Math Is Fun

Basic Arithmetic + Algebra

100

What is 356 ÷ 4?

Steps:

1. Divide 356 by 4.
2. 4 goes into 35 eight times (4 × 8 = 32).
3. Subtract 32 from 35, which gives a remainder of 3.
4. Bring down the next digit (6) to make 36.
5. 4 goes into 36 nine times (4 × 9 = 36).
6. There is no remainder.

Answer: 356 ÷ 4 = 89.

200

Solve for x: 2x + 5 = 13.

Steps:

1. Subtract 5 from both sides of the equation:
   2x + 5 − 5 = 13 − 5, which simplifies to:
   2x = 8.
2. Divide both sides by 2 to solve for x:
   2x / 2 = 8 / 2, which simplifies to:
   x = 4.

Answer: x = 4.

300

What is 723 ÷ 9?

Steps:

1. Divide 723 by 9.
2. 9 goes into 72 eight times (9 × 8 = 72).
3. Subtract 72 from 72, which gives a remainder of 0.
4. Bring down the next digit (3) to make 3.
5. 9 goes into 3 zero times.
6. The quotient is 80 with a remainder of 3, or 80 3/9, which simplifies to 80 1/3.

Answer: 723 ÷ 9 = 80 1/3 or 80.33.

400

Solve for y: 3y - 7 = 11.

Steps:

1. Add 7 to both sides of the equation:
   3y − 7 + 7 = 11 + 7, which simplifies to:
   3y = 18.
2. Divide both sides by 3 to solve for y:
   3y / 3 = 18 / 3, which simplifies to:
   y = 6

Answer: y = 6.

500

Solve for z: 4(z - 3) = 20

Steps:

1. Distribute the 4 on the left side:
   4z − 12 = 20
2. Add 12 to both sides:
   4z − 12 + 12 = 20 + 12, which simplifies to:
   4z = 32
3. Divide both sides by 4 to solve for z:
   4z / 4 = 32, which simplifies to:
   z = 8

Answer: z = 8.

Probabilities And Statistics

100

What is the mean of these numbers: 2, 4, 6, 8, 10?

Steps:

1. Add all the numbers together:
   2 + 4 + 6 + 8 + 10 = 30
2. Divide the sum by the number of numbers (5):
   30 / 5 = 6

Answer: The mean is 6.

200

A bag contains 3 red, 4 blue, and 5 green marbles. What is the probability of randomly selecting a red marble?

Steps:

1. Find the total number of marbles:
   3 + 4 + 5 = 12
2. The probability of selecting a red marble is the number of red marbles divided by the total number of marbles:
   3 / 12
3. Simplify the fraction:
   3 / 12 = 1 / 4

Answer: The probability of selecting a red marble is 1 / 4 or 0.25.

300

What is the median of the following numbers: 7, 10, 5, 12, 8?

Hint: the middle child

Steps:

1. Arrange the numbers in ascending order:
   5, 7, 8, 10, 12.
2. Since there are five numbers, the median is the middle number in the sorted list, which is the third number.

Answer: The median is 8.

400

A die is rolled once. What is the probability of rolling a number greater than 4?

Steps:

1. List the numbers on a standard die: 1, 2, 3, 4, 5, and 6.
2. Identify the numbers greater than 4: 5 and 6 (2 outcomes).
3. The total number of possible outcomes is 6.
4. The probability is the number of favorable outcomes divided by the total number of outcomes:
   2 / 6
5. Simplify the fraction:
   2 / 6 = 1 / 3

Answer: The probability of rolling a number greater than 4 is 1 / 3

500

What is the mode of this set of numbers: 3, 5, 7, 3, 8, 5, 3? 

Hint: Sam is MOSTly afraid of chickens named Jeff, mainly because he appears the most frequently.

Steps:

1. Count the occurrences of each number:
   • 3 appears 3 times.
   • 5 appears 2 times.
   • 7 and 8 each appear 1 time.
2. The mode is the number that appears most frequently.

Answer: The mode is 3.

Geometry + Pythagorean Theorem

100

What is the area of a circle with a radius of 5 cm?

Steps:

1. Use the area formula for a circle:
   A = πr², where r is the radius.
2. Substitute 5 cm for r:
   A = π(5)²
3. A = π × 25
4. Approximate using π ≈ 3.14:
   A ≈ 3.14 × 25 = 78.5 cm²

Answer: Area ≈ 78.5 cm².

200

Find the hypotenuse of a right triangle with legs of 6 cm and 8 cm.

Steps:

1. Use the Pythagorean theorem:
   a² + b² = c², where a and b are the legs, and c is the hypotenuse.
2. Substitute 6 for a and 8 for b:
   6² + 8² = c²
3. Calculate:
   36 + 64 = c²
   100 = c²
4. Take the square root of both sides:
   c = sqrt(100)
5. c = 10

Answer: Hypotenuse = 10 cm.

300

A ladder is leaning against a wall. The base of the ladder is 4 feet from the wall, and the ladder is 13 feet long. How high up the wall does the ladder reach?

Hint: figure out which sides of the triangle are given

Steps:

1. Use the Pythagorean theorem:
   a² + b² = c², where a is the distance from the wall (4 feet), b is the height up the wall, and c is the ladder length (13 feet).
2. Substitute the values:
   4² + b² = 13²
3. Calculate 4² and 13²:
   16 + b² = 169
4. Subtract 16 from both sides:
   b² = 153
5. Take the square root of both sides:
   b = sqrt(153) ≈ 12.37 feet.

Answer: The ladder reaches approximately 12.37 feet up the wall.

400

What is the perimeter of a rectangle with a length of 10 cm and a width of 7 cm?

Steps:

1. Use the perimeter formula for a rectangle:
   P = 2 × (length + width)
2. Substitute the values for length and width:
   P = 2 × (10 + 7)
3. Calculate inside the parentheses:
   P = 2 × 17 = 34

Answer: The perimeter is 34 cm.

500

A rectangular field has a diagonal length of 15 meters. One side of the field is 9 meters. What is the length of the other side? 

Hint: figure out which sides of the triangle are given

Steps:

1. Use the Pythagorean theorem:
   a² + b² = c², where a is one side (9 meters), b is the unknown side length, and c is the diagonal (15 meters).
2. Substitute the values:
   9² + b² = 15²
3. Calculate 9² and 15²:
   81 + b² = 225
4. Subtract 81 from both sides:
   b² = 144
5. Take the square root of both sides:
   b = sqrt(144) = 12 meters.

Answer: The length of the other side is 12 meters.

Fractions And Decimals

100

Convert 3/4 to a decimal.

Steps:

1. Divide the numerator (3) by the denominator (4).
2. 3 ÷ 4 = 0.75.

Answer: 3/4 = 0.75

200

Convert 7 / 8 to a decimal.

Steps:

1. Divide the numerator (7) by the denominator (8).
2. 7 ÷ 8 = 0.875

Answer: 7 / 8 = 0.875

300

Convert 0.45 to a fraction in simplest form.

Steps:

1. Write 0.45 as a fraction: 45 / 100
2. Simplify by dividing the numerator and the denominator by their greatest common factor (5):
   (45 ÷ 5) / (100 ÷ 5) = 9 / 20

Answer: 0.45 = 9 / 20

400

Add 3 / 4 and 5 / 6

Steps:

1. Find a common denominator. The least common multiple of 4 and 6 is 12.
2. Convert 3 / 4 and 5 / 6 to have a denominator of 12:
   • 3 / 4 = (3 × 3) / (4 × 3) = 9 / 12
   • 5 / 6 = (5 × 2) / (6 × 2) = 10 / 12
3. Add the fractions:
   (9 / 12) + (10 / 12) = 19 / 12
4. Simplify if needed; in this case, 19 / 12 is an improper fraction, so it can also be written as 1 7 / 12

Answer: (3 / 4) + (5 / 6) = (19 / 12)

500

Subtract 1.25  from 3.5

Steps:

1. Line up the decimal points and subtract:
   3.50 − 1.25 = 2.25

Answer: 3.5 − 1.25 = 2.25

Word Problems

100

If you buy 3 books at $12 each, how much do you spend?

Steps:

1. Multiply the number of books by the price per book:
   3 × 12 = 36

Answer: You spend $36.

200

Sara bought 5 notebooks for $2.75 each and 3 pens for $1.50 each. How much did she spend in total?

Steps:

1. Calculate the cost of the notebooks:
   5 × 2.75 = 13.75
2. Calculate the cost of the pens:
   3 × 1.50 = 4.50
3. Add the two amounts together:
   13.75 + 4.50 = 18.25

Answer: Sara spent $18.25 in total.

300

A rectangular garden has a length of 12 meters and a width of 9 meters. If fencing costs $4 per meter, how much will it cost to fence the entire garden?

Steps:

1. Find the perimeter of the garden using the perimeter formula for a rectangle:
   P = 2 × (length + width)
   P = 2 × (12 + 9) = 2 × 21 = 42
2. Multiply the perimeter by the cost per meter:
   42 × 4 = 168

Answer: It will cost $168 to fence the entire garden.

400

A train travels 120 miles in 2 hours. At this rate, how far will it travel in 5 hours?

Steps:

1. First, find the rate of travel by dividing the distance by time:
   Rate = 120 / 2 = 60 miles per hour.
2. Multiply the rate by 5 hours:
   60 × 5 = 300

Answer: The train will travel 300 miles in 5 hours.

500

If you flip a coin 3 times, what is the probability that you get exactly 2 heads?

Steps:

1. List all possible outcomes when flipping a coin 3 times:
   • HHH, HHT, HTH, THH, TTH, THT, HTT, TTT (8 outcomes total).
2. Identify the outcomes with exactly 2 heads:
   • HHT, HTH, THH (3 outcomes).
3. Find the probability by dividing the number of favorable outcomes by the total number of outcomes:
   3 / 8

Answer: The probability of getting exactly 2 heads is 3 / 8 or 0.375.