Elementary School Math Quiz: Partition Shapes Into Equal Parts
20 questions · exam conditions
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Partition Shapes Into Equal PartsQuestion 1 of 20

Sam cuts a circle into 3 equal pieces. He eats 2 pieces and saves 1 piece for later. Which sentence correctly describes what Sam has left?

Sam has two thirds of the circle remaining for later
Sam has one third of the circle remaining for later
Sam has one half of the circle remaining for later
Sam has three thirds of the circle remaining for later
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Elementary School Math Quiz

Elementary School Math Quiz: Partition Shapes Into Equal Parts

Practice Partition Shapes Into Equal Parts in Elementary School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Partition Shapes Into Equal Parts, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Sam cuts a circle into 3 equal pieces. He eats 2 pieces and saves 1 piece for later. Which sentence correctly describes what Sam has left?

  1. Sam has two thirds of the circle remaining for later
  2. Sam has one third of the circle remaining for later (correct answer)
  3. Sam has one half of the circle remaining for later
  4. Sam has three thirds of the circle remaining for later
Explanation: Sam cut the circle into 3 equal parts (thirds) and saved 1 piece, so he has 13\frac{1}{3} (one third) remaining. Choice A describes what he ate, not what remains. Choice C incorrectly describes the remaining piece as a half. Choice D would mean he has the whole circle left.

Question 2

The figure shows four circles. Which circle is divided into thirds?

  1. Circle A
  2. Circle B
  3. Circle C (correct answer)
  4. Circle D
Explanation: Thirds means 3 equal parts. Circle C is cut into 3 parts that are all the same size, so it shows thirds. Circle A shows halves (2 equal parts) and Circle B shows fourths (4 equal parts). Circle D has 3 parts, but they are not the same size, so they are not thirds.

Question 3

In the figure, two identical rectangles are each shaded to show one half. Which statement is true?

  1. Only Rectangle A shows one half, because its shaded part is a rectangle.
  2. Only Rectangle B shows one half, because its shaded part is a triangle.
  3. Both rectangles show one half, even though the shaded parts have different shapes. (correct answer)
  4. Neither rectangle shows one half, because the shaded parts look different.
Explanation: One half means 2 equal parts. Rectangle A is cut down the middle, and one part is shaded. Rectangle B is cut corner to corner, and one triangle is shaded. Both shaded parts are half of the same-size rectangle, even though they are different shapes.

Question 4

Which way of dividing a circle shows thirds correctly?

  1. Draw 3 straight lines from the center to the edge, spaced evenly, to make 3 equal pie-shaped pieces (correct answer)
  2. Draw 2 straight lines across the circle, evenly spaced, to make 3 strips
  3. Draw 1 line across the middle to make 2 equal half-circle pieces
  4. Draw 4 straight lines from the center to the edge, spaced evenly, to make 4 equal pie-shaped pieces
Explanation: Thirds means 3 equal parts. Three straight lines from the center to the edge, spaced evenly, make 3 equal pie-shaped pieces. Two evenly spaced lines across a circle make a wide middle strip and two smaller end pieces, so those pieces are not equal. One straight cut through the center makes halves, and four evenly spaced lines from the center make fourths.

Question 5

Sam says the circle below is split into thirds. Is Sam correct? Use the picture to answer.

  1. Yes, because the circle is split into 3 parts.
  2. Yes, because there are more than 2 parts.
  3. No, because the 3 parts are not all equal in size. (correct answer)
  4. No, because a circle can only be split into halves.
Explanation: To be split into thirds, a shape must be divided into 3 equal parts. The circle has 3 parts, but they are different sizes, so it is not split into thirds.

Question 6

Look at the figure. Which sentence correctly describes the shaded part of the circle?

  1. A third of the circle is shaded.
  2. Half of the circle is shaded. (correct answer)
  3. A fourth of the circle is shaded.
  4. Three fourths of the circle is shaded.
Explanation: When you see a shape split into shaded and unshaded parts, your first job is to count the total equal pieces the shape is divided into, then count how many are shaded. That gives you the fraction. Common fractions on 2nd-grade tests are halves (2 equal pieces), thirds (3 equal pieces), and fourths (4 equal pieces). For this circle, the figure shows it split into 2 equal pieces, with 1 piece shaded. That means 1 out of 2 parts is shaded, which we call one half. So B is the match. Now look at why the others don't fit. A says "a third," which would require the circle to be cut into 3 equal pieces with 1 shaded — but this circle only has 2 pieces. C says "a fourth," which needs 4 equal pieces with 1 shaded; again, the wrong number of pieces. D says "three fourths," which not only needs 4 equal pieces, but also 3 of them shaded — far more shading than the figure shows. A helpful trick: before picking your answer, whisper to yourself, "How many equal pieces in all? How many are shaded?" Write it as shaded over total. Here, that's 12\frac{1}{2}. Matching that fraction to the words — half, third, fourth — makes these questions quick and safe from tricky wording traps like "three fourths."

Question 7

Look at the shaded circle in the figure. Which sentence best describes the whole circle?

  1. The whole is two halves.
  2. The whole is three thirds.
  3. The whole is four fourths. (correct answer)
  4. The whole is four halves.
Explanation: When you see a circle (or any shape) divided into equal parts, remember that the whole is always made up of all the equal pieces put together. The name of each piece depends on how many equal parts the whole is split into: 2 parts make halves, 3 parts make thirds, and 4 parts make fourths. Since the figure shows a circle divided into 4 equal parts, each piece is called a fourth. To make the whole circle, you need all 4 of those fourths. So the whole circle is four fourths, which matches choice C. You can also think of it as 44=1\frac{4}{4} = 1 whole. Choice A ("two halves") describes a circle cut into just 2 equal pieces — that's not what this figure shows. Choice B ("three thirds") would describe a circle cut into 3 equal pieces, which also doesn't match. Choice D ("four halves") is a tricky one: it mixes up the words. "Halves" means the whole was split into 2 parts, so you can't have four of them in one whole circle — that would actually be two whole circles! A helpful tip: match the number of pieces to the name of the pieces. Two pieces → halves, three pieces → thirds, four pieces → fourths. The top number (how many you have) and the bottom number (what they're called) should be the same when you're describing one whole thing.

Question 8

Look at the rectangle. Maya divides it into 4 equal parts by drawing one line across and one line down. Then she colors 3 of the parts blue. How much of the rectangle is NOT blue?

  1. one fourth of the rectangle (correct answer)
  2. three fourths of the rectangle
  3. the whole rectangle
  4. half of the rectangle
Explanation: The rectangle has 4 equal parts. 3 are blue and 1 is not blue. One part is one fourth of the rectangle. Three fourths is blue, the whole is all 4 parts, and half is 2 of the 4 parts.

Question 9

A garden is shaped like a rectangle. Which way divides it into 4 equal parts?

  1. Draw 1 line across the middle
  2. Draw 2 lines parallel to one side
  3. Draw 2 lines close together on one side
  4. Draw 1 line across the middle and 1 line down the middle (correct answer)
Explanation: One line across the middle and one line down the middle cut the rectangle into 4 equal parts. One line across the middle makes only 2 parts. Two lines parallel to one side make only 3 parts, and two lines close together on one side make 3 parts of very different sizes.

Question 10

Look at the shaded rectangle below. What fraction of the whole rectangle is shaded in total?

  1. Half of the rectangle (correct answer)
  2. A third of the rectangle
  3. A fourth of the rectangle
  4. Two thirds of the rectangle
Explanation: The rectangle is divided into 4 equal parts, and 2 of the 4 parts are shaded. Two fourths is the same as one half of the rectangle.

Question 11

Look at the shaded rectangle in the figure. What fraction of the rectangle is shaded?

  1. A half
  2. A third
  3. Three fourths
  4. Two thirds (correct answer)
Explanation: When you see a fraction question with a shaded shape, remember that a fraction has two parts: the denominator (bottom number) tells you how many equal pieces the whole is divided into, and the numerator (top number) tells you how many of those pieces are shaded. For a rectangle split into 3 equal parts with 2 parts shaded, you'd count the total pieces first (3), then count the shaded ones (2). That gives you 23\frac{2}{3}, or two thirds — which matches choice D. Now look at why the other choices don't fit. Choice A, a half, would only be correct if the rectangle were split into 2 equal parts with 1 shaded — that's 12\frac{1}{2}. Choice B, a third, describes just 1 shaded piece out of 3, or 13\frac{1}{3} — that counts only one shaded section instead of both. Choice C, three fourths, means 34\frac{3}{4}, which requires the rectangle to be split into 4 equal parts with 3 shaded — the wrong number of total pieces. A helpful strategy: always ask yourself two questions in this order — "How many equal parts in all?" (that's your bottom number) and "How many are shaded?" (that's your top number). Writing the fraction before looking at the answer choices helps you avoid getting tricked by choices that flip the numbers or use the wrong total.

Question 12

Refer to the figure. A square is divided so that one part is shaded. Which statement about the shaded part is true?

  1. The shaded part is one half of the square. (correct answer)
  2. The shaded part is one third of the square.
  3. The shaded part is one fourth of the square.
  4. The shaded part is not an equal share of the square.
Explanation: When a shape is divided into equal parts, the name of each part depends on how many equal pieces the whole is split into. Two equal parts are called halves, three equal parts are called thirds, and four equal parts are called fourths (or quarters). So your first job with a question like this is to count the equal pieces the shape is divided into. In this figure, the square is split into 2 equal parts, and 1 of those parts is shaded. Since the square is cut into 2 equal shares and you're looking at 1 of them, the shaded part is one half of the square, making A correct. B is wrong because "one third" would require the square to be divided into 3 equal parts, not 2. C is wrong because "one fourth" would need 4 equal parts — you'd see the square split into four equal pieces with one shaded. D is wrong because the two parts of the square are the same size; they are equal shares, so this statement doesn't fit. A helpful tip: whenever you see a fraction question with a picture, count the total equal parts first (that's your bottom number, the denominator), then count how many are shaded (that's your top number, the numerator). Two equal parts → halves. Three → thirds. Four → fourths. Memorizing this pattern makes these questions quick and reliable.

Question 13

Refer to the circle in the figure. What fraction of the circle is shaded?

  1. One half
  2. One third (correct answer)
  3. One fourth
  4. Three thirds
Explanation: The circle has 3 equal parts, and 1 whole part is shaded. The shaded part is one third of the circle. One half is half of the whole circle, one fourth is a quarter of it, and three thirds is the whole circle.

Question 14

The figure shows a rectangular cake that was cut for a party. How many thirds does the whole cake have?

  1. 1 third
  2. 2 thirds
  3. 4 thirds
  4. 3 thirds (correct answer)
Explanation: When you see a question about fractions like "thirds," think about what the word itself tells you. The prefix or root of the fraction name usually matches the number of equal pieces the whole is cut into. "Halves" means 2 equal pieces, "fourths" means 4 equal pieces, and "thirds" means 3 equal pieces. So if the cake is cut into thirds, the whole cake must be made up of exactly 3 equal parts. Put those 3 thirds back together and you get 1 whole cake. That makes D the correct choice. Choice A (1 third) describes just a single slice of the cake, not the whole thing. One third by itself is only a piece — you'd still need more slices to make a full cake. Choice B (2 thirds) is two of the three slices, which still leaves part of the cake missing. Choice C (4 thirds) is more than one whole cake, which doesn't match the picture of a single cake cut into equal pieces. A helpful way to remember this: the name of the fraction tells you how many equal pieces make one whole. Halves → 2, thirds → 3, fourths → 4, and so on. Whenever a question asks "how many   are in the whole?", just look at the fraction name and use that number.

Question 15

In the figure, a rectangular garden is divided into equal shares. What fraction of the whole garden is one share?

  1. One half
  2. One third
  3. One sixth
  4. One fourth (correct answer)
Explanation: When a shape is divided into equal shares, the fraction each share represents depends on the total number of equal parts. The rule is simple: if a whole is split into nn equal pieces, each piece is 1n\frac{1}{n} of the whole. So your job on questions like this is to carefully count how many equal parts the figure is divided into. Since the garden in the figure is divided into 4 equal shares, one share is 14\frac{1}{4} of the whole garden — that's "one fourth," making D correct. Now look at why the other choices don't fit. Choice A, one half, would only be right if the garden were split into 2 equal parts, but there are more than 2 pieces here. Choice B, one third, would require exactly 3 equal parts — again, not what the figure shows. Choice C, one sixth, is a trap for students who miscount or confuse "fourths" with "sixths"; it would apply only if the garden had 6 equal shares. A helpful strategy: whenever you see a fraction question with a picture, count the total equal parts first, then write "1 over that number." The bottom number (denominator) always tells you how many equal pieces make the whole, and the top number (numerator) tells you how many of those pieces you're talking about. More parts means each piece is smaller — so a garden cut into 6 pieces would have smaller shares than one cut into 4.

Question 16

In the diagram, a pizza is split among some friends. How many friends will get an equal share, and what is each share called?

  1. 2 friends; each share is a half.
  2. 3 friends; each share is a third. (correct answer)
  3. 4 friends; each share is a fourth.
  4. 3 friends; each share is a fourth.
Explanation: When a shape like a pizza is divided into equal parts, the number of parts tells you what to call each share. Two equal parts are called halves, three equal parts are called thirds, and four equal parts are called fourths (or quarters). The key is to count how many equal pieces the whole is split into. In this diagram, the pizza is cut into 3 equal slices, so 3 friends can each get one piece. Since the pizza is split into 3 equal parts, each share is called a third, making B correct. Choice A would only work if the pizza were cut into 2 equal pieces, but there are more than two slices here. Choice C describes a pizza cut into 4 equal parts, which doesn't match a pizza split into 3 slices. Choice D mixes things up: it correctly counts 3 friends but calls each share a "fourth" — the name of the share must match the number of equal parts, so 3 parts cannot be called fourths. A helpful tip: always match the name of the fraction to the total number of equal pieces the whole is divided into, not just to how many pieces someone takes. If you see 3 equal parts, think "thirds." If you see 4 equal parts, think "fourths." Counting the total slices first will keep you from falling for tricky answer choices that mix up the numbers and names.

Question 17

Refer to the figure. Sam and Tia each have a sandwich exactly the same size. Sam cuts his into 2 equal pieces and eats 1 piece. Tia cuts hers into 4 equal pieces and eats 1 piece. Who eats more sandwich?

  1. Sam, because a half is bigger than a fourth. (correct answer)
  2. Tia, because 4 is more than 2.
  3. They eat the same amount.
  4. Tia, because fourths are bigger than halves.
Explanation: When you compare fractions of the same whole, remember this key idea: the more pieces you cut something into, the smaller each piece becomes. Think about cutting a pizza — if you slice it into just 2 pieces, each piece is huge. If you slice that same pizza into 4 pieces, each slice is smaller because you're sharing the pizza among more parts. Sam cuts his sandwich into 2 equal pieces, so each piece is one-half (12\frac{1}{2}) of the sandwich. Tia cuts hers into 4 equal pieces, so each piece is one-fourth (14\frac{1}{4}) of the sandwich. Since both sandwiches are the same size, one-half is bigger than one-fourth. Sam eats more, which makes A correct. B falls into a common trap: thinking a bigger denominator means a bigger piece. Actually, the opposite is true — 4 pieces means each piece is smaller than if you only had 2 pieces. C is wrong because they each ate 1 piece, but the pieces were different sizes, so the amounts can't be equal. D flips the truth: fourths are actually smaller than halves, not bigger. Study tip: When comparing unit fractions (fractions with 1 on top), the fraction with the smaller bottom number is the bigger piece. A helpful trick: imagine sharing a cookie. Would you rather share it with 1 friend (halves) or 3 friends (fourths)? You get more when fewer people share!

Question 18

Ms. Lopez shows her class a rectangle divided into 3 equal parts. She colors 2 parts green and leaves 1 part white. What fraction of the rectangle is white?

  1. Two thirds
  2. One third (correct answer)
  3. One half
  4. Three thirds
Explanation: The rectangle has 3 equal parts: 1 is white and 2 are green. The white part is one third of the rectangle. Two thirds describes the green part, and three thirds describes the whole rectangle. One half is half of the whole rectangle, which is more than the white part.

Question 19

Jake has a rectangular pizza. He wants to share it equally among 4 people, including himself. After he cuts the pizza, Jake says, "Each person gets one fourth of the pizza, and the whole pizza is four fourths." What does Jake mean when he says the whole pizza is "four fourths"?

  1. The pizza was cut into 4 pieces and all 4 pieces together make the complete pizza (correct answer)
  2. The pizza is 4 times bigger than a regular pizza so it has extra fourths
  3. Each person gets 4 pieces of pizza since there are 4 people sharing
  4. The pizza needs to be cut 4 more times to make the right number of pieces
Explanation: The pizza is cut into 4 equal pieces, and putting all 4 pieces back together makes the whole pizza, which is what Jake means by 'four fourths,' matching A. B is incorrect because the pizza is not bigger than a regular pizza; it is just divided into 4 equal parts. C is incorrect because each of the 4 people gets 1 piece, not 4 pieces each. D is incorrect because the pizza is already cut into the right number of pieces; no more cuts are needed.

Question 20

Refer to the rectangle below. Which sentence correctly describes the whole rectangle?

  1. The whole is two halves.
  2. The whole is three thirds.
  3. The whole is four fourths. (correct answer)
  4. The whole is four halves.
Explanation: The rectangle is divided into 4 equal parts, so each part is a fourth. The whole rectangle is made up of four fourths.