Mixed numbers and improper fractions

Mixed numbers and improper fractions can name the same amount in different ways. Your child learns to count complete wholes together with equal parts, then express that amount as one fraction. The MOE Primary 4 syllabus names mixed numbers, improper fractions and their relationship. Understanding the relationship makes conversion a way of regrouping the amount, rather than a rule that changes its value.

• Recognise a mixed number as whole units together with a proper fraction, where the fraction describes equal parts of one unit.
• Convert a mixed number to an improper fraction by counting the parts in all the complete wholes and adding the remaining parts.
• Convert an improper fraction to whole units and a remaining fraction by dividing the numerator by the denominator.
• Keep the denominator during conversion because regrouping the parts does not change how many equal parts make one whole.
• Simplify the fraction part when appropriate, and use equal-sized fractional parts when comparing amounts written in different forms.

After converting an improper fraction, your child can multiply the whole-number part by the original denominator and add the remaining numerator before simplification. This must recover the original numerator, with the remainder smaller than the denominator.

The Basic question puts fractions and a mixed number in descending order. Intermediate questions here compare and order fractions, mixed numbers and whole numbers, recover a missing denominator, and read fifths on a number line. Challenge questions find an equivalent improper fraction from a numerator-and-denominator total or recover a missing numerator in a sum of fractions. Ask your child to choose a common form for a comparison and explain why the conversion preserves the value. On the number line, keep the completed wholes separate from the extra equal parts before writing the mixed number. If a conversion step is uncertain, compare your child's chosen form with the written working once they have attempted the question. The free ordering card supplies written working for converting the three quantities to comparable fractions, so your child can check their descending order. Multiple-choice Basic questions ask which figure or number line shows a given mixed number or improper fraction, or which improper fraction is NOT between two consecutive whole numbers.

Can an improper fraction be exactly a whole number? Yes. When the numerator is an exact multiple of the denominator, all the parts make complete wholes and none remain. An improper fraction has a numerator greater than or equal to its denominator, so the name includes fractions equal to one whole as well as larger amounts.

Why does my child multiply before adding in the conversion? Each complete whole contains as many equal parts as the denominator states. Multiplying counts those parts across the whole units; adding includes the extra parts from the fractional part. Ask your child what each number is counting, so the two operations have a clear meaning.

Should my child always turn mixed numbers into improper fractions to compare them? It is one useful method, but it is not always necessary. Mixed numbers with different whole-number parts can be compared by those parts first. If their whole-number parts match, compare the fractional parts using equivalent fractions when needed, keeping the whole unit the same.