Some friends shared a plate of nachos. Evan ate
1
6
of the nachos. Mickey ate
1
6
more than Sue. Sue ate the same amount of the nachos as Evan. Zoe ate
1
6
less than Mickey. Who ate the most nachos?
A number line from zero to one is shown, with tick marks labeled zero, one-sixth, two-sixths, three-sixths, four-sixths, five-sixths, and one.
Evan ate 1/6 of the nachos, which is between zero and one-sixth on the number line. Sue ate the same amount as Evan, so she also ate 1/6 of the nachos. Mickey ate 1/6 more than Sue, which is 2/6 or 1/3 of the nachos, which is between one-fourth and one-half on the number line. Zoe ate 1/6 less than Mickey, which is 1/6 + 1/6 or 2/6 of the nachos, which is the same as 1/3 of the nachos that Mickey ate. Therefore, Zoe also ate between one-fourth and one-half of the nachos.
Since Mickey and Zoe both ate the same amount and they ate more than Evan and Sue, the answer is that Mickey and Zoe both ate the most nachos, but they ate the same amount.
Some friends shared a plate of nachos. Evan ate
1
6
of the nachos. Mickey ate
1
6
more than Sue. Sue ate the same amount of the nachos as Evan. Zoe ate
1
6
less than Mickey. Who ate the most nachos?
A number line from zero to one is shown, with tick marks labeled zero, one-sixth, two-sixths, three-sixths, four-sixths, five-sixths, and one.
A.
Evan
B.
Mickey
C.
Zoe
D.
Sue
The correct answer is (B) Mickey.
Malik has a red wire that is 4 yards long and a blue wire that is 6 yards long.
He uses
2
4
of the red wire and
3
6
of the blue wire.
Conjecture: Malik uses the same amount of red and blue wire.
Which diagrams could you use to help justify the conjecture? Select all that apply.
We can use the bar model or the tape diagram to help justify the conjecture.
The bar model can be drawn as follows:
```
Red wire: ----------------- (4 yards)
|---| (2/4 of 4 yards)
Blue wire: --------------------- (6 yards)
|----| (3/6 of 6 yards)
```
We can see that both wires are divided into two equal parts, so Malik uses the same amount of red and blue wire (2/4 = 3/6).
The tape diagram can be drawn as follows:
```
2 2
[------][------]
| 4 | 6 |
[------][------]
R B
```
We can see that both wires are divided into two equal parts of 2 yards each, so Malik uses the same amount of red and blue wire.
Spencer is wrapping a present with ribbon. She has a pink ribbon that is 6 feet long and a blue ribbon that is 8 feet long. She uses
3
6
of the pink ribbon and
4
8
of the blue ribbon. Did she use the same amount of each ribbon? Justify your answer using the drop-down menus.
The fractions
3
6
and
4
8
Choose...
equivalent. However, because they refer to wholes that are
Choose...
size, Spencer
Choose...
the same amount of pink and blue ribbon.
The fractions 3/6 and 4/8 are equivalent. However, because they refer to wholes that are different sizes, Spencer did not use the same amount of pink and blue ribbon.
Spencer is wrapping a present with ribbon. She has a pink ribbon that is 6 feet long and a blue ribbon that is 8 feet long. She uses
3
6
of the pink ribbon and
4
8
of the blue ribbon. Did she use the same amount of each ribbon? Justify your answer using the drop-down menus.
The fractions
3
6
and
4
8
Choose...
equivalent. However, because they refer to wholes that are
Choose...
size, Spencer
Choose...
the same amount of pink and blue ribbon.
The fractions 3/6 and 4/8 are equivalent. Because they refer to wholes that are different sizes, Spencer did not use the same amount of pink and blue ribbon.
Elijah and Destiny are eating submarine sandwiches. The sandwiches are the same size.
Elijah eats
1
3
of his sandwich and Destiny eats
2
6
of her sandwich.
Elijah thinks Destiny ate more than he did because 2 is more than 1, and he ate only one-third while Destiny ate two-sixths. Use the drop-down menu to agree or disagree with Elijah. Then complete the sentence to explain your answer.
Elijah ate the same amount as Destiny.
Choose...
The fractions
1
3
and
2
6
are
Choose...
and name the same part of the whole.
Elijah and Destiny ate the same amount. The fractions 1/3 and 2/6 are equivalent and name the same part of the whole.
Use the diagram to answer all parts of the item. The fraction represented by the yellow part will be referred to as the yellow fraction, and the fraction represented by the green parts will be referred to as the green fraction.
Three equal-sized bars are shown. The top bar has no divisions. The middle bar is divided into 2 parts, with 1 part colored yellow. The bottom bar is divided into 10 parts, with 4 parts colored green.
Part A
Select which fractions are shown by the yellow fraction (first) and the green fraction (second).
A.
2
4
and
1
10
B.
1
2
and
4
10
C.
2
2
and
4
10
D.
1
2
and
5
2
1245
Part B
Find a fraction that is both equivalent to the yellow fraction and has the same denominator as the green fraction.
Drag the correct number into the box to complete the fraction.
______
10
Part A:
The yellow fraction represents 1/2, and the green fraction represents 4/10, which simplifies to 2/5. Therefore, the answer is (B) 1/2 and 2/5.
Part B:
To find a fraction that is both equivalent to 1/2 and has the same denominator as 2/5, we need to find the least common multiple (LCM) of 2 and 5, which is 10. Then we can convert 1/2 into a fraction with denominator 10:
1/2 = 5/10
Therefore, the equivalent fraction is 5/10.