Ratios
The ratio of red marbles to blue marbles in a bag is 2 : 3.
If there are 10 red marbles, how many blue marbles are in the bag?
15
What is:
–4 + 9 = ?
Answer: 5
Evaluate:
5 + 3 × 4 = ?
Answer: 17
(Order of operations: multiply first)
A triangle has angles measuring 50° and 60°.
What is the measure of the third angle?
Answer: 70°
Find the mean of the numbers:
4, 6, 8, 10
Answer: 7
Student thinking:
(4 + 6 + 8 + 10) ÷ 4 = 28 ÷ 4 = 7
Complete the equivalent ratio:
4 : 5 = 12 : ___
Answer: 15
(Student thinking: 4 → 12 is ×3, so 5 × 3 = 15)
What is:
7 − (–6) = ?
Answer: 13
(Remember: subtracting a negative = add)
Simplify:
3x + 5x = ?
Answer: 8x
Find the area of a triangle with:
Answer: 20 cm²
Student thinking:
½ × 8 × 5 = 20
Find the median of the data set:
3, 9, 5, 7, 11
Answer: 7
Student thinking:
Order numbers first → 3, 5, 7, 9, 11
Middle number = 7
The ratio of boys to girls in a club is 3 : 2.
There are 25 students total.
How many are boys?
Answer: 15 boys
(Student thinking: 3+2=5 parts → 25 ÷ 5 = 5 each part → 3×5=15)
The temperature was –2°C in the morning.
It increased 7°C during the day.
What is the temperature now?
Answer: 5°C
Solve for x:
x + 6 = 14
Answer: x = 8
A circle has a radius of 7 cm.
What is the circumference?
(Use π ≈ 3.14)
Answer: 43.96 cm
Student thinking:
C = 2πr
2 × 3.14 × 7 = 43.96
Find the mode:
2, 5, 5, 7, 9, 5, 11
Answer: 5
(Student thinking: mode = most frequent number)
A car travels 180 miles in 3 hours.
What is the unit rate in miles per hour?
Answer: 60 miles per hour
Which number is farther from zero?
–8 or 6
Answer: –8
(|–8| = 8 and |6| = 6)
Solve for x:
3x − 5 = 16
Answer: x = 7
(Add 5 first → divide by 3)
Find the volume:
length = 6 cm
width = 4 cm
height = 3 cm
Answer: 72 cm³
Student thinking:
6 × 4 × 3 = 72
A bag contains:
What is the probability of choosing a blue marble?
Answer: 5/10 or 1/2
Student thinking:
Total marbles = 10
Blue = 5
Probability = 5/10
The ratio of teachers to students at a school is 1 : 20.
If there are 15 teachers, how many students are there?
Answer: 300 students
(Student thinking: 1 → 15 means ×15
20 × 15 = 300)
A submarine starts at –12 meters below sea level.
It rises 5 meters, then rises 9 more meters.
Where is the submarine now?
Answer: 2 meters above sea level
Step thinking:
A number multiplied by 4, then increased by 3, equals 27.
What is the number?
Answer: 6
Student thinking:
On a scale drawing:
1 cm = 5 meters
A wall measures 4 cm on the drawing.
How long is the actual wall?
Answer: 20 meters
Student thinking:
4 × 5 = 20
Class A test scores:
70, 80, 90
Class B test scores:
60, 80, 100
Which class has the greater mean, or are they equal?
Answer: They are equal
Student thinking:
Class A mean = (70+80+90) ÷ 3 = 80
Class B mean = (60+80+100) ÷ 3 = 80