Hard Fractions — Fractions worksheet for Grade 7.
No signup required — instant download

A common denominator represents equal-sized pieces. When adding 1/4 + 1/6, we're combining different-sized pieces (fourths and sixths), so we need to convert them to the same size first (twelfths). With multiplication, we're finding a fraction OF a fraction (e.g., 1/2 × 1/3 = 1/6), which uses a different operation that doesn't require equal denominators. Division is the inverse of multiplication, so it follows the same rule.
A fraction is simplified (in lowest terms) when the numerator and denominator have no common factors other than 1. To check, find the greatest common factor (GCF) of both numbers. If the GCF is 1, the fraction is simplified. For example, 8/12 has a GCF of 4, so it simplifies to 2/3. The number 2/3 has a GCF of 1, so it cannot be simplified further.
In Grade 7, convert improper fractions to mixed numbers when the problem asks for the final answer as a mixed number or when the context makes sense (like dividing a pizza among people). However, leave answers as improper fractions when continuing with further operations, because improper fractions are easier to work with mathematically. Always check the problem instructions.
Division makes numbers smaller only when dividing by numbers greater than 1. When you divide by a fraction less than 1 (like 1/2), you're asking 'How many halves fit into this number?' The answer is larger because smaller pieces fit more times. For example, 4 ÷ 1/2 = 8 because eight halves make 4 wholes. This is why 'keep, change, flip' works—it converts division into multiplication, revealing why the answer can be larger.
Learn how to teach fractions to kids in grades 2–5 with proven strategies, visual models, and hands-on methods that build real understanding — not just memorized rules.
Make fractions click for your child with hands-on activities, visual models, and free printable worksheets. A parent's guide to teaching fractions from halves to mixed numbers for grades 2-4.
Learn how to teach ratios and proportions to middle schoolers with step-by-step strategies, real-world examples, and hands-on activities for grades 6–8.
Subscribe for new worksheets and homeschool tips. No spam, unsubscribe anytime.
Look for operation keywords: 'altogether' or 'combined' suggests addition; 'how much more' or 'difference' suggests subtraction; 'of' usually means multiplication (like '2/3 of 12'); 'divide into groups' or 'how many times' suggests division. Rewrite the problem in a mathematical sentence before solving. For example, 'Sarah has 3/4 of a gallon and uses 1/6 of a gallon' becomes 3/4 − 1/6 = ?