Dividing Fractions

What does dividing by a fraction mean?

Dividing usually answers the question "how many fit." If you ask how many 2-inch pieces fit in 6 inches, you are working out 6 ÷ 2 = 3. That part feels normal.

Dividing by a fraction asks the same question with smaller pieces. How many half-inch pieces fit in 6 inches? You get 12, because the pieces are smaller, so more of them fit.

Here is the part that surprises people. Dividing by a number smaller than 1 makes the answer bigger than the number you started with. It is not a trick. There are simply more small pieces than big ones.

What is this module?

The module shows the same division two ways.

How many fit: the strip is the amount you start with. You set the size of one piece and drag the handle. The strip fills with pieces, and each piece is numbered. The number of pieces is the answer.

Share: the strip is the amount you start with again, and you split it into equal shares. The size of one share is the answer. This is the "how much does each person get" kind of division.

You can type any fraction as the amount and as the piece size. A whole number like 3 is just 3/1.

What they're learning

The idea is that dividing by a fraction counts how many of those fractions fit inside. Your kid should be able to read the answer off the strip instead of memorizing a rule.

• The strip is the amount you start with. The piece size is what you divide by.
• Counting the pieces gives the answer.
• Dividing by a number less than 1 gives an answer bigger than the amount you started with.
• Sharing that same amount into equal parts is the other meaning of division.

Aliases

• Dividing fractions
• "How many fit" division
• Sharing division
• Fraction division

Refresher

Dividing by a fraction asks how many of that fraction fit inside the amount. If the pieces are smaller than 1, more of them fit, so the answer comes out bigger than the amount you started with. A whole number like 3 is just 3/1.

Try this together

Two or three minutes at the table is plenty. You do not need to teach a whole lesson.

1. Open How many fit. Leave the amount at 3 and the piece size at 1/2. Before dragging, ask how many pieces will fit. Then drag and count together.
2. Change the piece size to 1/4. Ask if more or fewer pieces will fit. More should fit, because the pieces are smaller.
3. Switch to Share. Set the amount to 1/2 and the shares to 3. Ask how big one share is. It is smaller than the half you started with.
4. In How many fit, set the amount to 3 and the piece size to 2/3. The strip does not finish on a whole piece. Ask your kid what the leftover part means.

If the piece is bigger than the strip, fewer than one piece fits. That is fine. The answer is just less than 1.

Words you might hear

These show up in the module and in the worksheet. You do not need to memorize them.

• Dividend: the amount you start with. It is the strip.
• Divisor: what you divide by. In the module it is the size of one piece, or the number of shares.
• Quotient: the answer to a division.
• Fraction: a part of a whole, like 1/2 or 3/4.

Dividing fractions is a big topic. If your kid can explain why 3 ÷ 1/2 is 6, they have the main idea.

Deeper dive

Take 6 ÷ 1/2. The question is how many half-inch pieces fit in 6 inches. Every whole inch holds two halves, so 6 inches hold 12 halves. The answer is 12, which is bigger than 6 because the pieces are smaller.

The other meaning of division is sharing: split the amount into equal parts and ask how big one part is. The module shows both meanings with the same strip.