Tina and Gray each had the same length of string. Tina used 3/4 of her string.
Using eighths, what fraction of the length of the string will Gray need to use to match the amount Tina used?
Use the number line to help find your answer.
We can use a number line to help us visualize the fraction of the string that Tina used and the fraction that Gray needs to use to match her. Let's represent the length of the string as 8 units, since we are asked to use eighths.
__ __ __ __ __ __ __ __
0 1 2 3 4 5 6 7 8
Tina used 3/4 of her string, which is 6 units:
__ __ __ __ __ __ XX XX
0 1 2 3 4 5 6 7 8
Tina used the units marked with X.
To find out what fraction of the length of the string Gray needs to use to match Tina, we need to divide 6 units by the total length of the string, which is 8 units:
6 ÷ 8 = 3/4
So, Gray needs to use 3/4 of the length of the string to match the amount Tina used. We can represent this on the number line as follows:
__ __ __ __ __ __ XX XX
0 1 2 3 4 5 6 7 8
Gray needs to use the units marked with X. They are lined up with the units Tina used, so Gray needs to use 3/4 of the length of the string to match her.
Complete the equations by entering the whole numbers that are equal to the fractions.
8
8
=
3
3
=
30
10
=
9
3
=
6
3
=
12
6
=
8/8 = 1
3/3 = 1
30/10 = 3
9/3 = 3
6/3 = 2
12/6 = 2
Which fractions are closer to 0 than to 1? Select all that apply.
A.
5
8
B.
2
6
C.
1
4
D.
4
6
E.
3
8
A fraction is closer to 0 than to 1 if its value is less than 1/2, since it is closer to 0 on the number line than to 1. We can simplify each fraction by dividing the numerator and denominator by their greatest common factor (GCF) to help us compare their values.
A. 5/8 cannot be simplified. Its value is greater than 1/2, so it is not closer to 0 than to 1.
B. 2/6 can be simplified to 1/3. Its value is less than 1/2, so it is closer to 0 than to 1.
C. 1/4 cannot be simplified. Its value is less than 1/2, so it is closer to 0 than to 1.
D. 4/6 can be simplified to 2/3. Its value is greater than 1/2, so it is not closer to 0 than to 1.
E. 3/8 cannot be simplified. Its value is less than 1/2, so it is closer to 0 than to 1.
Therefore, the fractions that are closer to 0 than to 1 are:
- 1/3
- 1/4
- 3/8
The answer is (B) and (C) and (E).
Cindy read for
3
6
of an hour on Friday. She read for
3
4
of an hour on Saturday. On Sunday, she read for
2
8
of an hour.
Use benchmark numbers to find on which day Cindy read the least amount of time.
A.
Friday
B.
Saturday
C.
Sunday
D.
Cindy read the same amount each day.
We can use benchmark fractions to compare the amounts of time Cindy read each day. A benchmark fraction is a common fraction that is easy to recognize and remember, such as 1/2 or 1/4.
Let's use 1/2 as our benchmark fraction and compare each fraction to it.
- Friday: 3/6 = 1/2, which means Cindy read for half an hour on Friday.
- Saturday: 3/4 is greater than 1/2, which means Cindy read for more than half an hour on Saturday.
- Sunday: 2/8 = 1/4, which means Cindy read for a quarter of an hour on Sunday.
Therefore, Cindy read the least amount of time on Sunday, so the answer is (C) Sunday.