Idea 10of 22Builds onScale down: divide both terms
Adding the same to both breaks a ratio
Why can't you add the same number to both terms?
Today you'll discover
- what adding does to the groups
- why multiplying keeps the mix
- how leftovers show a broken ratio
Think firstLia starts with 2 orange and 3 blue
Lia adds 2 to each: 4 orange and 5 blue. Is that still 2 for every 3?
Decide first, then press Next. Look for counters that do not fit in a group.
One dashed box of 2 orange circles and 3 blue squares. Then 4 orange and 5 blue packed: one box of 2 and 3, and a shaded box of 2 orange and 2 blue marked left over. Then 4 orange and 6 blue packing into two whole boxes. The last step shows 4 orange and 5 blue tried in groups of 1 orange and 2 blue.
See the whole ideathe big idea and the key word, in one place
The big idea
Equivalent ratios come from multiplying both terms, not from adding the same number.
Compare themAdding: 2 : 3 becomes 4 : 5, a new mix. Multiplying: 2 : 3 becomes 4 : 6, the same mix. Only the second packs into whole groups.
Easy to get wrongAdding a whole group is fine: 2 more orange and 3 more blue. Adding the same number to both terms is not.
Key word
- times as many
- a comparison by multiplying: 6 blue is 2 times as many as 3 blue
Ready to use it?
- Spot a ratio made by adding the same number.
- Fix it by multiplying both terms.