40 Fractions Practice Questions & Answers

1. 1. On a number line, the space from 0 to 1 is split into 6 equal jumps. Maya puts a dot 4 jumps from 0. What fraction is at the dot?

   • A.6/4
   • B.4/6✓ Answer
   • C.1/6
   • D.5/6

   Each jump is 1/6 because 0 to 1 is cut into 6 equal parts, so count the jumps (the spaces), not the tick marks. Four jumps of 1/6 land on 4/6. The tempting 5/6 comes from counting the tick at 0 as "one".

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2. 2. A number line goes from 0 to 2. The space from 0 to 1 is split into 4 equal jumps, and so is the space from 1 to 2. Diego's point is 5 jumps from 0. What fraction is at his point?

   • A.6/4
   • B.5/4✓ Answer
   • C.1/4
   • D.5/8

   The whole is the space from 0 to 1, so each jump is 1/4, even past 1. Five jumps of 1/4 make 5/4, which is one jump past 1. Choosing 5/8 means treating 0 to 2 as the whole.

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3. 3. A number line from 0 to 1 has 4 tick marks: one at 0, one at 1, and 2 more spaced equally between them. What fraction of the whole is each space between two ticks?

   • A.1/3✓ Answer
   • B.1/4
   • C.1/2
   • D.3/3

   Four tick marks make only 3 spaces, and the spaces are equal, so each space is 1/3 of the whole. Count the spaces, not the ticks. Picking 1/4 is the tick-counting mistake.

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4. 4. On a number line, the space from 0 to 1 is split into 4 equal jumps. Arjun marks the point 4/4. Where is his point?

   • A.One jump before the tick mark for 1
   • B.One jump past the tick mark for 1
   • C.Exactly halfway from 0 to 1
   • D.Exactly on the tick mark for 1✓ Answer

   Four jumps of 1/4 cover the whole space from 0 to 1, so 4/4 lands exactly on 1. Placing it one jump past 1 comes from counting the tick at 0 as the first jump.

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5. 5. A number line goes from 0 to 3. Each space from one whole number to the next is split into 2 equal jumps. Fatima's point is 3 jumps from 0. What fraction is at her point?

   • A.3/6
   • B.4/2
   • C.3/2✓ Answer
   • D.2/3

   Each whole (0 to 1, 1 to 2, 2 to 3) has 2 equal jumps, so each jump is 1/2. Three jumps of 1/2 make 3/2, halfway between 1 and 2. Choosing 3/6 means treating the whole line from 0 to 3 as one whole.

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6. 6. Kofi wants to put 3/6 on a number line that goes from 0 to 1. Which steps put it in the right place?

   • A.Split 0 to 1 into 3 equal jumps, then count 6 jumps from 0
   • B.Split 0 to 1 into 6 equal jumps, then count 3 jumps from 0✓ Answer
   • C.Split 0 to 1 into 3 equal jumps, then count 3 jumps from 0
   • D.Draw 6 evenly spaced ticks from 0 to 1, stop at the 3rd

   The bottom number, 6, tells how many equal jumps make the whole from 0 to 1, and the top number, 3, tells how many of those jumps to count from 0. Drawing 6 ticks instead of 6 jumps makes only 5 spaces, so the 3rd tick lands in the wrong place.

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7. 7. A ribbon is 1 meter long. Marks split it into 6 equal parts. Nina cuts off 5 of those parts in a row from one end. How long is the piece she cut?

   • A.4/6 meter
   • B.6/6 meter
   • C.5/6 meter✓ Answer
   • D.1/6 meter

   Think of the ribbon as a number line from 0 to 1 meter cut into 6 equal parts, so each part is 1/6 meter. Five parts of 1/6 meter make 5/6 meter. Choosing 1/6 meter gives the length of just one part, not the whole piece she cut.

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8. 8. On a number line, each space from one whole number to the next is split into 4 equal jumps. Between which two whole numbers is 7/4?

   • A.Between 2 and 3
   • B.Between 6 and 7
   • C.Between 1 and 2✓ Answer
   • D.Between 0 and 1

   Four jumps of 1/4 reach 1 (4/4 = 1), and four more would reach 2 (8/4 = 2). Seven jumps is past 1 but not yet at 2, so 7/4 is between 1 and 2. Choosing 0 and 1 comes from thinking every fraction is less than 1.

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9. 9. Priya draws four number lines. Which one shows a point at 2/3?

   • A.From 0 to 2 in 3 equal jumps; the point is 2 jumps from 0
   • B.From 0 to 1 in 2 equal jumps; the point is 3 jumps from 0
   • C.From 0 to 1 in 3 equal jumps; the point is 2 jumps from 0✓ Answer
   • D.From 0 to 1 in 3 equal jumps; the point is 2 jumps from 1

   For 2/3, the whole from 0 to 1 is cut into 3 equal jumps, and the point is 2 of those jumps from 0. Counting 2 jumps back from 1 lands on 1/3, and cutting 0 to 2 into 3 jumps makes each jump longer than 1/3.

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10. 10. A number line goes from 0 to 2. It has 8 equal jumps in all, from 0 to 2. Lucas's point is 3 jumps from 0. What fraction is at his point?

    • A.3/4✓ Answer
    • B.4/8
    • C.8/3
    • D.3/8

    The whole is 0 to 1, not 0 to 2. Eight equal jumps across 2 wholes means 4 jumps in each whole, so each jump is 1/4 and 3 jumps make 3/4. Choosing 3/8 is the common mistake of using the whole line as the whole.

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11. 11. Zara's sandwich is cut into 4 equal pieces. She eats 1 piece. What fraction of the sandwich did she eat?

    • A.1/4✓ Answer
    • B.1/3
    • C.1/2
    • D.3/4

    The bottom number is how many equal pieces make the whole sandwich (4), and the top number is how many she ate (1), so she ate 1/4. Choosing 3/4 names the part that is left, not the part she ate.

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12. 12. Sofia has a ribbon cut into 8 equal pieces. She uses 3 pieces for a bow. What fraction of the ribbon did she use?

    • A.1/8
    • B.5/8
    • C.8/3
    • D.3/8✓ Answer

    Each piece is 1/8 of the ribbon because the whole ribbon was cut into 8 equal pieces. Three pieces of 1/8 make 3/8. Choosing 5/8 names the pieces left over, and 1/8 is the size of just one piece.

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13. 13. Leo's family orders 4 pizzas, each cut a different way. Which pizza is cut into fourths?

    • A.Cut into 4 slices, with 2 big and 2 small ones
    • B.Cut into 4 slices, with 1 big and 3 small ones
    • C.Cut into 8 slices that are all the same size
    • D.Cut into 4 slices that are all the same size✓ Answer

    Fourths means the whole is cut into 4 EQUAL parts, so each slice is 1/4. Four slices of different sizes are not fourths, even though there are 4 of them, and 8 equal slices are eighths.

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14. 14. Aiko's mom cuts a cake into 6 equal pieces. What fraction of the cake is 1 piece?

    • A.5/6
    • B.1/6✓ Answer
    • C.1/2
    • D.6/6

    When a whole is cut into 6 equal pieces, each piece is the unit fraction 1/6: 1 piece out of 6 equal pieces. Choosing 5/6 names the 5 pieces that are left, and 6/6 is the whole cake.

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15. 15. Kenji has 5/8 of a pan of brownies. Each piece in the pan is 1/8 of the pan. How many pieces does Kenji have?

    • A.13 pieces
    • B.8 pieces
    • C.5 pieces✓ Answer
    • D.3 pieces

    A fraction like 5/8 means 5 parts that are each 1/8, so Kenji has 5 pieces. Choosing 8 pieces counts every piece in the whole pan, which is what the bottom number tells you.

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16. 16. Amara's class bakes a pan of cornbread and cuts it into equal pieces. Each piece is 1/8 of the pan. How many pieces are in the whole pan?

    • A.4 pieces
    • B.9 pieces
    • C.7 pieces
    • D.8 pieces✓ Answer

    The unit fraction 1/8 means the whole was cut into 8 equal pieces, so the pan holds 8 pieces. Choosing 7 comes from counting cuts instead of pieces: 7 cuts side by side make 8 pieces (and 9 counts the cut lines plus both edges).

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17. 17. A tray holds 6 cupcakes that are all the same size. Jamal puts sprinkles on 2 of them. What fraction of the cupcakes have sprinkles?

    • A.6/2
    • B.4/6
    • C.2/4
    • D.2/6✓ Answer

    The whole is all 6 cupcakes, so each cupcake is 1/6 of the group and 2 cupcakes are 2/6. Choosing 2/4 compares the cupcakes with sprinkles to the 4 without, instead of to all 6.

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18. 18. Ines used 3/8 of a ribbon. What does the 8 in 3/8 tell you?

    • A.Ines used 8 of the equal pieces of the ribbon
    • B.The whole ribbon was cut into 8 pieces of any size
    • C.The whole ribbon was cut into 8 equal pieces✓ Answer
    • D.Each equal piece of the ribbon is 8 inches long

    The bottom number tells how many equal pieces make the whole, and the top number tells how many of those pieces are counted. So the 8 means the ribbon was cut into 8 equal pieces, and the pieces must be equal, not just any size.

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19. 19. Wei ate 2/6 of a pizza. What does the 2 in 2/6 tell you?

    • A.The pizza was cut into 2 equal slices in all
    • B.Wei ate 2 of the 6 equal slices of that pizza✓ Answer
    • C.Wei left 2 of the 6 equal slices on the plate
    • D.Each of the slices Wei ate was 2 inches wide

    The top number counts how many equal parts are being talked about, and the bottom number tells how many equal parts make the whole. So 2/6 means Wei ate 2 of the 6 equal slices.

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20. 20. A chocolate bar breaks into 4 pieces of different sizes. Hana takes 1 piece. Did she take 1/4 of the bar?

    • A.No, because she would need to take all 4 pieces
    • B.Yes, because the bar broke into exactly 4 pieces
    • C.Yes, because she took exactly 1 of the 4 pieces
    • D.No, because the 4 pieces are not all the same size✓ Answer

    A piece is 1/4 only when the whole is cut into 4 EQUAL parts. These 4 pieces are different sizes, so one of them is not 1/4 of the bar, even though there are 4 pieces.

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21. 21. Maya and Leo have sandwiches that are the same size. Maya cuts hers into 2 equal pieces and eats 1 piece. Leo cuts his into 4 equal pieces. What fraction of his sandwich must Leo eat to eat the same amount as Maya?

    • A.1/4
    • B.4/4
    • C.2/4✓ Answer
    • D.3/4

    When each half is cut into 2 equal pieces, there are 4 pieces in all, and Maya's half is now 2 of those pieces. So 1/2 = 2/4. The tempting mistake is 1/4: keeping the top number 1 forgets that fourths are smaller pieces, so one fourth is less than one half.

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22. 22. Which fraction is equal to 1/2?

    • A.3/6✓ Answer
    • B.2/3
    • C.3/4
    • D.2/8

    A fraction equals 1/2 when the shaded parts are exactly half of all the equal parts. 3 is half of 6, so 3/6 = 1/2. 2/8 is a common wrong pick because it has the same top number as 2/4, but 2 is only a quarter of 8.

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23. 23. Two strips of paper are the same size. The first strip is split into 3 equal parts, and 2 parts are shaded. The second strip is split into 6 equal parts. How many sixths must be shaded so both strips show the same amount?

    • A.4/6✓ Answer
    • B.3/6
    • C.5/6
    • D.2/6

    Each third of the first strip is the same size as 2 sixths. Two thirds is 2 groups of 2 sixths, which is 4 sixths, so 2/3 = 4/6. Picking 2/6 comes from copying the top number without noticing that sixths are smaller pieces than thirds.

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24. 24. Two number lines are the same length and both go from 0 to 1. The top line is split into 4 equal parts. The bottom line is split into 8 equal parts. A point sits at 3/4 on the top line. Which point on the bottom line is in exactly the same place?

    • A.4/8
    • B.3/8
    • C.7/8
    • D.6/8✓ Answer

    Fractions at the same point on a number line are equal. Each fourth on the top line covers 2 eighths on the bottom line, so 3 fourths line up with 6 eighths, and 3/4 = 6/8. Choosing 3/8 keeps the top number 3 but lands much closer to 0.

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25. 25. A paper strip is split into 3 equal parts, and 1 part is shaded, so it shows 1/3. Ana cuts every part into 2 equal pieces. Which sentence tells what the strip shows now?

    • A.There are 4 equal parts, 2 are shaded, so it shows 2/4.
    • B.There are 4 parts not shaded, 2 shaded, so it shows 2/4.
    • C.There are 6 equal parts and 1 is shaded, so it shows 1/6.
    • D.There are 6 equal parts and 2 are shaded, so it shows 2/6.✓ Answer

    Cutting every part into 2 doubles the number of parts (3 becomes 6) and also doubles the shaded parts (1 becomes 2), while the shaded amount stays the same. So the strip shows 2/6, which equals 1/3. Writing 2/4 is the shaded-over-unshaded mistake: the bottom number must count all 6 parts, not just the 4 unshaded ones.

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26. 26. Which list shows three fractions that are ALL equal to 1/2?

    • A.2/4, 2/6, 2/8
    • B.3/4, 4/6, 5/8
    • C.2/4, 3/6, 4/8✓ Answer
    • D.1/4, 1/6, 1/8

    In each fraction equal to 1/2, the top number is exactly half of the bottom number: 2 is half of 4, 3 is half of 6, and 4 is half of 8. The list 2/4, 2/6, 2/8 is the trap: keeping the same top number while the pieces get smaller makes each fraction smaller, not equal.

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27. 27. Kenji and Sofia have pizzas that are the same size. Kenji's pizza is cut into 4 equal slices, and he eats 1 slice. Sofia's pizza is cut into 8 equal slices. How many slices must Sofia eat to eat the same amount as Kenji?

    • A.3 of the 8 slices
    • B.2 of the 8 slices✓ Answer
    • C.1 of the 8 slices
    • D.4 of the 8 slices

    An eighth-slice is half the size of a fourth-slice, so it takes 2 eighths to cover one fourth. That means 1/4 = 2/8, and Sofia must eat 2 slices. Answering 1 slice forgets that Sofia's slices are smaller than Kenji's.

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28. 28. Two strips of paper are the same size. One is split into 4 equal parts with 3 shaded, so it shows 3/4. The other is split into 8 equal parts with 6 shaded, so it shows 6/8. Why are 3/4 and 6/8 equal?

    • A.Each fourth is the same size as 2 eighths, so both cover the same amount.✓ Answer
    • B.6 and 8 are both even numbers, so 6/8 must be the same size as 3/4.
    • C.3 plus 3 is 6 and 4 plus 4 is 8, so adding the same number keeps it equal.
    • D.Both strips have exactly 1 part left unshaded, so the shaded parts match.

    Equal fractions cover the same amount of the same-size whole. Splitting each fourth into 2 eighths turns 3 shaded fourths into 6 shaded eighths, so the shaded length does not change. The adding idea fails: 3 + 3 and 4 + 4 happen to work here, but 1/2 with 1 added to each number gives 2/3, which is not equal to 1/2.

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29. 29. Which fraction is the same as the whole number 3?

    • A.3/6
    • B.3/3
    • C.1/3
    • D.3/1✓ Answer

    A whole number can be written as a fraction with 1 on the bottom: each whole is 1 part, and you count 3 of them. So 3 = 3/1. The common mix-up is 3/3, but 3/3 is only 1 whole.

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30. 30. At a bake sale, every pie is the same size and is cut into 3 equal pieces. Tyrone buys 6 pieces, which is 6/3 of a pie. How many whole pies is that?

    • A.9 whole pies
    • B.3 whole pies
    • C.2 whole pies✓ Answer
    • D.6 whole pies

    Every 3 pieces make 1 whole pie, so count groups of 3 in 6 pieces: 3 + 3 = 6 makes 2 groups. So 6/3 = 2 whole pies. Answering 3 pies uses the bottom number, which only tells how many pieces make one pie.

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31. 31. Priya's garden bed is split into 6 equal rows. She plants carrots in all 6 rows. Which tells the fraction of the bed with carrots?

    • A.6/6, which is equal to 1 whole bed✓ Answer
    • B.6/6, which is a little less than 1 bed
    • C.1/6, which is one row of the whole bed
    • D.6/1, which is equal to 6 whole beds

    The bed has 6 equal rows and all 6 have carrots, so the fraction is 6/6. When the top and bottom numbers match, every part is used, so 6/6 = 1 whole bed. Thinking 6/6 is less than 1 is a common mistake; nothing is left over.

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32. 32. Coach Amara has 4 whole oranges. None of them are cut. Which fraction tells how many whole oranges she has?

    • A.4/1✓ Answer
    • B.4/8
    • C.4/4
    • D.1/4

    Each uncut orange is 1 whole part, so the bottom number is 1 and the top number counts the oranges: 4/1 = 4. 4/4 is the tempting wrong answer, but 4/4 equals only 1 whole orange cut into 4 equal parts.

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33. 33. Zoe and Omar have ribbons that are the same length. Zoe uses 3/8 of her ribbon. Omar uses 5/8 of his ribbon. Which comparison is true?

    • A.3/8 = 5/8
    • B.3/8 > 5/8
    • C.5/8 < 3/8
    • D.3/8 < 5/8✓ Answer

    When the bottom numbers match, the pieces are the same size, so more pieces means a bigger fraction. 3 eighths is fewer pieces than 5 eighths, so 3/8 < 5/8. Saying they are equal because both are eighths ignores how many pieces were used.

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34. 34. Which comparison of 1/6 and 1/3 is true?

    • A.1/3 < 1/6
    • B.1/6 < 1/3✓ Answer
    • C.1/6 = 1/3
    • D.1/6 > 1/3

    When the top numbers match, compare the size of the pieces. Cutting the same whole into 6 equal parts makes smaller pieces than cutting it into 3, so 1/6 < 1/3. Picking 1/6 > 1/3 is the mistake of thinking a bigger bottom number means a bigger fraction.

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35. 35. Two cakes are the same size. Which sentence correctly compares 2/8 of one cake and 2/4 of the other cake?

    • A.2/8 < 2/4, because eighths are smaller pieces than fourths.✓ Answer
    • B.2/8 > 2/4, because 8 is a bigger number than 4 is.
    • C.2/8 = 2/4, because both of them have 2 as the numerator.
    • D.2/8 > 2/4, because eighths are bigger pieces than fourths.

    Both fractions have 2 pieces, so compare how big each piece is. A cake cut into 8 equal parts has smaller pieces than one cut into 4, so 2 eighths is less than 2 fourths. Saying 2/8 is bigger because 8 > 4 is whole-number thinking.

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36. 36. Lena eats 1/2 of a small pizza. Max eats 1/2 of a large pizza. Did they eat the same amount of pizza?

    • A.No, Max ate more, because half of a big pizza is bigger.✓ Answer
    • B.Yes, they ate the same, because 1/2 is always one amount.
    • C.Yes, they ate the same, because each of them ate 1/2.
    • D.No, Lena ate more, because a small pizza has bigger halves.

    Fractions can only be compared when they are parts of the same-size whole. Half of a large pizza is more pizza than half of a small pizza, so Max ate more. The answer that says both ate 1/2 forgets that the two wholes are different sizes.

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37. 37. All of these fractions are parts of the same-size whole: 2/3, 2/4, 2/6 and 2/8. Which fraction is the smallest?

    • A.2/4
    • B.2/8✓ Answer
    • C.2/3
    • D.2/6

    All four fractions have 2 pieces, so the one with the smallest pieces is the smallest. Eighths are the smallest pieces because the whole is cut into the most parts, so 2/8 is smallest. Choosing 2/3 comes from thinking the smallest bottom number gives the smallest fraction.

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38. 38. Ava and Ben have garden beds that are the same size. Ava plants beans in 4/6 of her bed. Ben plants beans in 5/6 of his bed. Who planted beans in more of the bed?

    • A.Neither, because both of the beds are cut in sixths.
    • B.Ben, because 5 sixths is more parts than 4 sixths.✓ Answer
    • C.Ava, because 4 sixths leaves more of her bed empty.
    • D.Ava, because her fraction has the smaller numerator.

    The beds are the same size and both are split into sixths, so each sixth is the same size. Then the fraction with more sixths is greater: 5/6 > 4/6, so Ben planted more. Saying neither ignores that Ben used more of the same-size parts.

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39. 39. Ming and Rafael have chocolate bars that are the same size. Ming's bar is cut into 4 equal pieces. Rafael's bar is cut into 8 equal pieces. Each of them eats 3 pieces. Which sentence is true?

    • A.Rafael ate more, because his bar has more pieces in it.
    • B.Ming ate more, because fourths are bigger than eighths.✓ Answer
    • C.They ate the same, because each one ate 3 pieces.
    • D.Rafael ate more, because 8 is a bigger number than 4.

    Ming ate 3/4 and Rafael ate 3/8. The top numbers match, so compare piece size: a bar cut into 4 equal pieces has bigger pieces than one cut into 8, so 3/4 > 3/8. Saying they ate the same counts pieces without checking how big each piece is.

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40. 40. Which comparison is true? All the fractions are parts of the same-size whole.

    • A.3/6 > 3/4
    • B.5/8 < 3/8
    • C.3/4 > 3/6✓ Answer
    • D.2/3 < 2/6

    Check each one with the matching number. 3/4 and 3/6 both have 3 pieces, and fourths are bigger than sixths, so 3/4 > 3/6 is true. 2/3 < 2/6 is false because thirds are bigger than sixths, and 5/8 < 3/8 is false because 5 eighths is more than 3 eighths.

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