Sharing 3 cakes among 4 children used to be "0 each, remainder 3". That is not much help.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Share the leftover too
Cut each cake into 4. Every child gets 3 of the quarters, which is 3/4 of a cake.
So a fraction is a division
3 ÷ 4 = 3/4. The top number is what is shared, and the bottom is how many share it.
A rule that breaks
You can divide a smaller number by a bigger one. The answer is simply less than 1.
The fraction bar is a division sign
3/4 means 3 ÷ 4. Share 3 pizzas between 4 people and each gets three quarters. This is not a new fact about fractions — it is what a fraction has meant all along, now stated explicitly.
The remainder finally has a name
17 ÷ 5 = 3 remainder 2 in Grade 4. Now you can say the answer exactly: 3 2/5. The leftover 2 is 2 of the 5 pieces each whole was going to be cut into. Remainders were never an incomplete answer; you just lacked the notation.
Three ways to express one division
17 ÷ 5 can be 3 r 2, or 3 2/5, or 3.4. All three are correct and each suits a different context: buses need the remainder handled separately, recipes want the fraction, money wants the decimal. Choosing the right form is part of answering well.
Reading improper fractions as divisions
17/5 is 17 ÷ 5, which is why converting it to a mixed number is a division: 17 ÷ 5 = 3 remainder 2, giving 3 2/5. The conversion rule you learned by procedure in Grade 4 turns out to be nothing but a division.
Step 2: Try It Yourself
Tap and try it out.
3/4
1/1
3/4 is less than 1/1.
Compare how much of the whole each one covers.
Step 3: Watch an Example
One step at a time.
Watch Leo Share 5 Pizzas Among 4
Leo shares 5 pizzas equally among 4 people.
- Step 1
He gives each person one whole pizza, using 4.
Step 4: Your Turn
Practice makes it stick.
The Ribbon
Problem 1 of 2
7 metres of ribbon shared among 8 people. What is the top number of the fraction each gets?
The Cakes
Problem 2 of 2
9 cakes shared among 4. How many whole cakes does each get?
whole cakes
Division as a Fraction
1 of 4
2 ÷ 5 as a fraction. What is the top number?
2 of 4
2 ÷ 5 as a fraction. What is the bottom number?
3 of 4
11 ÷ 3. How many whole ones?
4 of 4
Can you divide 4 by 6?
Step 5: Quick Check
Show what you know.
Question 1 of 2
5 ÷ 8 as a fraction. What is the top number?
Question 2 of 2
Must the number being divided be the bigger one?
What You Learned
- a ÷ b can be written a/b.
- The leftover is shared out too, instead of being left over.
- Dividing a smaller number by a bigger one gives an answer under 1.