Problem 1
How many three-digit numbers can be made from the digits 1, 2, 3, and 4 if no digit is repeated?
Grade 5 math problems: printable worksheet
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Problem 2
A square with a perimeter of 48 cm was cut into four identical small squares. What is the sum of the perimeters of all the small squares in centimeters?
Problem 3
In the sequence 7, 12, 17, 22, each next number is 5 more. What is the twentieth term?
Problem 4
Three cards are chosen from seven cards of different colors. The red card must be included, and the blue card must not be included. How many different sets can be made?
Problem 5
Find the sum of numbers from 1 to 30 that are not divisible by 3.
Problem 6
A pedestrian left a village at 6 km/h. One hour later, a cyclist followed at 18 km/h. How many hours after setting off will the cyclist catch the pedestrian?
Problem 7
How many even four-digit numbers can be made from the digits 1, 2, 3, 4, using each exactly once?
Problem 8
A rectangle has an area of 96 cm² and one side is 8 cm long. What is its perimeter in centimeters?
Problem 9
Two distinguishable six-sided dice are rolled. In how many ways can the sum of the numbers drawn be equal to 7?
Problem 10
From eight different books you need to choose two for the trip. The order of the books is not important. How many options are there to choose from?
Answer key and solutions
Problem 1. Answer: 24
There are four choices for the hundreds digit, three for the tens digit, and two for the units digit: 24.
Problem 2. Answer: 96
The side of the large square is 12 cm, the small one is 6 cm. Four perimeters of 24 cm each give 96.
Problem 3. Answer: 102
After the first term to the twentieth there are 19 additions of 5: 7 + 95 = 102.
Problem 4. Answer: 10
Red has already been selected, blue has been excluded. Of the five remaining, we choose two: 5 × 4 ÷ 2 = 10.
Problem 5. Answer: 300
The sum of all numbers is 465. Multiples of 3 give 3 × (1 + … + 10) = 165. The difference is 300.
Problem 6. Answer: 0.5
By the time the cyclist leaves, the pedestrian is 6 km ahead. Approach speed 12 km/h, time 0.5 hours.
Problem 7. Answer: 12
Last digit 2 or 4, two choices. The remaining three digits can be rearranged 3 × 2 × 1 in the following ways: 12.
Problem 8. Answer: 40
Other side 96 ÷ 8 = 12 cm. Perimeter 2 × (8 + 12) = 40 cm.
Problem 9. Answer: 6
The ordered pairs (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) are suitable: six.
Problem 10. Answer: 28
The first book can be selected in 8 ways, the second 7. Each pair is counted twice, so 28.