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Praxis Core Academic Skills for Educators Collection2026 Core Spec
Number And QuantityMEDIUMVerified Curriculum5 min read

Number and Quantity

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Chapter 1

Number and Quantity

Course: Core Academic Skills For Educators Combined Test 5752
Subject: Core Academic Skills Educators Mathematics 5733
Chapter: Number And Quantity

1. Understanding Integers, Decimals, and Fractions

Integers are whole numbers that include all positive numbers, their negative counterparts, and zero. They do not contain fractional or decimal parts. Examples include –15, –2, 0, 3, and 42. Integers are used in real-life situations to represent changes in quantity such as temperature differences, gains or losses in finance, and elevation above or below sea level.

Decimals are numbers that use a decimal point to represent parts of a whole, based on the base-ten place value system. Each position to the right of the decimal point represents a negative power of ten: tenths, hundredths, thousandths, and so on. Decimals are common in money, precise measurements, and scientific data.

Fractions are expressions representing a part of a whole, consisting of a numerator (top number) and a denominator (bottom number). Fractions may be:

  • Proper (numerator smaller than denominator, e.g., 3/5)
  • Improper (numerator greater than or equal to denominator, e.g., 7/4)
  • Mixed numbers (a whole number and a proper fraction combined, e.g., 2 1/3)

Fractions and decimals can represent the same value; for example, 1/4 is equivalent to 0.25.

2. Operations with Integers

Addition

  • When both integers have the same sign, add their absolute values and keep the sign. Example: –7 + (–3) = –10.
  • When integers have different signs, subtract the smaller absolute value from the larger and give the result the sign of the number with the larger absolute value. Example: 8 + (–5) = 3.

Subtraction

  • Convert subtraction to addition of the opposite number: a – b = a + (–b). Example: 6 – (–4) = 6 + 4 = 10.

Multiplication and Division

  • Same sign → positive result; different signs → negative result. Example: (–5) × (–2) = 10; (–12) ÷ 4 = –3.

3. Operations with Decimals

Addition and Subtraction

  • Align decimal points vertically so that place values match.
  • Add zeros if necessary to make the decimals have the same number of digits. Example: 4.35 + 2.4 = 4.35 + 2.40 = 6.75.

Multiplication

  • Ignore decimal points and multiply as whole numbers.
  • Count the total number of decimal places in both numbers and place the decimal in the product accordingly. Example: 2.5 × 0.06 = 0.15 (two decimal places total).

Division

  • If dividing by a decimal, shift the decimal point in both the divisor and dividend the same number of places to make the divisor a whole number. Example: 4.5 ÷ 0.3 = 45 ÷ 3 = 15.

4. Operations with Fractions

Addition and Subtraction

  • Find the least common denominator (LCD) of the fractions.
  • Convert each fraction to an equivalent form with the LCD.
  • Add or subtract numerators, keeping the denominator the same.
  • Simplify the result if possible. Example: 1/4 + 2/3 → LCD = 12 → 3/12 + 8/12 = 11/12.

Multiplication

  • Multiply numerators together and denominators together.
  • Simplify before multiplying if possible to reduce calculation size. Example: 2/5 × 15/8 = (2 × 15) / (5 × 8) = 30/40 → 3/4.

Division

  • Multiply the first fraction by the reciprocal of the second. Example: (3/4) ÷ (2/5) = (3/4) × (5/2) = 15/8 = 1 7/8.

5. Converting Between Fractions, Decimals, and Percents

  • Fraction to decimal: Divide numerator by denominator. Example: 3/8 = 0.375.
  • Decimal to fraction: Place the decimal over the appropriate power of ten and simplify. Example: 0.4 = 4/10 = 2/5.
  • Decimal to percent: Multiply by 100 and add the percent symbol. Example: 0.625 × 100 = 62.5%.
  • Percent to decimal: Divide by 100. Example: 75% = 0.75.
  • Percent to fraction: Convert to decimal first, then to fraction. Example: 40% = 0.4 = 2/5.

6. Order of Operations

When performing operations that involve integers, decimals, and fractions in the same problem, follow the order of operations (PEMDAS):

  • Parentheses
  • Exponents
  • Multiplication and Division (from left to right)
  • Addition and Subtraction (from left to right)

Example: 5 + 3 × (8 – 2)² ÷ 6 = 5 + 3 × 36 ÷ 6 = 5 + 108 ÷ 6 = 5 + 18 = 23.

7. Working with Mixed Numbers and Improper Fractions

  • Convert mixed numbers to improper fractions when performing operations to simplify the calculation process.
  • After calculation, improper fractions can be converted back to mixed numbers if required for clarity.

Example: 2 1/3 + 4 2/5 Convert to improper fractions: 7/3 + 22/5 Find LCD (15): 35/15 + 66/15 = 101/15 = 6 11/15.

8. Real-Life Applications

  • Budgeting — Combining expenses in decimal form while managing savings in fractional form, such as 1/3 of income for rent.
  • Cooking — Scaling recipes using fractional quantities, converting them to decimals for use with digital scales.
  • Construction — Converting between fractional inches and decimal inches for accurate cuts.
  • Science experiments — Using decimals for precise measurements and fractions for ratios in mixtures.
  • Sports statistics — Converting between fractional win ratios and decimal averages.

9. Common Mistakes to Avoid

  • Adding or subtracting fractions without finding a common denominator first.
  • Forgetting to align decimal points in addition or subtraction.
  • Ignoring sign rules when multiplying or dividing integers.
  • Placing the decimal point incorrectly in multiplication results.
  • Performing rounding too early in multi-step calculations, leading to compounding errors.