Converting between mixed numbers (e.g., 2¾) and improper fractions (e.g., 11/4), understanding when each form is appropriate.
Where your child meets this in real life: Expressing measurements like 1½ metres, recipe quantities, or time durations
SEAGReady breaks mixed numbers and improper fractions into 3 steps, taught in order so each skill builds on the last.
Identify improper fractions (where numerator ≥ denominator) and understand that they represent values ≥ 1 whole
Convert improper fractions to mixed numbers using division with remainders
Convert mixed numbers to improper fractions using: (whole × denominator) + numerator = new numerator
Three free sample questions from our mixed numbers and improper fractions course. Every question comes with a full explanation, and hints that guide without giving the answer away.
Ciara is sorting fraction cards. She picks up the card showing 9/5. Is this an improper fraction?
Answer: A. Yes, because 9 is greater than 5
Look at the numerator (9) and denominator (5). Since 9 > 5, the numerator is bigger than the denominator. When the top is bigger than the bottom, it's an improper fraction. So yes, 9/5 is an improper fraction.
Stuck? Start here: Compare the top number (numerator) with the bottom number (denominator).
Oisin has 9/4 of a chocolate bar. Convert this to a mixed number.
Answer: A. 2¼
Divide the numerator by the denominator: 9 ÷ 4 = 2 remainder 1 - Quotient (2) = whole number part - Remainder (1) = new numerator - Keep denominator (4) 9/4 = 2¼
Stuck? Start here: Divide the numerator (9) by the denominator (4).
Siobhan needs 3½ cups of sugar for a recipe. Write this as an improper fraction.
Answer: A. 7/2
Use the formula: (whole × denominator) + numerator 3½ = (3 × 2) + 1 = 6 + 1 = 7 Keep denominator: 2 3½ = 7/2 (seven halves)
Stuck? Start here: First multiply the whole number by the denominator: 3 × 2 = ?
This is the exact interactive worked example your child sees in SEAGReady. Step through it and watch the method build up.
Aoife is sorting fraction cards for a maths game. She needs to find which fractions are 'improper' (equal to or greater than 1 whole).
Is 7/4 an improper fraction? How many wholes and parts does it represent?
7/4 = ?
Step 1 of 4
Aoife is sorting fraction cards for a maths game. She needs to find which fractions are 'improper' (equal to or greater than 1 whole).
Is 7/4 an improper fraction? How many wholes and parts does it represent?
7/4 is an improper fraction. It equals 1 whole and 3/4.
The key insight: When the top number is bigger than the bottom, you have MORE than 1 whole!
Watch out: 7/4 is a proper fraction because 4 is smaller than 7. It's the other way round! When the numerator (top) is bigger, the fraction is improper.
These are the misconceptions we see most often in mixed numbers and improper fractions, including the ones our practice questions are specifically designed to catch.
Struggling with mixed numbers and improper fractions? The real gap is often in one of these earlier topics.
SEAGReady finds the exact step where your child gets stuck, teaches it with worked examples like the one above, and brings it back for review so it sticks.