40 Shapes & Equal Parts Practice Questions & Answers

1. 1. Which statement is true about every square?

   • A.Every square is also a rectangle.✓ Answer
   • B.Every square has 2 long and 2 short sides.
   • C.Every square has exactly 2 square corners.
   • D.No square can ever be called a rhombus.

   A rectangle is any 4-sided shape with 4 square corners. A square has 4 square corners, so it always counts as a rectangle; it just also has 4 equal sides. The most common mistake is thinking a square cannot be a rhombus, but a square has 4 equal sides, so it is a rhombus too.

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2. 2. Which shape is both a rhombus and a rectangle?

   • A.A shape with 2 long sides, 2 short sides, and 4 square corners
   • B.A shape with 4 equal sides and 4 square corners✓ Answer
   • C.A shape with 4 sides of different lengths and no square corners
   • D.A shape with 4 equal sides and no square corners

   A rhombus needs 4 equal sides, and a rectangle needs 4 square corners. Only a shape with both attributes, which is a square, belongs to both groups. A shape with 4 equal sides but no square corners is a rhombus only.

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3. 3. Which statement is true?

   • A.Every quadrilateral is a rectangle.
   • B.Every square is a rhombus.✓ Answer
   • C.Every rectangle is a square.
   • D.Every rhombus is a square.

   A rhombus is any 4-sided shape whose 4 sides are all the same length. Every square has 4 equal sides, so every square is a rhombus. The reverse is not true: a rectangle with 2 long and 2 short sides is not a square, and a rhombus with no square corners is not a square.

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4. 4. A shape has 4 straight sides. Each side is 5 cm long. None of its corners are square corners (right angles). Which name fits this shape?

   • A.A rhombus✓ Answer
   • B.A rectangle
   • C.A square
   • D.A pentagon

   Check two things: are the sides equal, and are the corners square corners? All 4 sides are equal, so it is a rhombus. It cannot be a square or a rectangle, because both of those need 4 square corners.

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5. 5. A shape has 4 sides that are 3 cm, 7 cm, 3 cm, and 7 cm long. All 4 of its corners are square corners (right angles). Which statement about this shape is true?

   • A.It is a rhombus, since opposite sides match.
   • B.It is a rectangle, but it is not a square.✓ Answer
   • C.It is a square, but it is not a rectangle.
   • D.It is a pentagon, since it has 5 parts.

   It has 4 square corners, so it is a rectangle. Its sides are not all equal (3 cm is not 7 cm), so it is not a square and not a rhombus. Matching opposite sides are not enough for a rhombus; all 4 sides must be equal.

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6. 6. A shape has 4 sides that are each 6 cm long and 4 square corners (right angles). Which list names the shape correctly?

   • A.Square, rectangle, rhombus, and quadrilateral✓ Answer
   • B.Square, rectangle, and rhombus, but not quadrilateral
   • C.Square, rhombus, and quadrilateral, but not rectangle
   • D.Square, rectangle, and quadrilateral, but not rhombus

   This shape is a square. It has 4 sides, so it is a quadrilateral; it has 4 square corners, so it is a rectangle; and its 4 sides are equal, so it is a rhombus. A shape can have more than one correct name.

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7. 7. Which shape is a quadrilateral but is NOT a rectangle, a rhombus, or a square?

   • A.A shape with sides of 1, 9, 1, and 9 cm and 4 square corners
   • B.A shape with 5 sides of 3 cm each and no square corners
   • C.A shape with 4 sides of 6 cm each, turned to stand on one corner
   • D.A shape with 4 sides of 2, 3, 4, and 5 cm and no square corners✓ Answer

   Check each group in turn. The shape with sides 2, 3, 4, and 5 cm has 4 sides, so it is a quadrilateral, but its sides are not equal and it has no square corners, so it is not a rhombus, rectangle, or square. Turning a shape does not change its group, so the turned shape with 4 equal sides is still a rhombus.

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8. 8. Ravi draws a rhombus. How many vertices (corners) does it have?

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

   A rhombus is a quadrilateral, and every quadrilateral has 4 sides and 4 vertices, one where each pair of sides meets. A child who answers 8 has usually counted the 4 sides and the 4 corners together.

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9. 9. Which attribute do a rectangle and a rhombus ALWAYS share?

   • A.Both have 4 sides of equal length.
   • B.Both have 2 long and 2 short sides.
   • C.Both have 4 square corners.
   • D.Both have exactly 4 sides.✓ Answer

   Look for what is true of every member of both groups. A rhombus does not need square corners, and a rectangle does not need equal sides, but both are always shapes with exactly 4 sides. That shared attribute is what makes them both quadrilaterals.

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10. 10. Which shape is NOT a quadrilateral?

    • A.A closed shape with 4 straight sides and no square corners
    • B.A closed shape with 4 straight sides of different lengths
    • C.A closed shape with 4 equal sides, tilted onto one corner
    • D.A closed shape with 5 straight sides and 5 corners✓ Answer

    Count the sides: a quadrilateral is a closed shape with exactly 4 straight sides. The shape with 5 sides is a pentagon, so it is not a quadrilateral. Unequal sides, missing square corners, or tilting do not stop a 4-sided shape from being a quadrilateral.

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11. 11. Lucia draws a square. Then she turns her paper so the square stands on one corner. What is true about the shape now?

    • A.It is now a diamond, a new shape that is not a square.
    • B.It is now a triangle, since one corner points straight up.
    • C.It is still a square, since its sides and corners did not change.✓ Answer
    • D.It is now a rhombus but not a square, since it is tilted.

    A shape's name depends on its sides and corners, not on which way it is turned. Turning the paper does not change the 4 equal sides or the 4 square corners, so it is still a square (and still a rhombus and a rectangle too).

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12. 12. Omar sorts shapes. He puts every shape that has 4 square corners (right angles) into one group. Which kind of shape ALWAYS belongs in Omar's group?

    • A.Every square✓ Answer
    • B.Every rhombus
    • C.Every 4-sided kite shape
    • D.Every quadrilateral

    Ask whether the attribute is required for that kind of shape. Every square must have 4 square corners, so every square belongs. A rhombus only needs equal sides, and a quadrilateral only needs 4 sides, so many of those have no square corners.

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13. 13. A sorting diagram has two circles that overlap. One circle is for rhombuses. The other circle is for rectangles. Which shapes go in the part where the two circles overlap?

    • A.Rectangles, since all of their corners are square corners
    • B.Rhombuses, since all of their sides are the same length
    • C.Squares, since they have 4 equal sides and 4 square corners✓ Answer
    • D.No shapes, since nothing can be a rhombus and a rectangle

    The overlap holds shapes that belong to both groups at once. A square has 4 equal sides (a rhombus) and 4 square corners (a rectangle), so squares go in the middle. A rhombus with no square corners stays only in the rhombus circle.

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14. 14. A closed shape has 3 straight sides and 1 curved side. Is it a quadrilateral?

    • A.No, because a quadrilateral needs 4 equal sides.
    • B.No, because a quadrilateral needs 4 square corners.
    • C.Yes, because it has 4 sides, and a side may be curved.
    • D.No, because every side of a quadrilateral is straight.✓ Answer

    A quadrilateral must have exactly 4 sides, and every side must be a straight line. This shape has a curved side, so it is not a quadrilateral. Square corners and equal sides are not required for a quadrilateral, so those reasons are wrong.

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15. 15. Jamal draws 4 straight lines. They meet at 3 corners, but there is a gap where the last corner should be, so the shape is not closed. Is it a quadrilateral?

    • A.No, because a quadrilateral must be closed.✓ Answer
    • B.No, because it does not have 4 square corners.
    • C.Yes, because it is made of 4 straight sides.
    • D.Yes, because it has at least 3 corners.

    A quadrilateral is a closed shape: its 4 straight sides must connect all the way around with 4 corners. Jamal's figure has a gap, so it is open and is not a quadrilateral. Square corners are not needed, so that reason is wrong.

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16. 16. Which shape has the same number of sides as a rhombus?

    • A.A hexagon
    • B.A triangle
    • C.A rectangle✓ Answer
    • D.A pentagon

    A rhombus is a quadrilateral, so it has 4 sides. A rectangle also has 4 sides, even though its sides are not always equal. A triangle has 3 sides, a pentagon 5, and a hexagon 6.

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17. 17. A closed shape has 4 straight sides. Two sides next to each other are each 3 cm long. The other two sides, also next to each other, are each 5 cm long. It has no square corners (right angles). Which name is correct?

    • A.A rhombus
    • B.A square
    • C.A quadrilateral✓ Answer
    • D.A rectangle

    Every closed shape with 4 straight sides is a quadrilateral. This one is not a rhombus or a square, because its sides are not all equal (3 cm and 5 cm), and it is not a rectangle or a square, because it has no square corners.

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18. 18. Which shape is a rhombus but is NOT a square?

    • A.A shape with sides of 7, 3, 7, and 3 cm and 4 square corners
    • B.A shape with sides of 7, 3, 7, and 3 cm and no square corners
    • C.A shape with 4 sides of 7 cm each and 4 square corners
    • D.A shape with 4 sides of 7 cm each and no square corners✓ Answer

    A rhombus needs 4 equal sides, and a square needs 4 equal sides plus 4 square corners. The shape with four 7 cm sides and no square corners is a rhombus but not a square. The shape with four 7 cm sides and 4 square corners is a square, and the 7, 3, 7, 3 shapes are not rhombuses at all.

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19. 19. Kai puts these shapes in one group: a square, a rhombus with no square corners, a rectangle with 2 long and 2 short sides, and a 4-sided shape whose sides are all different lengths. Which rule fits every shape in Kai's group?

    • A.Each shape has exactly 4 sides and 4 vertices.✓ Answer
    • B.Each shape has 2 long sides and 2 short sides.
    • C.Each shape has 4 square corners at its vertices.
    • D.Each shape has 4 sides of the very same length.

    Test each rule against every shape. The rhombus and the uneven shape have no square corners, the rectangle and uneven shape do not have equal sides, and the square does not have 2 long and 2 short sides. The only rule all four meet is 4 sides and 4 vertices, which means they are all quadrilaterals.

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20. 20. Mia cuts a rectangular sandwich into 4 parts. All 4 parts have equal area. What fraction of the whole sandwich is each part?

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

    Count the equal parts: when a whole is cut into 4 parts with equal area, each part is 1/4 of the whole. The bottom number tells how many equal parts make the whole. A common mistake is 1/3, which comes from counting cuts (3 straight cuts make 4 strips) instead of parts.

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21. 21. A round pizza is cut through its center into 6 slices that are all the same size. What fraction of the pizza is one slice?

    • A.1/6 of the pizza✓ Answer
    • B.1/3 of the pizza
    • C.1/2 of the pizza
    • D.1/8 of the pizza

    Each slice is one of 6 equal parts, so each slice is 1/6 of the pizza. It takes only 3 straight cuts through the center to make 6 slices, so a child who counts the cuts picks 1/3. Always count the equal pieces, not the cuts.

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22. 22. Diego has a square sheet of grid paper with 16 small squares (4 rows of 4). He cuts the top half into 2 pieces, each 2 squares by 2 squares. He cuts the bottom half corner to corner into 2 triangles. Each of the 4 pieces covers 4 small squares. Which statement is true?

    • A.Only the 2 square pieces are 1/4, because only those 2 match
    • B.No piece is 1/4 of the sheet, because the 4 pieces differ in shape
    • C.Each piece is 1/4 of the sheet, because all 4 cover equal area✓ Answer
    • D.Each triangle is 1/8 of the sheet, because it is half a rectangle

    Equal parts means equal area, not the same shape. Every piece covers 4 of the 16 small squares, so all 4 pieces are equal parts and each one is 1/4 of the sheet. A triangle is half of the bottom half, and half of a half is 1/4, not 1/8.

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23. 23. Lena cuts a rectangular granola bar into 4 pieces. Two pieces are big and two pieces are small. Is each piece 1/4 of the bar?

    • A.Yes, because 2 big and 2 small pieces even out
    • B.No, because the 4 pieces do not all have equal area✓ Answer
    • C.Yes, because the bar was cut into exactly 4 pieces
    • D.No, because each big piece is 1/2 of the whole bar

    A piece is 1/4 only when the whole is cut into 4 parts with equal area. Lena's pieces are different sizes, so none of them is 1/4, even though there are 4 pieces. A big piece cannot be 1/2 either, because the two big pieces and the two small pieces together make the whole bar.

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24. 24. Ravi cuts a hexagon into triangles that all have equal area. Each triangle is 1/6 of the hexagon. How many of these triangles make the whole hexagon?

    • A.12 triangles
    • B.1 triangle
    • C.6 triangles✓ Answer
    • D.3 triangles

    When each part is 1/6, it takes 6 of those equal parts to make 1 whole, because 6/6 = 1. Only 3 straight cuts through the center are needed to make 6 triangles, so counting cuts gives the wrong answer of 3.

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25. 25. Omar and Priya each have a sheet of paper. The sheets are rectangles of the same size. Omar cuts his into 4 equal strips. Priya cuts hers once across the middle and once down the middle, making 4 equal rectangles. Which statement is true?

    • A.Only Omar's sheet shows fourths, because his parts are long strips
    • B.Both sheets show fourths, because each has 4 equal-area parts✓ Answer
    • C.Only Priya's sheet shows fourths, because her parts are more square
    • D.Neither sheet shows fourths, because the two ways of cutting differ

    There is more than one way to cut a shape into fourths. Each sheet is cut into 4 parts with equal area, so each part is 1/4 of its sheet. Because the sheets are the same size, Omar's strip and Priya's small rectangle cover the same amount of paper even though their shapes differ.

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26. 26. A flag is a rectangle with 3 stripes. The stripes all have equal area. One stripe is red. What fraction of the flag is red?

    • A.1/4 of the flag
    • B.1/3 of the flag✓ Answer
    • C.1/2 of the flag
    • D.1/6 of the flag

    The flag is cut into 3 equal parts, and the red stripe is 1 of them, so red is 1/3 of the flag. A child who compares the 1 red stripe to the 2 other stripes may say 1/2, but the bottom number must count all 3 equal parts of the whole.

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27. 27. Which shape is divided into fourths?

    • A.A square cut by 3 lines into 4 strips of different widths
    • B.A rectangle cut by 4 straight lines into strips of equal width
    • C.A circle cut by 2 straight lines that cross near its edge
    • D.A square cut by 1 line across and 1 line down through its middle✓ Answer

    Fourths means 4 parts with equal area. Two lines through the middle of a square, one across and one down, make 4 matching parts, so each is 1/4. Four lines make 5 strips, not 4, and parts of different sizes are never fourths.

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28. 28. Ms. Kim's garden is a rectangle. She splits it into 8 flower beds, in 2 rows of 4, that all have equal area. What fraction of the garden is one flower bed?

    • A.1/6 of the garden
    • B.1/4 of the garden
    • C.1/2 of the garden
    • D.1/8 of the garden✓ Answer

    The garden is split into 8 equal parts in all, so one bed is 1/8 of the garden. Counting only the 4 beds in one row gives 1/4, but the bottom number must count every equal part in the whole garden: 2 rows of 4 is 8 beds.

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29. 29. Ava folds a square napkin corner to corner and cuts along the fold. She gets 2 triangles that match exactly. What fraction of the napkin is one triangle?

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

    One cut corner to corner splits the square into 2 parts with equal area, so each triangle is 1/2 of the napkin. Some children pick 1/4 because a triangle looks smaller than a square, but shape does not matter, only how many equal parts make the whole.

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30. 30. Ben has a round pancake. He cuts it straight across the middle into 2 halves. Then he cuts only one of the halves into 2 equal pieces. Now there are 3 pieces. What fraction of the pancake is the biggest piece?

    • A.1/6 of the pancake
    • B.1/2 of the pancake✓ Answer
    • C.1/3 of the pancake
    • D.1/4 of the pancake

    The biggest piece was never cut again, so it is still one of the 2 equal halves: 1/2 of the pancake. There are 3 pieces, but they are not equal, so 1/3 is wrong. A piece is 1/3 only when the whole is cut into 3 equal parts.

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31. 31. Zara has a rectangle of paper. She cuts it in half with one straight cut. Then she cuts one of the halves in half again. What fraction of the whole paper is one of the 2 small pieces?

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

    Half of a half is 1/4, because the 2 small pieces together fill one half, and 4 pieces that size would fill the whole paper. Zara has 3 pieces, but they are not equal, so a small piece is not 1/3.

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32. 32. A rectangle of grid paper has 12 small squares (2 rows of 6). Jun cuts it into 3 pieces: one square piece and two L-shaped pieces. Each piece covers 4 small squares. Which statement is true?

    • A.No piece is 1/3 of the rectangle, because the 3 shapes are not alike
    • B.Each L-shaped piece is 1/6 of the rectangle, because an L has 6 sides
    • C.Only the square piece is 1/3, because its four sides are all equal
    • D.Each piece is 1/3 of the rectangle, because all 3 cover equal area✓ Answer

    Equal parts are parts with equal area, and they do not need to be the same shape. Each piece covers 4 of the 12 small squares, so the rectangle is cut into 3 equal parts and each piece is 1/3. The 6 sides of an L shape have nothing to do with what fraction of the rectangle it is.

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33. 33. A round cake is cut into slices that all have equal area. Each slice is 1/8 of the cake. How many slices make the whole cake?

    • A.8 slices✓ Answer
    • B.4 slices
    • C.16 slices
    • D.1 slice

    If each slice is 1/8, then 8 of them make the whole cake, because 8/8 = 1. Only 4 straight cuts through the center are needed to make 8 slices, so counting cuts gives 4. The top number 1 tells about one slice, not the whole cake.

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34. 34. A hexagon is cut into 3 rhombuses. All 3 rhombuses have equal area. What fraction of the hexagon is one rhombus?

    • A.1/3 of the hexagon✓ Answer
    • B.1/2 of the hexagon
    • C.1/4 of the hexagon
    • D.1/6 of the hexagon

    The hexagon is made of 3 equal parts, so each rhombus is 1/3 of it. A common mistake is 1/6, which comes from counting the hexagon's 6 sides instead of the 3 equal parts. The bottom number counts equal parts, not sides.

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35. 35. Luis cuts a hexagon with one straight line from one corner to the opposite corner. The 2 pieces match exactly. What fraction of the hexagon is one piece?

    • A.1/6 of the hexagon
    • B.1/4 of the hexagon
    • C.1/2 of the hexagon✓ Answer
    • D.1/3 of the hexagon

    One cut makes 2 pieces that match, so the hexagon is cut into 2 equal parts and each piece is 1/2. Each piece has 3 of the hexagon's 6 sides, which tempts some children to say 1/3 or 1/6, but fractions count equal parts, not sides.

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36. 36. Tomás cuts a square tile into 4 parts with equal area. He paints all 4 parts blue. What fraction of the tile is blue?

    • A.4/8 of the tile
    • B.1/4 of the tile
    • C.4/4 of the tile✓ Answer
    • D.3/4 of the tile

    When every equal part of a whole is used, the fraction is the whole: 4 fourths is 4/4, which equals 1 whole tile. Choosing 1/4 names just one part, but Tomás painted all 4 of the equal parts.

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37. 37. Sofia cuts a round pie with 2 straight cuts. The cuts cross far from the center, so she gets 4 pieces of different sizes. Which statement is true?

    • A.The pieces are halves, because she made exactly 2 cuts
    • B.The pieces are fourths, because both cuts are straight
    • C.The pieces are fourths, because there are exactly 4 of them
    • D.The pieces are not fourths, because their areas are not equal✓ Answer

    To be fourths, the 4 pieces must have equal area. Sofia's pieces are different sizes, so none of them is 1/4 of the pie, even though there are 4 pieces. Counting pieces or cuts is not enough; always check that the parts are equal.

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38. 38. A chocolate bar is a rectangle made of 8 equal squares, in 2 rows of 4. Kenji breaks off one square. What fraction of the whole bar is one square?

    • A.1/6 of the bar
    • B.1/2 of the bar
    • C.1/4 of the bar
    • D.1/8 of the bar✓ Answer

    The bar has 2 rows of 4, which is 8 equal squares in all, so one square is 1/8 of the bar. Looking at just one row of 4 gives 1/4, but the whole bar has 8 equal parts.

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39. 39. Kai and Nora each have a square cracker. The crackers are the same size. Kai cuts his corner to corner both ways into 4 matching triangles. Nora cuts hers into 4 matching small squares. Which statement about one of Kai's triangles and one of Nora's small squares is true?

    • A.Each triangle is 1/8 of a cracker, because it is half a small square
    • B.Each piece is 1/4 of a cracker, so the two have the same area✓ Answer
    • C.The triangle is bigger, because it touches two of the corners
    • D.The small square is bigger, because a triangle is half a square

    Each cracker is cut into 4 parts with equal area, so every triangle and every small square is 1/4 of a cracker. Because the crackers are the same size, the two pieces cover the same amount of cracker even though their shapes are different.

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40. 40. Hana wants to cut a rectangular pan of brownies into 3 parts with equal area. Which plan works?

    • A.Cut 2 lines across anywhere, since any 3 pieces make thirds
    • B.Cut 2 lines across, spaced so all 3 strips are the same width✓ Answer
    • C.Cut 1 line across and 1 line down, with both going through the middle
    • D.Cut 3 lines across, spaced so all of the strips are the same width

    Thirds means 3 parts with equal area. Two cuts make 3 strips, and spacing them evenly makes the strips equal, so each is 1/3. Three cuts would make 4 strips, and cuts placed anywhere can make pieces of different sizes.

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