№ 1 · Arithmetic · Grade 6
Grade 6 math problems with answers
Problems on fractions, ratios, percentages, equations, divisibility, combinatorics, and geometry. Hints help children build and check each solution step by step.
30 problems with worked solutions.
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Topic collections
№ 2 · Arithmetic · Grade 6
Seven twelfths of a number equal 84. What is the number?
№ 3 · Arithmetic · Grade 6
Three segments have lengths in the ratio 3:4:5, and their total length is 144 centimeters. What is the length of the longest segment?
№ 4 · Arithmetic · Grade 6
A price of 800 rubles was increased by 15 percent, then the new price was reduced by 10 percent. What is the final price in rubles?
№ 5 · Arithmetic · Grade 6
Five containers have an average mass of 42 kilograms. Four containers together weigh 158 kilograms. How many kilograms does the fifth container weigh?
№ 6 · Arithmetic · Grade 6
A number was multiplied by 4, then 18 was subtracted from the result. The result was 70. What was the original number?
№ 7 · Counting · Grade 6
Using the digits 1, 2, 3, and 4, four-digit even numbers are formed without repeating a digit. How many numbers are possible?
№ 8 · Counting · Grade 6
There are 12 participants at a meeting. Each person shakes hands with every other participant exactly once. How many handshakes occur?
№ 9 · Geometry · Grade 6
A triangle has a base of 18 centimeters and a height of 14 centimeters to that base. What is the area of the triangle?
№ 10 · Geometry · Grade 6
A rectangular box is 8 decimeters long, 5 decimeters wide, and 3 decimeters high. What is its total surface area?
№ 11 · Patterns · Grade 6
Continue the sequence 3, 7, 13, 21, 31. The difference between consecutive numbers increases by 2 each time. What is the next number?
№ 12 · Time and calendars · Grade 6
A cyclist rode 48 kilometers at 12 kilometers per hour, then another 30 kilometers at 10 kilometers per hour. How many hours did the whole trip take?
№ 13 · Money and measurement · Grade 6
A jacket cost 2400 rubles. First it received a 15 percent discount, then a coupon for 140 rubles was used. How many rubles were paid?
№ 14 · Word problems · Grade 6
Three shelves hold 98 books. The first shelf has twice as many books as the second, and the third has 10 more books than the second. How many books are on the first shelf?
№ 15 · Logic · Grade 6
Find the smallest positive integer that leaves a remainder of 2 when divided by 5 and a remainder of 4 when divided by 7.
№ 16 · Logic · Grade 6
Two ribbons of 84 and 126 centimeters must be cut into equal pieces of the greatest possible length with no remainder. How long is each piece?
№ 17 · Logic · Grade 6
One beacon flashes every 18 seconds and another every 24 seconds. They flash together now. After how many seconds will they flash together again?
№ 18 · Geometry · Grade 6
A rectangle on the coordinate plane has opposite vertices at (−2, 1) and (5, 6), with sides parallel to the axes. What is its area?
№ 19 · Counting · Grade 6
Two people must be chosen from 8 participants for a team, with no difference between their roles. How many choices are possible?
№ 20 · Logic · Grade 6
There are chickens and rabbits in a yard. Altogether there are 18 heads and 50 legs. How many rabbits are there?
№ 21 · Patterns · Grade 6
The first row of an auditorium has 11 seats. Each following row has 7 more seats than the previous row. How many seats are in the twentieth row?
№ 22 · Time and calendars · Grade 6
A tank initially contains 30 liters of water. Each hour 50 liters flow in while 14 liters flow out. How many liters will be in the tank after 5 hours?
№ 23 · Money and measurement · Grade 6
Three identical notebooks and two identical pens cost 760 rubles together. One notebook costs 120 rubles. How many rubles does one pen cost?
№ 24 · Counting · Grade 6
A code consists of three different letters chosen from A, B, C, and D. How many codes are possible if letter order matters?
№ 25 · Geometry · Grade 6
A trapezoid has bases of 12 and 20 centimeters and a height of 9 centimeters. What is its area?
№ 26 · Arithmetic · Grade 6
Three quarters of a number were increased by 12, giving 57. What is the original number?
№ 27 · Word problems · Grade 6
A prize fund of 180 thousand rubles was divided among three teams in the ratio 2:3:4. How many thousand rubles did the team with the largest share receive?
№ 28 · Logic · Grade 6
There are three closed boxes labeled 'apples', 'pears', and 'apples and pears'. All three labels are wrong. How many fruits must be taken from one chosen box to determine all the contents?
№ 29 · Time and calendars · Grade 6
What is the smaller angle in degrees between the hour and minute hands at 3 hours 30 minutes?
№ 30 · Counting · Grade 6