Subtracting mixed numbers and calculating with fractions
Subtract mixed numbers, open up a whole when needed, solve expressions with complex fractions and scale up a recipe.
📖 Start here: read the steps of the “Lesson” in order (1, 2, 3 …) and answer each question. Then continue with “Practice”.
- Germany: grade 6
- Iran: grade 5
Guide
To subtract mixed numbers you can subtract the whole numbers first and then the fractions. If the fraction of the first number is smaller than the second, open up a whole and turn it into a fraction: 315 = 265. Then subtract.
Another way is to turn both into improper fractions: 514 = 214. Then subtract the numerators, keep the denominator, and turn the answer back into a mixed number.
A common mistake is to subtract "small from big" in the fractions: in 215 − 35, you must not do 35 − 15. Open up a whole first.
In an expression with several operations, work out the top of the fraction first, then divide. Dividing by a fraction means multiplying by its reciprocal. A fraction whose numerator or denominator is a fraction is a complex fraction (fraction of fractions).
To scale up a recipe, first work out the amount for one person or one glass, then multiply by the number.