Why write 7/4 as 1 and 3/4?
Both forms describe exactly the same amount. One is better for seeing how much it is, and the other is better for calculating with it.
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1 lesson for “Mixed numbers and improper fractions”
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Why does 18/24 turn into 3/4?
The fraction looks different and describes the same amount. The rule that allows this is the same rule that makes adding fractions possible at all.
Try this lessonWhy is 5/8 smaller than 2/3?
Five is a bigger number than two and eight is a bigger number than three, yet five eighths is the smaller amount. Bigger numbers on the page are smaller pieces of the whole.
Try this lessonWhy do I flip the second fraction?
Amara shared 1/2 of a sandwich into 2/3-sized portions and wrote 1/3. She multiplied by 2/3 instead of flipping it first.
Try this lessonWhat do two negatives in a row do?
Priya multiplied -3 by -4 and wrote -12. She remembered that negatives matter, but she got the rule backwards.
Try this lessonWhat does minus a negative really mean?
Diego saw 5 - (-3) and wrote 2, as if the problem were 5 - 3. But the two minus signs are doing different jobs.
Try this lessonWhich pair of numbers factors x^2 + 7x + 12?
A trinomial like x^2 + 7x + 12 hides a pair of numbers. Find the pair, and the factored form falls into place.
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