Expressions and Equations
Mrs. Lin has a garden that is 15 feet long. She wants to divide it into equal sections for different vegetables. If each section is 3 feet long, write an equation to find how many sections she'll have.
15 / 3 = x
Emily wants to put a decorative border around her rectangular garden. If the garden is 12 feet long and 8 feet wide, what is the perimeter of the garden?
Solution: Perimeter = 2 × (Length + Width) = 2 × (12 + 8) = 40 feet.
Jason has 3/8 of a pizza, and his friend Mike has 5/8 of the same pizza. How much pizza do they have together?
3/8 + 5/8 = 8/8 = 1 whole pizza.
Write the number 45,678 in expanded form using base 10 notation.
45,678 = (4 × 10,000) + (5 × 1,000) + (6 × 100) + (7 × 10) + (8 × 1)
Sarah recorded the following temperatures for five days: 60°F, 65°F, 70°F, 62°F, and 68°F. What was the average temperature for these days?
65°F
The school collected $480 from selling tickets to a fundraiser. Each ticket costs $8. Write an expression to find out how many tickets were sold and then solve it.
480 / 8 = number of tickets sold; 60
A small park is shaped like a square with each side measuring 50 meters. Calculate the area of the park.
Solution: Area = Side × Side = 50 × 50 = 2,500 square meters.
Sarah has 5/6 of a cake, and she gives away 1/3 of it. How much cake does she have left?
First, find a common denominator (6 for both fractions).
5/6 - 1/3 = 5/6 - 2/6 = 3/6 = 1/2 of the cake left
Round the number 12,345 to the nearest hundred.
The number 12,345 rounded to the nearest hundred is 12,300 because 45 is less than 50.
The test scores of five students were 85, 90, 75, 80, and 95. Find the median score.
Arrange scores in order: 75, 80, 85, 90, 95.
The median is the middle number, which is 85.
At a pizza party, there are 4 pizzas, and each pizza is cut into 8 slices. If each student at the party eats 2 slices, write an equation to determine how many students can be fed with the pizza.
Equation: (4 × 8) ÷ 2 = number of students
15
One angle in a triangle measures 50 degrees, and another angle measures 60 degrees. What is the measure of the third angle?
Solution: The sum of the angles in a triangle is 180 degrees. So, 180 - (50 + 60) = 70 degrees.
If a recipe calls for 2/3 cup of milk and you want to make half of the recipe, how much milk do you need?
2/3 × 1/2 = (2 × 1) / (3 × 2) = 2/6 = 1/3 cup of milk.
Add 4,789 to 3,456
8245
If you have a bag with 4 red marbles, 3 blue marbles, and 2 green marbles, what is the probability of drawing a blue marble?
Total marbles = 4 + 3 + 2 = 9
Probability of blue = 3/9 = 1/3
During the book fair, each book costs $5. If you have $25, how many books can you buy? Write an equation to solve this problem.
Equation: 25 ÷ 5 = x
If each edge of a cube-shaped storage box is 3 feet long, what is the volume of the box?
Solution: Volume of a cube = Edge³ = 3 × 3 × 3 = 27 cubic feet.
Emma has 3/4 of a yard of ribbon. She wants to cut it into pieces that are each 1/8 of a yard long. How many pieces will she get?
Divide by the reciprocal: 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 pieces.
Subtract 2,456 from 5,678.
3,222
In a class, the number of siblings students have is: 0, 1, 2, 1, 3, 1, 2. What is the mode of this data?
The mode is the number that appears most frequently, which is 1.
Mr. Patel needs to distribute 36 pencils equally among his 9 students. Write an expression to find out how many pencils each student gets, then solve it.
Expression: 36 ÷ 9 = pencils per student
Draw a shape that has exactly two lines of symmetry. How many lines of symmetry does an equilateral triangle have?
An example of a shape with two lines of symmetry could be a rectangle (horizontal and vertical).
An equilateral triangle has 3 lines of symmetry (one through each vertex to the midpoint of the opposite side).
Which is greater, 3/5 or 5/8?
Convert to common denominators (like 40):
3/5 = 24/40, 5/8 = 25/40. Therefore, 5/8 is greater than 3/5.
How many times greater is 10,000 than 100 when thinking about powers of 10?
10,000 is 100 times greater than 100
A survey at school shows that out of 20 students, 12 prefer pizza, 6 prefer burgers, and 2 prefer salads. If one student is chosen at random, what is the probability they prefer pizza?
Probability of preferring pizza = Number of students who prefer pizza / Total number of students = 12/20 = 3/5