Convert 57/5 to a mixed number
- 57 ÷ 5 = 11 remainder 2
- The quotient becomes the whole number, the remainder becomes the numerator
- 57/5 = 11 2/5
Year 9 maths lesson · Fractions
Mixed Numbers and Improper Fractions
Convert between mixed numbers and improper fractions in both directions. Improper-to-mixed uses division with remainders; mixed-to-improper uses multiply-then-add.
- About 4–7 minutes
- 5 quick questions as you go
- Then about 5 minutes of practice
The lesson didn't load. Refresh the page to try again.
Worked examples
Convert 50/7 to a mixed number
- 50 ÷ 7 = 7 remainder 1
- 50/7 = 7 1/7
Convert 10 2/5 to an improper fraction
- Misconception: student tries 10 + 2 = 12, giving 12/5 (wrong)
- Correct: multiply whole × denominator — 10 × 5 = 50
- Add the numerator: 50 + 2 = 52
- 10 2/5 = 52/5
Convert 6 3/8 to an improper fraction
- 6 × 8 = 48
- 48 + 3 = 51
- 6 3/8 = 51/8
Before this lesson
It helps to be comfortable with:
- Fractions
- Division with remainders
Lesson transcript
Everything the lesson says, word for word
Student: Hey Alex, what are we working on today?
Teacher: Do you know what that number is?
Student: 57 fifths? I could draw that… circles split into 5 pieces, shade in 57 of them…
Student: That’s going to be a LOT of circles.
Teacher: Right. But think about what you’re actually doing — you’re trying to figure out how many wholes you can make from 57 fifths.
Teacher: Each whole is 5 fifths. So really you’re asking, how many 5s fit into 57?
Teacher: Let’s skip the pictures and do that a faster way.
Teacher: Did you know the fraction line means divide?
Student: I think my teacher said that once…
Teacher: It’s really important. Fractions and division are the same thing. It comes up everywhere — algebra, converting fractions to decimals on your calculator… loads of things. But today, let’s just use it to convert improper fractions.
Teacher: So 57 over 5 is the same as 57 divided by 5. How many 5s go into 57?
Student: Well, I know 11 fives are 55… so that’s 11 times with 2 left over.
Teacher: So 57 divided by 5 is 11 remainder 2. So 11 whole times and the 2 still needs dividing by 5 — so the answer is 11 and 2 fifths.
Student: Oh I see! The remainder just becomes the numerator.
Teacher: Try this one. What’s 50 over 7?
Student: 50 divided by 7… well I know 7 sevens are 49, so that’s 7 times with 1 left over. So it’s 7 and 1 seventh!
Teacher: Perfect.
Teacher: Now what about the other way? Can you turn 10 and 2 fifths into an improper fraction?
Student: So I just put the numbers together… 10 plus 2 is 12… so 12 over 5?
Teacher: Not quite. Think about what those 10 wholes actually mean. Each whole was made up of 5 fifths. So 10 wholes is 10 lots of 5 — that’s 50 fifths. Then add the 2 that were left over.
Student: Oh! 50 fifths plus 2 makes 52 fifths. That makes way more sense.
Teacher: Try this one. Turn 6 and 3 eighths into an improper fraction.
Student: OK so… the whole number times the denominator… 6 times 8 is 48…
Student: Then add the numerator… 48 plus 3 is 51. So it’s 51 over 8!
Teacher: Exactly right. Multiply the whole number by the denominator, then add the numerator. That’s all there is to it.
Teacher: Right, try these questions then.
More Fractions lessons
- Simplifying and Equivalent FractionsSimplify fractions and find equivalent fractions using common factors.
- Adding and Subtracting FractionsFind common denominators and add or subtract fractions with confidence.
- Multiplying FractionsMultiply fractions together and multiply fractions by whole numbers.
- Dividing FractionsDivide fractions and divide whole numbers by fractions — multiply by the reciprocal.
- Fractions of an AmountCalculate a fraction of a quantity — a key everyday maths skill.
- Expressing a Quantity as a FractionWrite one quantity as a fraction of another and simplify.
- Finding the Original AmountIf you know a fraction of an amount, work backwards to find the whole.
Next lesson: Adding and Subtracting Fractions →All Year 9 Number lessonsAll lessons