Monday
Monday: How Many Fit?
Rocket tips a bag of paper strips onto the Numbers Desk. "Finish-line ribbons for Field Day," he says. "Each lane gets one ribbon, a quarter of a strip long."
"We have 3 whole strips," says Raven. "What do you notice about the quarters?"
Rocket folds one strip in half, then in half again. "Four quarters in each strip. So 3 strips make 12 ribbons."
Nova hovers over the pile, her light tracing the folds. "You just divided by a fraction," she says.
"I did?" Rocket says. "I only counted."
"Counting how many quarters fit is division," says Raven. "Three divided by one fourth."
Nova hums. "Write it as a number sentence. See what it tells you."
Division asks: how many fit?
Division answers two kinds of questions. How many groups fit? And how much is in each group?
3 ÷ 1/4 asks: how many 1/4 strips fit into 3 whole strips? Count them on a number line.
From 0 to 3 there are 12 jumps of 1/4. So 3 ÷ 1/4 = 12.
Notice the answer is bigger than 3. Dividing by a fraction smaller than 1 gives more pieces, not fewer.
The amount being divided (3) is the dividend. The number you divide by (1/4) is the divisor. The answer is the quotient.
A shortcut you can trust
Each whole holds 4 fourths. So 3 wholes hold 3 × 4 = 12 fourths.
Dividing by 1/4 is the same as multiplying by 4. We call 4 the reciprocal of 1/4: the fraction flipped over.
Check it with multiplication: 12 ribbons × 1/4 strip each = 3 strips. Multiplying undoes the dividing.
- Read the question.
- Tap your answer.
- Read the question.
- Tap your answer.
| Sentence | True or false? |
|---|---|
| 3 ÷ 1/4 = 12 | ? |
| 2 ÷ 1/2 = 1 | ? |
| 5 ÷ 1/5 = 25 | ? |
| 1 ÷ 1/3 = 3 | ? |
Fold a second strip the same way, then fold it once more. Count the eighths in one strip.
Write both counts as division sentences: 1 ÷ 1/4 and 1 ÷ 1/8.
Strong start. Tomorrow you divide a fraction by a fraction, with strips first and a shortcut second.