Class 7 Fractions and Decimals Worksheet – Operations and Conversions

Master fractions and decimals with this worksheet for Class 7 with addition, subtraction, multiplication, division, and conversions. Includes solved examples and real-world problems to help your child handle complex calculations with confidence.

What are Fractions and Decimals?

Fractions and decimals are two ways of representing parts of a whole. At Class 7, we move beyond basic operations into multi-step problems that combine both.

We convert between fractions and decimals, work with mixed numbers, find the LCD for unlike fractions, and apply these skills to real-world scenarios like recipes, measurements, shopping, and speed calculations. The ability to switch fluently between fractions and decimals is essential at this level.

Key Operations

Addition and Subtraction of Fractions: Find the Lowest Common Denominator (LCD), convert both fractions, then add or subtract the numerators. The denominator stays the same.

Multiplication of Fractions: Multiply the numerators together and the denominators together, then simplify the result.

Division of Fractions: Flip the second fraction (take its reciprocal) and multiply. So a/b ÷ c/d becomes a/b × d/c.

Decimal Operations: For addition and subtraction, align the decimal points before calculating. For multiplication, multiply as whole numbers then place the decimal point based on the total number of decimal places in both numbers.

Conversions

Fraction to Decimal: Divide the numerator by the denominator.

Decimal to Fraction: Write the decimal as a fraction with the appropriate denominator based on decimal places — for example, 0.375 becomes 375/1000 — then simplify.

Solved Example

A recipe needs 2¾ cups of flour. You want to make 1½ times the recipe. How much flour do you need?

Step-by-Step Solution

Convert the mixed numbers to improper fractions. 2¾ becomes 11/4 and 1½ becomes 3/2.

Multiply the fractions: 11/4 × 3/2 = 33/8.

Convert back to a mixed number: 33 ÷ 8 = 4 remainder 1, so the answer is 4⅛ cups.

Convert to decimal for verification: 33 ÷ 8 = 4.125 cups.

Answer: 4⅛ cups or 4.125 cups of flour are needed.

Practice Problems

• Priya bought 3.5 kg of apples at ₹80 per kg and 2.25 kg of oranges at ₹60 per kg. Find the total cost. → Decimal Multiplication in a Real-world Context
• A water tank is 3/5 full. Adding 120 litres makes it 4/5 full. Find the total capacity of the tank. → Working Backwards with Fractions
• A rectangular garden is 12.5 m long and 8.4 m wide. Find its perimeter. → Decimal Addition Applied to Geometry
• Rajesh spends 2/5 of his salary on rent, 1/4 on food, and 1/10 on transport. What fraction is left? If his salary is ₹40,000, how much remains? → Adding Unlike Fractions and Finding Remainders
• A car travels 156.8 km in 2.8 hours. Find the average speed, then calculate distance covered in 4.5 hours at the same speed. → Division and Multiplication with Decimals
• A shopkeeper marks an item at ₹850 and offers 12.5% discount. Find the selling price. If profit is ₹106.25, find the cost price. → Multi-step Decimal Problem with Percentages

Scoring Guide

• 20–24 marks: Excellent! You are ready for rational numbers, algebraic expressions with fractions, and advanced percentage applications.
• 15–19 marks: Very Good! Practice fraction division and finding the LCD for unlike fractions. Work on converting between fractions and decimals regularly.
• 10–14 marks: Good Effort! Review basic operations with common denominators. Practice decimal alignment and multiplication tables, which are essential for fraction work.
• 0–9 marks: Keep Trying! Go back to Class 6 fraction basics. Practice simplification and decimal operations step by step with a tutor or teacher.

Tips and Common Mistakes

Always convert mixed numbers to improper fractions before multiplying or dividing. Trying to work directly with mixed numbers leads to errors almost every time.

When dividing fractions, do not divide the numerators and denominators separately. Flip the second fraction and multiply. This is the single most misunderstood operation at this level.

For addition and subtraction of unlike fractions, finding the LCD is the critical first step. Using the wrong common denominator makes the entire calculation incorrect.

When multiplying decimals, count the total decimal places in both numbers carefully. Placing the decimal point in the wrong position changes the answer by a factor of 10 or more.

Always simplify fractions to their lowest form after calculating. Leaving 8/12 instead of writing 2/3 is incomplete.

Memorise common fraction-to-decimal conversions: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 1/8 = 0.125. These come up repeatedly and knowing them instantly saves time.

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