Family IV · What fraction operations mean.
Working With Fractions
Why we need common units to add and subtract, why multiplying can make a number smaller, and why dividing can make it bigger.
- Slice 16
Adding Different Pieces
Is (one half) + (one fourth) equal to (two sixths)?
Sounds like “(one half) + (one fourth) is (two sixths). You add the tops and add the bottoms.”
The big idea Pieces can only be counted together when they are the same size. Change to a common unit first: (one half) + (one fourth) = (two fourths) + (one fourth) = (three fourths).
- Slice 17
Keep the Unit When Adding
Is (one fifth) + (two fifths) equal to (three tenths)?
Sounds like “(one fifth) + (two fifths) is (three tenths), because five plus five is ten.”
The big idea Adding like parts changes how many parts there are, not their size: (one fifth) + (two fifths) = (three fifths).
- Slice 18
Taking Pieces Away
Is (three fourths) − (one half) equal to (two halves)?
Sounds like “(three fourths) take away (one half) is (two halves). Three minus one, four minus two.”
The big idea Subtraction takes away an amount. Use the same-size pieces for both amounts, then take away: (three fourths) − (one half) = (three fourths) − (two fourths) = (one fourth).
- Slice 19
Multiplication Can Make Smaller
Why does multiplying by a fraction make a number smaller?
Sounds like “Times always makes it bigger, so (one half) × (one half) has to be more than (one half).”
The big idea Multiplying by a fraction less than one takes only part of an amount, so the answer is smaller: (one half) × (one half) = (one fourth).
- Slice 20
Division Can Make Bigger
Why does dividing by a fraction give a bigger answer?
Sounds like “Dividing makes things smaller, so (one half) ÷ (one fourth) is less than (one half).”
The big idea Dividing by a fraction asks how many of those pieces fit. When the pieces are smaller than one whole, the answer is bigger than the amount: (one half) ÷ (one fourth) = 2.