6th Grade Math
A class has red, blue, and green markers in a ratio of 3:5:2.
If there are 40 markers in total, how many of each color are there?
Red = 12, Blue = 20, Green = 8
A recipe uses 3 cups of flour to make 12 muffins.
How many muffins can be made with 7.5 cups of flour?
3 cups → 12 muffins → 4 muffins per cup.
7.5 cups × 4 muffins/cup = 30 muffins.
Solve for x: 4x−7=21
Answer: x=7
A turtle crawls 18 meters in 6 minutes.
At this rate, how far will it crawl in 15 minutes?
45 meters
Riley is hiking along a canyon trail. She descends 85 feet, then climbs 60 feet, and then descends another 25 feet.
What is her final elevation change from where she started?
Start 0 → descend 85 ⇒ −85
Climb 60 ⇒ −85 + 60 = −25
Descend 25 ⇒ −25 − 25 = −50
A line passes through the points (2,3) and (5,15).
a) Find the slope.
b) Write the equation of the line in slope-intercept form y=mx+b
Answer: slope 4; equation y=4x−5
The temperature at 6 a.m. was –3°F.
By the afternoon, it increased by 12°F and then dropped by 5°F.
What is the final temperature?
Final temperature = 4°F
A gym charges a monthly membership fee plus $4 for each class attended.
If Mari spent $72 in a month and took 8 classes, what is the monthly membership fee?
Total = membership fee + $4·(number of classes)
$72 = fee + $4·8 = fee + $32 ⇒ fee = $72 − $32 = $40
A right triangle has legs of length 9 cm and 12 cm. What is the length of the hypotenuse?
hypotenuse = 15 cm
A theme park charges $8 for admission plus $3 per ride.
Write an expression for the total cost for r rides, and find the cost if a student rides 7 rides.
Expression: 8 + 3r; Cost for 7 rides = $29
A circular garden has a radius of 6 meters.
What is the area of the garden?
(Use π ≈ 3.14)
Area = πr² = 3.14 × 6² = 3.14 × 36 = 113.04 m²
A cylindrical water tank has radius 3 meters and height 10 meters.
Use π≈3.14
What is the tank’s volume (in cubic meters)?
V≈282.6 m³
A rectangular prism has a length of 10 cm, width of 4 cm, and height of 6 cm.
What is its surface area?
Surface area = 248 cm²
A bag contains 5 red marbles, 3 blue marbles, and 2 green marbles.
If one marble is drawn at random, what is the probability it is not blue?
Total marbles = 5 + 3 + 2 = 10
Not blue = 10 − 3 = 7 ⇒ probability = 7/10 = 0.7 = 70%
On a map, 1 cm represents 15 kilometers. A road measures 7.2 cm on the map. How many kilometers is the road in real life?
108 kilometers.