Other High School 450 words

Decimals, Fractions, and Percentages: Worksheet Problems

~3 min read

Abstract

This worksheet collection guides students through three essential mathematical skills: converting decimals to fractions in simplest form, changing fractions to decimal equivalents, and solving percentage-based word problems. The material includes worked examples demonstrating method, followed by scaffolded practice exercises. Topics covered range from basic decimal-to-fraction conversion using place value and division, to applied percentage calculations involving discounts, profit margins, value-added tax (VAT), and proportional reasoning.

📝 How to Write This Type of Paper Writing guide — click to expand

▼

What makes this paper effective

Clear two-part structure for each topic: worked example first, then scaffolded practice exercises that increase in difficulty.
Explicit method explanations (e.g., identifying place value to set denominator, recognizing when long division is required) help students understand the "why" behind the process.
Real-world context in percentage problems—pocket money, wages, museum discounts, retail markup, VAT, vehicle sales—makes abstract concepts tangible and motivates engagement.
Consistent notation and formatting (bullet points, clear alignment of steps) reduce cognitive load and support independent practice.

Key academic technique demonstrated

The worksheet employs the mastery-learning progression: introduce concept with annotated worked example → provide guided practice with similar but varied cases → extend to applied problem-solving. This scaffolding is especially effective in procedural topics like decimal-fraction conversion, where understanding the underlying principle (place value, divisibility, long division) transfers across many item types.

Structure breakdown

The paper comprises three independent, modular sections: (1) Decimal→Fraction conversion using place value and simplification; (2) Fraction→Decimal conversion using equivalence or long division; (3) Percentage problems spanning retail, wage, tax, and inventory contexts. Each section follows the same pedagogical pattern: explanation + model + exercises. This modular design allows flexible pacing and supports differentiated instruction.

Converting Decimals to Fractions

Worksheet

Method: Changing a decimal into a fraction in its simplest form

Example

Change 0.56 to a fraction in its simplest form.

0.56 is read as "fifty-six hundredths," so the denominator is 100.

0.56 = 56/100

Now simplify by finding the greatest common divisor (GCD) of 56 and 100. The GCD is 4.

Therefore: 0.56 = 56/100 = 14/25

Exercises

Change the following to fractions in their simplest form.

Converting Fractions to Decimals

(a) 0.4 (b) 0.8 (c) 0.25
(d) 0.75 (e) 0.15 (f) 0.08
(g) 0.125 (h) 0.65 (i) 0.48
(j) 0.02 (k) 0.52 (l) 0.06
(m) 0.82 (n) 0.14 (p) 0.94
(q) 0.28 (r) 0.77 (s) 0.53

Worksheet

Method: Changing a fraction to a decimal

Examples

(a) Change 2/5 to a decimal:

The denominator 5 is a factor of 100. We can rewrite the fraction with denominator 100:

2/5 = 40/100 = 0.40 (or 0.4)

(b) Change 1/3 to a decimal:

The denominator 3 is not a factor of 100. Remember that the fraction line means division. Therefore, we must work out 1 ÷ 3.

1 ÷ 3 = 0.333... (the 3 repeats infinitely)

When the denominator does not divide evenly into 10, 100, 1000, or higher powers of 10, use long division to find the decimal equivalent.

1 Locked Section · 280 words remaining

Percentage Problems and Applications · 280 words

"Real-world percentage calculations: discounts, profit, VAT, attendance"

You’re 41% through this paper. Sign up to read the remaining 1 section.

130,000+ paper examples AI writing assistant Citation generator Cancel anytime

Key Concepts in This Paper

Place Value Fraction Simplification Decimal Equivalence Long Division Percentage Increase Percentage Decrease Discount Calculation Profit and Loss VAT Proportional Reasoning