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NYS Math Grade 4 study materials
NYS Math Grade 4 study resources

NYS Math Grade 4 practice questions

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Question 1Mathematics

A number has 7 in the ten-thousands place, 4 in the hundreds place, and 0 in every other place. What is the number written in standard form?

  1. 7,400
  2. 74,000
  3. 700,040
  4. 70,400 Correct answer.

Explanation

Each digit's value depends on its place. Seven ten-thousands is 70,000 and four hundreds is 400, so combining them with zeros in the remaining places gives 70,400.

Question 2Mathematics

Which comparison is true?

  1. 56,208 = 56,280
  2. 56,208 > 56,280
  3. 56,280 < 56,208
  4. 56,208 < 56,280 Correct answer.

Explanation

Compare the numbers digit by digit from the left. The first three digits (5, 6, 2) match, but in the tens place 0 is less than 8, so 56,208 is less than 56,280.

Question 3Mathematics

A number is rounded to the nearest thousand and the result is 8,000. Which number could it be?

  1. 7,459
  2. 8,612 Correct answer.
  3. 7,500
  4. 8,499

Explanation

To round to the nearest thousand, look at the hundreds digit. A number rounds to 8,000 when it lies from 7,500 through 8,499, and 8,612 lies above that range while 7,459 lies below it.

Question 4Mathematics

What is 407 × 6?

  1. 2,422
  2. 2,842
  3. 2,442 Correct answer.
  4. 2,402

Explanation

Multiply each place: 6 × 7 = 42 ones, 6 × 0 tens = 0 tens, and 6 × 4 hundreds = 24 hundreds. Regrouping gives 2,442.

Question 5Mathematics

A baker makes 96 muffins and packs them equally into 8 boxes. How many muffins are in each box?

  1. 16
  2. 14
  3. 10
  4. 12 Correct answer.

Explanation

Dividing 96 by 8 gives the number in each box. Since 8 × 12 = 96, each box holds 12 muffins.

Question 6Mathematics

What is the value of the expression 36 ÷ 6 + 4 × 3?

  1. 18
  2. 12
  3. 24 Correct answer.
  4. 30

Explanation

Order of operations requires multiplication and division before addition. So 36 ÷ 6 = 6 and 4 × 3 = 12, then 6 + 12 = 18.

Question 7Mathematics

Which list shows the fractions in order from least to greatest?

  1. 1/2, 1/3, 1/4, 1/5
  2. 1/3, 1/5, 1/2, 1/4
  3. 1/5, 1/4, 1/3, 1/2 Correct answer.
  4. 1/4, 1/2, 1/3, 1/5

Explanation

When the numerators are all 1, the fraction with the largest denominator is the smallest because the whole is split into more pieces. So the order from least to greatest is 1/5, 1/4, 1/3, 1/2.

Question 8Mathematics

Which fraction is equivalent to 3/4?

  1. 6/8 Correct answer.
  2. 3/8
  3. 4/5
  4. 5/6

Explanation

Multiplying the numerator and denominator by the same number keeps a fraction's value. Since 3 × 2 = 6 and 4 × 2 = 8, the fraction 6/8 is equivalent to 3/4.

Question 9Mathematics

A recipe uses 2/3 cup of sugar. How much sugar is needed for 3 batches of the recipe?

  1. 2 cups Correct answer.
  2. 2 1/3 cups
  3. 6/9 cup
  4. 1 2/3 cups

Explanation

Multiplying 2/3 by 3 means adding 2/3 three times, which is 6/3. Since 6 ÷ 3 = 2, three batches need 2 cups of sugar.

Question 10Mathematics

Which decimal is equal to 7/10?

  1. 0.07
  2. 7.0
  3. 0.7 Correct answer.
  4. 0.007

Explanation

The fraction 7/10 means seven tenths. In decimal notation, seven tenths is written as 0.7, with the 7 in the tenths place.

Question 11Mathematics

Which statement correctly compares 0.45 and 0.5?

  1. 0.45 < 0.5 Correct answer.
  2. 0.45 > 0.5
  3. 0.45 = 0.5
  4. 0.5 < 0.45

Explanation

Line up the tenths place: 0.5 has 5 tenths while 0.45 has only 4 tenths. Since 4 tenths is less than 5 tenths, 0.45 is less than 0.5.

Question 12Mathematics

A rectangle has a length of 9 inches and a width of 4 inches. What is its area?

  1. 26 square inches
  2. 13 square inches
  3. 36 square inches Correct answer.
  4. 18 square inches

Explanation

The area of a rectangle is length times width. Multiplying 9 × 4 gives 36 square inches.

Question 13Mathematics

A square has a side length of 6 centimeters. What is its perimeter?

  1. 12 cm
  2. 18 cm
  3. 24 cm Correct answer.
  4. 36 cm

Explanation

A square has four equal sides, so the perimeter is 4 times the side length. Four times 6 cm equals 24 cm.

Question 14Mathematics

An angle measures more than 90 degrees but less than 180 degrees. What type of angle is it?

  1. Obtuse angle Correct answer.
  2. Right angle
  3. Straight angle
  4. Acute angle

Explanation

An obtuse angle has a measure greater than 90 degrees and less than 180 degrees. A right angle is exactly 90 and a straight angle is exactly 180.

Question 15Mathematics

A quadrilateral has two pairs of parallel sides, four right angles, and two adjacent sides of different lengths. In this question, a trapezoid has exactly one pair of parallel sides. Which shape could it be?

  1. Rhombus
  2. Trapezoid
  3. Triangle
  4. Rectangle Correct answer.

Explanation

A rectangle has two pairs of parallel sides and four right angles, and it can have adjacent sides of different lengths. A rhombus must have all four sides equal. Under the stated definition, a trapezoid has exactly one pair of parallel sides.

Question 16Mathematics

A line of symmetry divides a figure into two parts that are mirror images. How many lines of symmetry does a square have?

  1. 1
  2. 8
  3. 4 Correct answer.
  4. 2

Explanation

A square has four lines of symmetry: one horizontal, one vertical, and two diagonal lines through opposite corners. Each line folds the square onto matching halves.

Question 17Mathematics

A pattern starts 3, 6, 12, 24, ... and continues by the same rule. What are the next two numbers?

  1. 30, 36
  2. 48, 96 Correct answer.
  3. 36, 48
  4. 27, 30

Explanation

Each term is double the term before it: 3 × 2 = 6, 6 × 2 = 12, and 12 × 2 = 24. Doubling 24 gives 48, and doubling 48 gives 96.

Question 18Mathematics

A bag has 5 red marbles, 3 blue marbles, and 2 green marbles. If one marble is picked without looking, what is the probability it is blue?

  1. 1/10
  2. 3/10 Correct answer.
  3. 1/3
  4. 3/7

Explanation

There are 5 + 3 + 2 = 10 marbles in all, and 3 of them are blue. The probability of picking blue is the number of blue marbles over the total, or 3/10.

Question 19Mathematics

Liam started reading at 4:35 p.m. and read for 50 minutes. At what time did he finish?

  1. 5:35 p.m.
  2. 5:15 p.m.
  3. 5:25 p.m. Correct answer.
  4. 5:05 p.m.

Explanation

Adding 50 minutes to 4:35 means adding 25 minutes to reach 5:00 and then 25 more minutes, giving 5:25 p.m.

Question 20Mathematics

A juice carton holds 2 liters. How many milliliters is that?

  1. 20 mL
  2. 20,000 mL
  3. 2,000 mL Correct answer.
  4. 200 mL

Explanation

One liter equals 1,000 milliliters, so 2 liters equals 2 × 1,000 = 2,000 milliliters.

Question 21Mathematics

A rectangle is 8 cm long and 5 cm wide. A second rectangle is 16 cm long and 5 cm wide. How does the area of the second rectangle compare to the first?

  1. It is twice as large. Correct answer.
  2. It is the same.
  3. It is four times as large.
  4. It is three times as large.

Explanation

The first area is 8 × 5 = 40 square cm and the second is 16 × 5 = 80 square cm. Doubling the length while keeping the width the same doubles the area.

Question 22Mathematics

A number rounds to 600 when rounded to the nearest hundred and rounds to 1,000 when rounded to the nearest thousand. Which number fits both rules?

  1. 451
  2. 649 Correct answer.
  3. 1,450
  4. 549

Explanation

A number rounds to 600 when it is from 550 to 649, and it rounds to 1,000 when it is from 500 to 1,499. The number 649 is in both ranges, so it satisfies both rules.

Question 23Mathematics

A number machine follows this rule: multiply by 4, then subtract 7. If the output is 29, what was the input?

  1. 11
  2. 5
  3. 9 Correct answer.
  4. 7

Explanation

Work backward from the output: add 7 to 29 to get 36, then divide by 4 to get 9. Checking forward, 9 × 4 = 36 and 36 − 7 = 29.

Question 24Mathematics

A chef uses 3/4 pound of cheese for one pan of lasagna. How many pounds are needed for 6 pans?

  1. 4 1/2 pounds Correct answer.
  2. 3 3/4 pounds
  3. 5 1/4 pounds
  4. 4 pounds

Explanation

Multiply 3/4 by 6 to get 18/4, which simplifies to 4 1/2. So six pans need 4 1/2 pounds of cheese.

Question 25Mathematics

A rectangular garden is 12 meters long and 7 meters wide. A fence is built around the entire edge. What length of fence is needed?

  1. 84 meters
  2. 19 meters
  3. 38 meters Correct answer.
  4. 42 meters

Explanation

The perimeter of a rectangle is 2 × (length + width). Adding 12 + 7 gives 19, and doubling that gives 38 meters of fence.

Question 26Mathematics

Which number has a 7 in the thousands place?

  1. 3,970
  2. 47,205 Correct answer.
  3. 70,412
  4. 12,704

Explanation

In a place-value chart the thousands place is the fourth digit from the right. In 47,205 the digits are 4 ten-thousands, 7 thousands, 2 hundreds, 0 tens, and 5 ones, so the 7 sits in the thousands place.

Question 27Mathematics

What is 4,000 + 300 + 60 + 8 written in standard form?

  1. 4,368 Correct answer.
  2. 4,386
  3. 4,860
  4. 4,638

Explanation

Expanded form lists each place value separately, so the thousands digit is 4, the hundreds digit is 3, the tens digit is 6, and the ones digit is 8. Writing those digits in order gives 4,368.

Question 28Mathematics

A number rounds up to 500 when rounded to the nearest hundred. Which number could it be?

  1. 462 Correct answer.
  2. 551
  3. 449
  4. 549

Explanation

When rounding to the nearest hundred, whole numbers from 450 through 499 round up to 500. The number 462 is in this interval; its tens digit is 6, so it rounds up to 500.

Question 29Mathematics

A library has 6 shelves with 24 books on each shelf. How many books are on the shelves in all?

  1. 144 Correct answer.
  2. 30
  3. 124
  4. 164

Explanation

Equal groups call for multiplication: 6 groups of 24 books. Using place value, 6 × 20 = 120 and 6 × 4 = 24, and 120 + 24 = 144.

Question 30Mathematics

What is the remainder when 47 is divided by 5?

  1. 1
  2. 3
  3. 4
  4. 2 Correct answer.

Explanation

Five times 9 is 45, and 47 − 45 = 2, so 47 ÷ 5 = 9 remainder 2. The remainder must be less than the divisor, and 2 is less than 5.

Question 31Mathematics

A group of 4 friends shares 38 stickers equally and gives away any leftovers. How many stickers does each friend get?

  1. 8
  2. 10
  3. 9 Correct answer.
  4. 12

Explanation

Divide 38 by 4: 4 × 9 = 36, and 38 − 36 = 2, so the quotient is 9 with a remainder of 2. Each friend receives the whole-number quotient, 9 stickers, and 2 are left over.

Question 32Mathematics

Which number is a multiple of both 3 and 4?

  1. 18
  2. 30
  3. 14
  4. 24 Correct answer.

Explanation

A multiple of both 3 and 4 must be divisible by each with no remainder. Since 24 ÷ 3 = 8 and 24 ÷ 4 = 6, 24 is a common multiple.

Question 33Mathematics

Which list shows all the factor pairs of 36?

  1. 2 × 18, 3 × 12, 4 × 9, 6 × 6
  2. 1 × 36, 2 × 18, 3 × 12, 4 × 9
  3. 1 × 36, 2 × 18, 3 × 12, 6 × 6
  4. 1 × 36, 2 × 18, 3 × 12, 4 × 9, 6 × 6 Correct answer.

Explanation

Factor pairs multiply to 36 and are listed with the smaller factor first. Checking in order gives 1 × 36, 2 × 18, 3 × 12, 4 × 9, and 6 × 6, and no factor between 6 and 36 pairs with a whole number greater than 1.

Question 34Mathematics

Which statement about the number 51 is true?

  1. It is prime because it is not divisible by 2.
  2. It is prime because it is odd.
  3. It is neither prime nor composite.
  4. It is composite because it has factors other than 1 and itself. Correct answer.

Explanation

A composite number has at least one factor other than 1 and itself. Since 51 = 3 × 17, it has factors 3 and 17, so it is composite even though it is odd.

Question 35Mathematics

What is 5/8 + 2/8?

  1. 7/16
  2. 7/8 Correct answer.
  3. 3/8
  4. 10/8

Explanation

When fractions have the same denominator, add the numerators and keep the denominator. So 5/8 + 2/8 = 7/8, and the sum is less than 1 whole.

Question 36Mathematics

A student says 2/3 is greater than 3/4 because 3 is greater than 4. Which comparison is correct?

  1. 2/3 = 3/4
  2. 2/3 < 3/4 Correct answer.
  3. 3/4 < 2/3
  4. 2/3 > 3/4

Explanation

Compare the fractions using a common denominator of 12: 2/3 = 8/12 and 3/4 = 9/12. Since 8/12 is less than 9/12, the correct statement is 2/3 < 3/4.

Question 37Mathematics

Which decimal is equal to 3/100?

  1. 0.3
  2. 3.0
  3. 0.003
  4. 0.03 Correct answer.

Explanation

The denominator 100 means the decimal has two places after the decimal point, with 3 in the hundredths place. So 3/100 = 0.03.

Question 38Mathematics

What is 4.6 + 2.75?

  1. 7.35 Correct answer.
  2. 6.81
  3. 7.21
  4. 7.45

Explanation

Line up the decimal points and write 4.6 as 4.60 so both numbers have hundredths. Then 4.60 + 2.75 = 7.35.

Question 39Mathematics

A ribbon is 1.5 meters long. How many centimeters long is the ribbon?

  1. 15 cm
  2. 0.015 cm
  3. 150 cm Correct answer.
  4. 1,500 cm

Explanation

One meter equals 100 centimeters, so multiply meters by 100 to convert. Then 1.5 × 100 = 150 centimeters.

Question 40Mathematics

A rectangular rug is 6 feet long and 4 feet wide. What is the perimeter of the rug?

  1. 24 feet
  2. 48 feet
  3. 20 feet Correct answer.
  4. 10 feet

Explanation

Perimeter is the distance around a shape, found by adding all four sides. For a rectangle, 2 × (6 + 4) = 2 × 10 = 20 feet.

Question 41Mathematics

A square has an area of 49 square inches. What is the length of one side?

  1. 7 inches Correct answer.
  2. 24.5 inches
  3. 12 inches
  4. 14 inches

Explanation

The area of a square is the side length multiplied by itself. Since 7 × 7 = 49, the side length is 7 inches.

Question 42Mathematics

A rectangle is 10 cm long and 3 cm wide. A second rectangle is 10 cm long and 6 cm wide. How does the area of the second rectangle compare with the area of the first?

  1. The area is 3 square centimeters greater.
  2. The area is 6 square centimeters greater.
  3. The area is twice as great. Correct answer.
  4. The area is 3 times as great.

Explanation

The first area is 10 × 3 = 30 square centimeters and the second is 10 × 6 = 60 square centimeters. Since 60 is 2 × 30, doubling the width while keeping the length doubles the area.

Question 43Mathematics

A figure is made of two identical squares placed side by side with no overlap. Each square has a side length of 5 cm. What is the perimeter of the combined figure?

  1. 40 cm
  2. 20 cm
  3. 30 cm Correct answer.
  4. 25 cm

Explanation

Two squares side by side form a rectangle 10 cm long and 5 cm wide. Its perimeter is 2 × (10 + 5) = 30 cm, because the two shared sides are inside the figure and are not counted.

Question 44Mathematics

Which unit is best for measuring the mass of a pencil?

  1. liters
  2. meters
  3. grams Correct answer.
  4. kilograms

Explanation

Mass measures how heavy an object is, and a pencil is a light object. A gram is a small metric unit of mass, so grams are the sensible choice.

Question 45Mathematics

A straight angle is split into two angles. One of the angles measures 65 degrees. What is the measure of the other angle?

  1. 295 degrees
  2. 25 degrees
  3. 125 degrees
  4. 115 degrees Correct answer.

Explanation

A straight angle measures 180 degrees, so the two angles must add to 180. Subtract: 180 − 65 = 115 degrees.

Question 46Mathematics

A triangle has two angles that each measure 50 degrees. What is the measure of the third angle?

  1. 100 degrees
  2. 80 degrees Correct answer.
  3. 50 degrees
  4. 130 degrees

Explanation

The three angles of any triangle add to 180 degrees. The two known angles total 100 degrees, so the third angle is 180 − 100 = 80 degrees.

Question 47Mathematics

A quadrilateral has exactly one pair of parallel sides. Which shape is it?

  1. rhombus
  2. trapezoid Correct answer.
  3. square
  4. parallelogram

Explanation

A trapezoid is defined as a quadrilateral with exactly one pair of parallel sides. The other listed shapes each have two pairs of parallel sides.

Question 48Mathematics

A figure is drawn on a grid. Point A is at (2, 3) and point B is at (7, 3). What is the distance between the points?

  1. 4 units
  2. 9 units
  3. 3 units
  4. 5 units Correct answer.

Explanation

Both points have the same y-coordinate, so they lie on a horizontal line. Subtract the x-coordinates: 7 − 2 = 5 units.

Question 49Mathematics

A pattern uses the rule add 7, starting at 4: 4, 11, 18, 25, ... Which number appears in this pattern?

  1. 38
  2. 32 Correct answer.
  3. 40
  4. 35

Explanation

Continuing the rule gives 25 + 7 = 32, then 39. Every term is 4 plus a multiple of 7, and 32 = 4 + 4 × 7, so 32 belongs to the pattern.

Question 50Mathematics

A spinner has 8 equal sections numbered 1 through 8. What is the probability of spinning a number greater than 5?

  1. 3/8 Correct answer.
  2. 2/8
  3. 5/8
  4. 6/8

Explanation

The numbers greater than 5 are 6, 7, and 8, which are 3 favorable outcomes out of 8 equally likely sections. The probability is therefore 3/8.