }$

Accepted Answer

The answer of Explain a strategy you could use to...

Question 7

Why is a common denominator needed to add and subtract fractions?

Accepted Answer

The answer of Why is a common denominator needed to...

Question 8

Three children took a hike, carrying one heavy backpack. One child carried the backpack for 3/8 of the hike, and a second carried it for 1/6 of the hike. For what part of the hike did the third child carry the backpack? Which child carried the backpack for the greatest part of the hike?

Accepted Answer

The answer of Three children took a hike, carrying one...

Question 9

Jody mows 1/8 of the yard then takes a break. After the break, Jody mows another 1/3 of the yard then stops for lunch. After lunch, Jody mows another 1/6 of the yard and then goes swimming. What part of the yard does Jody still have to mow?

Accepted Answer

The answer of Jody mows 1/8 of the yard then...

Question 10

The vegetable farmer has planted 1/3 of a field in cherry tomatoes, 1/5 of the field in large tomatoes, and 2/7 of the field in popcorn. The farmer plans to plant sweet corn in the remaining part of the field. What part of the field will be in sweet corn? Use number sense to describe this part with a more familiar fraction.

Accepted Answer

The answer of The vegetable farmer has planted 1/3 of...

Question 11

Emmy wants to read an assigned book in four days. She reads 2/3 of the book the first day, only 1/15 of the book the second day, and another 1/15 of the book on the third day.
A) What part of the book must she read the fourth day?
B) On which day did Emmy read the most?

Accepted Answer

The answer of Emmy wants to read an assigned book...

Question 12

Judy has a 10-page paper to write. The first day she writes $1 \frac { 1 } { 2 }$ 
 pages, takes a break, and then writes $3 \frac { 3 } { 4 }$ 
 pages more. The next day, she writes another $2 \frac { 1 } { 3 }$ 
 pages. How many pages does she still have to write?

Accepted Answer

The answer of Judy has a 10-page paper to write....

Question 13

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 14

Use a drawing to help explain why $\frac { 3 } { 4 } \times \frac { 5 } { 7 }$ 
 is equal to $\frac { 3 \times 5 } { 4 \times 7 }$ 
. Be explicit.

Accepted Answer

The answer of Use a drawing to help explain why...

Question 15

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

Accepted Answer

If one or both of the numbers are fractions (less than 1), their product will be less than each of the numbers.

Question 16

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

To find the cost of 0.67 pounds of cheese at $1.89 per pound, you multiply the price per pound by the number of pounds: 0.67 × 1.89.

Question 17

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

Accepted Answer

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

Question 18

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 19

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

The answer of Which location on the number line indicated...

Question 20

A) Imagine you were to shade in 3/4 of 2/3 of this rectangle. What would it look like?  
B) Show exactly where 2/3 is. It is 2/3 of what?
C) Show exactly where 3/4 is. It is 3/4 of what?

Accepted Answer

The answer of A) Imagine you were to shade in...

Quiz 7: Computing With Fractions

Make up a story problem that could be solved by 312−2133 \frac { 1 } { 2 } - 2 \frac { 1 } { 3 }321​−231​ and illustrates the comparison view of subtraction.

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

Four identical pizzas are shared among three people. Show two ways that the pizzas could be cut.

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

Why is a common denominator needed to add and subtract fractions?

Three children took a hike, carrying one heavy backpack. One child carried the backpack for 3/8 of the hike, and a second carried it for 1/6 of the hike. For what part of the hike did the third child carry the backpack? Which child carried the backpack for the greatest part of the hike?

Jody mows 1/8 of the yard then takes a break. After the break, Jody mows another 1/3 of the yard then stops for lunch. After lunch, Jody mows another 1/6 of the yard and then goes swimming. What part of the yard does Jody still have to mow?

Emmy wants to read an assigned book in four days. She reads 2/3 of the book the first day, only 1/15 of the book the second day, and another 1/15 of the book on the third day. A) What part of the book must she read the fourth day? B) On which day did Emmy read the most?

Judy has a 10-page paper to write. The first day she writes 1121 \frac { 1 } { 2 }121​ pages, takes a break, and then writes 3343 \frac { 3 } { 4 }343​ pages more. The next day, she writes another 2132 \frac { 1 } { 3 }231​ pages. How many pages does she still have to write?

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.

Use a drawing to help explain why 34×57\frac { 3 } { 4 } \times \frac { 5 } { 7 }43​×75​ is equal to 3×54×7\frac { 3 \times 5 } { 4 \times 7 }4×73×5​ . Be explicit.

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

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?

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

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

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

A) Imagine you were to shade in 3/4 of 2/3 of this rectangle. What would it look like? B) Show exactly where 2/3 is. It is 2/3 of what? C) Show exactly where 3/4 is. It is 3/4 of what?

Make up a story problem that could be solved by $3 \frac { 1 } { 2 } - 2 \frac { 1 } { 3 }$ and illustrates the comparison view of subtraction.

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

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

Judy has a 10-page paper to write. The first day she writes $1 \frac { 1 } { 2 }$ pages, takes a break, and then writes $3 \frac { 3 } { 4 }$ pages more. The next day, she writes another $2 \frac { 1 } { 3 }$ pages. How many pages does she still have to write?

Use a drawing to help explain why $\frac { 3 } { 4 } \times \frac { 5 } { 7 }$ is equal to $\frac { 3 \times 5 } { 4 \times 7 }$ . Be explicit.