Teaching Visually – Mixed Numbers and Improper Fractions without Rules

Students often see writing mixed numbers as improper fractions and vice versa as a “conversion” procedure involving rules, e.g.

  • multiply the whole number with the denominator and add it to the numerator to get the new numerator (mixed numbers to improper fractions),
  • divide the numerator by the denominator, write the quotient as the whole number and leave the remainder as the numerator (improper fractions to mixed numbers).

These rule-based approach often results in common mistakes such as:

Singapore Math Mixed numbers to improper fractions
Common Mistakes – mixed numbers to improper fractions

But how do we teach mixed numbers and improper fractions without rules?

Instead of teaching the rules, we now prefer to use pictorial representations to let the students understand the relationships between these two fraction representations. For example,

Singapore Math Mixed numbers and improper fractions
Teaching visually – mixed numbers and improper fractions

Not only is it intuitive to see how 2 and 3/4 is the same as 11 quarters, it is also easy to understand why 11 quarters can be arranged into 2 wholes and 3 remaining quarters.

Working with pictorial representations makes students realize these are just two ways of representing the same quantity and no real “conversion” is involved!

More Fraction Resources

For more fraction resources, refer to our main fractions page.

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