Ratios, fractions, negative numbers, equations, area and data, with every step shown and a paper copy to print.
1.A fruit bowl holds 6 apples and 9 oranges. What is the ratio of apples to oranges in simplest form?
2.In a class of 28 students, 12 walk to school and the rest ride the bus. What is the ratio of walkers to bus riders?
3.A printer prints 96 pages in 8 minutes at a steady rate. What is its unit rate?
4.A trail mix uses 3 cups of raisins for every 8 cups of oats. How many cups of raisins are used for each cup of oats?
5.In a table of equivalent ratios, 3 scoops of drink mix go with 4 cups of water and 6 scoops go with 8 cups. How many cups of water go with 15 scoops?
6.A 12-ounce box of cereal costs $3.00 and an 18-ounce box costs $3.96. Which box is the better buy?
7.A cyclist rides 45 miles in 3 hours at a constant speed. At that speed, how far does the cyclist ride in 5 hours?
8.A jacket has a regular price of $80. A sale takes 45% off. How many dollars are taken off the price?
9.Twelve students in a club are sixth graders. That is 40% of the club. How many students are in the club?
10.A quiz has 25 questions and Maya answers 21 of them correctly. What percent of the questions does she answer correctly?
11.A ribbon is 4.5 feet long. There are 12 inches in 1 foot. How long is the ribbon in inches?
12.A runner drinks 2,500 milliliters of water in a day. There are 1,000 milliliters in 1 liter. How many liters is that?
13.A ribbon 7/8 yard long is cut into pieces that are each 1/16 yard long. How many pieces are there?
14.A baker has 2/3 pound of butter and uses 1/6 pound in each batch of rolls. How many batches can the baker make?
15.What is 2 1/2 ÷ 1 1/4?
16.What is 7,654 ÷ 43?
17.What is 14.6 − 8.75?
18.What is 3.6 × 0.45?
19.What is 9.52 ÷ 0.4?
20.What is the greatest common factor of 56 and 84?
21.One bus leaves a station every 6 minutes and another leaves every 9 minutes. Both leave at noon. After how many minutes do they next leave together?
22.Which expression equals 42 + 28 and has the greatest common factor of 42 and 28 outside the parentheses?
23.A diver is 35 feet below sea level. If sea level is 0, which number represents the diver's elevation in feet?
24.In which quadrant of the coordinate plane is the point (−4, 7)?
25.The point (5, −2) is reflected across the x-axis. What are the coordinates of the new point?
Print covers the next 25 questions. Share this set copies a link to the same questions in the same order.
Exam mode: 25 questions, no time limit.
Your totals on this device
0answered
0right
none yetpercent right
none yetbest exam score
Seen 0 of 63 questions
More options
Which questions to ask
Missed and Flagged fill up as you go.
Unofficial practice questions, not affiliated with any school, district, state or test publisher. Bank checked October 10, 2026.
A 12-ounce box of cereal costs $3.00 and an 18-ounce box costs $3.96. Which box is the better buy?Common Core State Standards for Mathematics, 6.RP.A.3.b: unit rate problems, including unit pricing and constant speed
A cyclist rides 45 miles in 3 hours at a constant speed. At that speed, how far does the cyclist ride in 5 hours?Common Core State Standards for Mathematics, 6.RP.A.3.b: unit rate problems, including unit pricing and constant speed
A fruit bowl holds 6 apples and 9 oranges. What is the ratio of apples to oranges in simplest form?Common Core State Standards for Mathematics, 6.RP.A.1: use ratio language to describe a relationship between two quantities
A jacket has a regular price of $80. A sale takes 45% off. How many dollars are taken off the price?Common Core State Standards for Mathematics, 6.RP.A.3.c: a percent of a quantity as a rate per 100
A printer prints 96 pages in 8 minutes at a steady rate. What is its unit rate?Common Core State Standards for Mathematics, 6.RP.A.2: the unit rate a/b associated with a ratio a:b
Show all 63 questions (58 more)
Ratios and Proportional Relationships, continued
A quiz has 25 questions and Maya answers 21 of them correctly. What percent of the questions does she answer correctly?Common Core State Standards for Mathematics, 6.RP.A.3.c: a percent of a quantity as a rate per 100
A ribbon is 4.5 feet long. There are 12 inches in 1 foot. How long is the ribbon in inches?Common Core State Standards for Mathematics, 6.RP.A.3.d: ratio reasoning to convert measurement units
A runner drinks 2,500 milliliters of water in a day. There are 1,000 milliliters in 1 liter. How many liters is that?Common Core State Standards for Mathematics, 6.RP.A.3.d: ratio reasoning to convert measurement units
A trail mix uses 3 cups of raisins for every 8 cups of oats. How many cups of raisins are used for each cup of oats?Common Core State Standards for Mathematics, 6.RP.A.2: the unit rate a/b associated with a ratio a:b
In a class of 28 students, 12 walk to school and the rest ride the bus. What is the ratio of walkers to bus riders?Common Core State Standards for Mathematics, 6.RP.A.1: use ratio language to describe a relationship between two quantities
In a table of equivalent ratios, 3 scoops of drink mix go with 4 cups of water and 6 scoops go with 8 cups. How many cups of water go with 15 scoops?Common Core State Standards for Mathematics, 6.RP.A.3.a: tables of equivalent ratios and their missing values
Twelve students in a club are sixth graders. That is 40% of the club. How many students are in the club?Common Core State Standards for Mathematics, 6.RP.A.3.c: finding the whole, given a part and the percent
The Number System 16
A baker has 2/3 pound of butter and uses 1/6 pound in each batch of rolls. How many batches can the baker make?Common Core State Standards for Mathematics, 6.NS.A.1: word problems that divide a fraction by a fraction
A diver is 35 feet below sea level. If sea level is 0, which number represents the diver's elevation in feet?Common Core State Standards for Mathematics, 6.NS.C.5: positive and negative numbers for quantities with opposite directions
A ribbon 7/8 yard long is cut into pieces that are each 1/16 yard long. How many pieces are there?Common Core State Standards for Mathematics, 6.NS.A.1: quotients of fractions
A submarine's position is recorded as −120 meters. What is |−120|?Common Core State Standards for Mathematics, 6.NS.C.7.c: absolute value as distance from 0
In which quadrant of the coordinate plane is the point (−4, 7)?Common Core State Standards for Mathematics, 6.NS.C.6.b: signs of the numbers in an ordered pair and the quadrants
One bus leaves a station every 6 minutes and another leaves every 9 minutes. Both leave at noon. After how many minutes do they next leave together?Common Core State Standards for Mathematics, 6.NS.B.4: greatest common factor and least common multiple
The point (5, −2) is reflected across the x-axis. What are the coordinates of the new point?Common Core State Standards for Mathematics, 6.NS.C.6.b: ordered pairs that differ only by signs are reflections across an axis
What is 2 1/2 ÷ 1 1/4?Common Core State Standards for Mathematics, 6.NS.A.1: quotients of fractions
What is 3.6 × 0.45?Common Core State Standards for Mathematics, 6.NS.B.3: adding, subtracting, multiplying and dividing multi-digit decimals
What is 9.52 ÷ 0.4?Common Core State Standards for Mathematics, 6.NS.B.3: adding, subtracting, multiplying and dividing multi-digit decimals
What is 14.6 − 8.75?Common Core State Standards for Mathematics, 6.NS.B.3: adding, subtracting, multiplying and dividing multi-digit decimals
What is 7,654 ÷ 43?Common Core State Standards for Mathematics, 6.NS.B.2: dividing multi-digit numbers
What is the distance between the points (−3, 4) and (5, 4) on the coordinate plane?Common Core State Standards for Mathematics, 6.NS.C.8: distances between points with the same first or second coordinate
What is the greatest common factor of 56 and 84?Common Core State Standards for Mathematics, 6.NS.B.4: greatest common factor and least common multiple
Which expression equals 42 + 28 and has the greatest common factor of 42 and 28 outside the parentheses?Common Core State Standards for Mathematics, 6.NS.B.4: the distributive property and a common factor of two whole numbers
Which list shows −8, −3.5, 0 and 2 in order from least to greatest?Common Core State Standards for Mathematics, 6.NS.C.7.a: inequalities as positions of two numbers on a number line
Expressions and Equations 19
A child must be taller than 48 inches to ride a roller coaster. Which inequality shows the heights h, in inches, of children who may ride?Common Core State Standards for Mathematics, 6.EE.B.8: inequalities of the form x > c or x < c
A machine fills 40 bottles each minute. Which equation gives the number of bottles b filled in m minutes?Common Core State Standards for Mathematics, 6.EE.C.9: an equation for a dependent variable in terms of an independent variable
A table shows x = 1, 2, 3, 4 and y = 4, 7, 10, 13. Which equation relates y to x?Common Core State Standards for Mathematics, 6.EE.C.9: relating a table to an equation
In the expression 9x + 5, what is the coefficient of x?Common Core State Standards for Mathematics, 6.EE.A.2.b: the parts of an expression: term, factor, coefficient
Jon has saved $85, which is 5 times as much as his sister has saved. The equation 5s = 85 models this. How much has his sister saved?Common Core State Standards for Mathematics, 6.EE.B.7: equations of the form x + p = q and px = q
The perimeter of a rectangle is P = 2l + 2w. What is P when l = 7.5 centimeters and w = 4 centimeters?Common Core State Standards for Mathematics, 6.EE.A.2.c: expressions that arise from formulas
Tickets to a school play cost $8 each. Which expression gives the cost, in dollars, of t tickets?Common Core State Standards for Mathematics, 6.EE.B.6: variables and expressions for real-world problems
What is the solution of (2/3)x = 10?Common Core State Standards for Mathematics, 6.EE.B.7: equations of the form x + p = q and px = q
What is the solution of x + 4.7 = 13.2?Common Core State Standards for Mathematics, 6.EE.B.7: equations of the form x + p = q and px = q
What is the value of 2⁵ + 4²?Common Core State Standards for Mathematics, 6.EE.A.1: numerical expressions with whole-number exponents
What is the value of 3a² − 4 when a = 5?Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluating expressions at given values, in the conventional order
What is the value of 5³?Common Core State Standards for Mathematics, 6.EE.A.1: numerical expressions with whole-number exponents
What is the value of 18 − 12 ÷ 3 × 2?Common Core State Standards for Mathematics, 6.EE.A.2.c: evaluating expressions at given values, in the conventional order
Which expression is equivalent to 4m + 3 + 2m?Common Core State Standards for Mathematics, 6.EE.A.4: when two expressions are equivalent
Which expression is equivalent to 5(2x + 3)?Common Core State Standards for Mathematics, 6.EE.A.3: properties of operations and equivalent expressions
Which expression is equivalent to 18a + 12b?Common Core State Standards for Mathematics, 6.EE.A.3: properties of operations and equivalent expressions
Which expression means "9 less than the product of 6 and n"?Common Core State Standards for Mathematics, 6.EE.A.2.a: expressions that record operations with numbers and letters
Which value of n makes the inequality n − 6 > 10 true?Common Core State Standards for Mathematics, 6.EE.B.5: substitution to test whether a number makes an equation or inequality true
Which value of x makes the equation 3x + 4 = 19 true?Common Core State Standards for Mathematics, 6.EE.B.5: substitution to test whether a number makes an equation or inequality true
Geometry 9
A box has a base area of 24 square inches and a height of 3 1/2 inches. Using V = Bh, what is its volume?Common Core State Standards for Mathematics, 6.G.A.2: the formulas V = lwh and V = Bh
A parallelogram has a base of 12 inches and a height of 7.5 inches. What is its area?Common Core State Standards for Mathematics, 6.G.A.1: area of triangles, special quadrilaterals and polygons
A rectangle has vertices at (2, 1), (2, 6), (9, 6) and (9, 1). How long is the side from (2, 6) to (9, 6)?Common Core State Standards for Mathematics, 6.G.A.3: polygons in the coordinate plane and the lengths of their sides
A rectangular prism is 5 inches long, 3 inches wide and 2 inches high. What is its surface area?Common Core State Standards for Mathematics, 6.G.A.4: nets and surface area
A right rectangular prism is 2 1/2 feet long, 2 feet wide and 1 1/2 feet high. What is its volume?Common Core State Standards for Mathematics, 6.G.A.2: volume of right rectangular prisms with fractional edge lengths
A trapezoid has parallel sides of 8 meters and 12 meters and a height of 5 meters. What is its area?Common Core State Standards for Mathematics, 6.G.A.1: area of triangles, special quadrilaterals and polygons
A triangle has a base of 16 centimeters and a height of 11 centimeters. What is its area?Common Core State Standards for Mathematics, 6.G.A.1: area of triangles, special quadrilaterals and polygons
An L-shaped garden is made of a 10-foot by 4-foot rectangle joined to a 6-foot by 3-foot rectangle, with no overlap. What is its total area?Common Core State Standards for Mathematics, 6.G.A.1: area of polygons by composing and decomposing
The net of a cube is six squares, each with sides of 4 centimeters. What is the surface area of the cube?Common Core State Standards for Mathematics, 6.G.A.4: nets and surface area
Statistics and Probability 7
A dot plot of pets owned by 10 students has four dots at 0, three dots at 1, two dots at 2 and one dot at 5. How many pets do the students own in all?Common Core State Standards for Mathematics, 6.SP.B.4: numerical data in dot plots, histograms and box plots
A statistical question is one whose answers are expected to vary. Which of these is one?Common Core State Standards for Mathematics, 6.SP.A.1: a statistical question anticipates variability in the data
The data set 3, 5, 6, 8, 10, 12, 15 is in order. What is its interquartile range?Common Core State Standards for Mathematics, 6.SP.B.5.c: measures of variability: interquartile range and mean absolute deviation
Five houses on a street sold for $180,000, $185,000, $190,000, $195,000 and $900,000. Which measure best describes a typical price?Common Core State Standards for Mathematics, 6.SP.B.5.d: choosing a measure of center to fit the shape of the data
What is the mean absolute deviation of 3, 5, 9 and 11?Common Core State Standards for Mathematics, 6.SP.B.5.c: measures of variability: interquartile range and mean absolute deviation
What is the mean of 6, 9, 4, 11 and 10?Common Core State Standards for Mathematics, 6.SP.B.5.c: measures of center: median and mean
What is the median of 12, 7, 15, 9, 20 and 11?Common Core State Standards for Mathematics, 6.SP.B.5.c: measures of center: median and mean
How this list was compiled: Our own questions. Outline: the Common Core State Standards for Mathematics, grade 6, https://www.thecorestandards.org/Math/Content/6/introduction/, with the five domain pages (Ratios and Proportional Relationships, The Number System, Expressions and Equations, Geometry, Statistics and Probability) and the glossary, https://www.thecorestandards.org/Math/Content/mathematics-glossary/glossary/, read 2026-10-10. Each question names the standard it practices and links to that domain page. Every answer is arithmetic on the numbers the question prints, and each one was worked out again on 2026-10-10. The two conversion factors (12 inches in 1 foot, 1,000 milliliters in 1 liter) are printed in their questions and were checked in NIST Handbook 44 (2026), Appendix C, https://www.nist.gov/document/2026-nist-handbook-44-appendix-c, read 2026-10-10. Licence: Own work. Questions, answer choices and explanations were written for this site. Nothing is copied or reworded from a state test, a released form, a sample item, a textbook or another practice test.
How it works
Unofficial sixth grade math practice: 63 questions written for this page to the five domains of the Common Core grade 6 standards. It follows no single state's test, so no test length or pass mark is implied.
Read the full guide
What the 63 questions cover
Expressions and Equations has 19 questions, The Number System 16, Ratios and Proportional Relationships 12, Geometry 9, and Statistics and Probability 7. The weight falls on ratios and rates, dividing fractions, negative numbers, and writing and solving equations.
A missed question names its skill
Each explanation shows the working and ends with its standard, such as 6.RP.A.3.c for percents or 6.NS.A.1 for dividing fractions, so a missed question points to the exact skill to review.
For a percent, find 10% first and build the rest from it.
Check an equation by putting your answer back in place of the letter.
Questions and answers
Is there a 6th grade math practice test PDF?
Yes, by printing. The questions print as a paper test, with an answer key if you want one, and the print window can save that paper as a PDF. There is nothing to sign up for.
Is this a standardized testing practice test for 6th grade math?
It practices the Common Core grade 6 skills and follows no single test. For one test's own design, try the STAAR, PSSA or MCAS grade 6 math pages.
What math should a 6th grader know?
The Common Core names four critical areas for grade 6: ratios and rates; dividing fractions and working with negative numbers; writing and solving expressions and equations; and statistical thinking. Area, surface area and volume are taught as well.
Does this 6th grade math test come with answers?
Yes. On screen, each answer is marked as soon as it is chosen, with the working shown. On paper, the answer key is optional and prints after the questions.