Working with Fractions: common misconceptions

If your child says… “I multiply both the top and bottom by 6.”

Ask together

Does taking more thirds turn them into smaller parts?

What’s true

Multiplying adds more thirds without changing their size.

If your child says… “I add the top numbers and add the bottom numbers.”

Ask together

Do two rows of four cells give six cells or eight?

What’s true

Multiply selected rows by selected columns, and total rows by total columns.

If your child says… “I can cancel only numbers that match.”

Ask together

Can both 2 and 4 be divided by 2?

What’s true

Unequal numbers can share a factor.

If your child says… “Multiplying by a fraction always makes things smaller.”

Ask together

Is three halves more than one copy of 6?

What’s true

A positive amount shrinks below one copy, stays at one, and grows above one.

If your child says… “I turn both fractions upside down.”

Ask together

Did one half need turning over to remove the two-thirds multiplier?

What’s true

Only the divisor turns over when division becomes multiplication.

If your child says… “Starting with a small fraction must give a smaller answer.”

Ask together

Does starting with one half prevent an answer of 1?

What’s true

For positive numbers, divisors below 1 enlarge answers, above 1 shrink them, and 1 preserves them.

If your child says… “The bigger number must come first in division.”

Ask together

Are we sharing two rotis or half a roti?

What’s true

The amount being shared comes first, even when it is smaller.

If your child says… “One third for later means one third of twelve.”

Ask together

Which peanuts are still available after the snack portion leaves?

What’s true

The later share comes from the six remaining peanuts.