Number and Quantity

Quick Answer: Number and Quantity makes up about 20 questions (~36%) of the Praxis Core Math subtest. You'll need to work with whole numbers, fractions, decimals, percentages, ratios, and order of operations. A four-function on-screen calculator is available, but efficiency matters—know when to use it and when mental math is faster.

This content area tests your ability to understand and work with numbers in various forms. Success requires fluency in converting between representations and applying arithmetic to real-world contexts.

Order of Operations (PEMDAS)

The order of operations is critical for evaluating expressions correctly:

Worked Example: Order of Operations

Problem: Evaluate $3 + 4 × (2³ - 6) ÷ 2$

Step-by-Step Solution:

1. Parentheses first (evaluate inside):

   • Inside the parentheses: 2³ - 6
   • Calculate exponent: 2³ = 8
   • Then subtract: 8 - 6 = 2

2. Expression becomes: 3 + 4 × 2 ÷ 2

3. Multiplication and division (left to right):

   • 4 × 2 = 8
   • 8 ÷ 2 = 4

4. Addition:

   • 3 + 4 = 7

Calculator Tip: Your on-screen calculator follows standard order of operations. For the expression above, enter: 3 + 4 × 2 ÷ 2 = and you'll get 7.

Fractions

Key Fraction Operations

Finding Common Denominators

To add 2/5 + 1/3:

1. Find LCD (Least Common Denominator): LCD of 5 and 3 is 15
2. Convert fractions:
   • 2/5 = 6/15 (multiply by 3/3)
   • 1/3 = 5/15 (multiply by 5/5)
3. Add: 6/15 + 5/15 = 11/15

Worked Example: Mixed Numbers

Problem: A recipe calls for 2⅓ cups of flour and 1¾ cups of sugar. How much total dry ingredient is needed?

Solution:

1. Convert to improper fractions:

   • 2⅓ = 7/3
   • 1¾ = 7/4

2. Find common denominator (12):

   • 7/3 = 28/12
   • 7/4 = 21/12

3. Add: 28/12 + 21/12 = 49/12

4. Convert back: 49/12 = 4 1/12 cups

Decimals

Place Value

Decimal Operations

Adding/Subtracting: Line up decimal points

• 12.45 + 3.7 → 12.45 + 3.70 = 16.15

Multiplying: Count total decimal places

• 2.3 × 1.5 = 3.45 (one decimal place × one decimal place = two decimal places)

Dividing: Move decimal point to make divisor whole

• 4.5 ÷ 0.09 = 450 ÷ 9 = 50

Calculator Tip: Decimals are ideal for calculator use. The on-screen calculator handles them accurately—just be careful with decimal point placement when entering numbers.

Converting Between Forms

Fraction ↔ Decimal ↔ Percentage

Conversion Rules:

• Fraction → Decimal: Divide numerator by denominator
• Decimal → Percentage: Multiply by 100 (move decimal 2 places right)
• Percentage → Decimal: Divide by 100 (move decimal 2 places left)
• Decimal → Fraction: Write as fraction over power of 10, then simplify

Worked Example: Percentage Calculation

Problem: A teacher purchased supplies for $84. If this was 70% of her budget, what was her total budget?

Solution:

1. Set up equation: 84 = 0.70 × Budget
2. Solve: Budget = 84 ÷ 0.70 = $120

Calculator Tip: Enter 84 ÷ 0.70 = to get 120.

Ratios and Proportions

Understanding Ratios

A ratio compares two quantities. If a class has 12 boys and 18 girls:

• Ratio of boys to girls: 12:18 = 2:3
• Ratio of boys to total: 12:30 = 2:5

Solving Proportions

Cross-multiply to solve proportions:

$\frac{a}{b} = \frac{c}{d} \implies a \times d = b \times c$

Worked Example: Proportion

Problem: If 3 textbooks cost $45, how much do 7 textbooks cost?

Solution:

1. Set up proportion: 3/45 = 7/x
2. Cross-multiply: 3x = 45 × 7 = 315
3. Solve: x = 315 ÷ 3 = $105

Unit Rates

A unit rate expresses a ratio with denominator of 1.

Example: If you drive 240 miles in 4 hours:

• Unit rate: 240 ÷ 4 = 60 miles per hour

Real-World Applications

Percentage Increase/Decrease

Worked Example: Percentage Decrease

Problem: A school's enrollment dropped from 800 to 720 students. What was the percentage decrease?

Solution:

1. Find change: 800 - 720 = 80
2. Calculate percentage: 80 ÷ 800 × 100% = 10% decrease