Fractions on a Number Line

Show your work for each problem.

1.
A number line from to is divided into equal parts. Where is located?
1. a)At
2. b)At the first mark after
3. c)At the second mark after
4. d)At the third mark after
Answer: At the first mark after
means 1 out of 4 equal parts. Since the numerator is 1, we count 1 part from , which places us at the first mark.
2.
A number line from to is divided into equal parts. A point is at the second mark. What fraction is this?
Answer: 2/5
The line is divided into 5 equal parts, so the denominator is 5. The point is at the second mark, so the numerator is 2. The fraction is .
3.
Where is located on a number line from to ?
1. a)Exactly in the middle
2. b)At
3. c)Closer to
4. d)Closer to
Answer: Exactly in the middle
divides the interval from to into 2 equal parts. Taking 1 part puts us exactly halfway, in the middle between and .
4.
How many equal parts should you divide the interval to into to place ?
Answer: 8
The denominator tells us how many equal parts to divide the interval into. For , the denominator is 8, so we divide into 8 equal parts.
5.
Place on a number line from to .
Answer: 3rd mark
1. What is the denominator of ? 4
2. Into how many equal parts do you divide the interval? 4
3. What is the numerator? 3
4. At which mark from is ? 3
6.
Which fraction is located at the same point as on a number line?
1. a)
2. b)
3. c)
4. d)
Answer:
because both 2 and 4 can be divided by 2. Equivalent fractions occupy the same point on the number line.
7.
A fraction is located at the 5th mark on a number line divided into 6 equal parts from to . What is this fraction?
Answer: 5/6
The line is divided into 6 parts (denominator = 6). The point is at the 5th mark (numerator = 5). The fraction is .
8.
Is between and , or past on the number line?
Answer: past 1
1. What is the numerator of ? 5
2. What is the denominator of ? 4
3. Is the numerator greater than, less than, or equal to the denominator? greater
4. When numerator > denominator, is the fraction past ? yes
9.
Which fraction is closest to on the number line?
1. a)
2. b)
3. c)
4. d)
Answer:
is closest to because is only away from . Compare: , , , .
10.
Convert to a mixed number and describe its position on a number line.
Answer: 1 3/4
1. How many times does 4 go into 7? 1
2. What is the remainder when 7 is divided by 4? 3
3. Write the mixed number (whole part and fraction part): 1 3/4
4. Between which two whole numbers is ? 1 and 2
11.
On a number line divided into eighths, which mark represents ?
1. a)The 6th mark
2. b)The 8th mark
3. c)The 3rd mark
4. d)The 4th mark
Answer: The 6th mark
(multiply both by 2). On a line divided into 8 parts, is at the 6th mark.
12.
A number line from to is divided into 8 equal parts. What fraction is at the 5th mark?
Answer: 5/4
The line spans 2 units divided into 8 parts, so each part is . The 5th mark is .
13.
Place on a number line. What is its position as a mixed number?
Answer: 1 2/3
1. Is greater than 1? (Is 5 > 3?) yes
2. How many whole groups of 3 are in 5? 1
3. What is the remainder? 2
4. Write as a mixed number: 1 2/3
14.
Which statement is true about and on a number line?
1. a)They are at the same point
2. b) is to the right of
3. c) is past
4. d) is to the right of
Answer: is to the right of
because (same denominator). On a number line, larger numbers are to the right, so is to the right of .
15.
Order these fractions from least to greatest using a number line: , ,
Answer: 1/4, 1/2, 3/4
1. Which fraction is closest to ? 1/4
2. Which fraction is in the middle between and ? 1/2
3. Which fraction is closest to ? 3/4
4. Write them in order from least to greatest: 1/4, 1/2, 3/4