Lessons · Teaching · what a fraction actually is
A fraction is one number, not two
Three quarters is a single number that sits between zero and one. The denominator says how many equal parts one whole was cut into; the numerator says how many of those parts you have. It is also a division waiting to happen: three quarters is three divided by four.
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In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.
What it is for
Almost every fraction error an adult makes comes from treating the two digits as separate numbers. Add the tops, add the bottoms, and you get a rule that gives one half plus one half equals two quarters, which is one half. A learner who can point to three quarters on a number line has stopped seeing two numbers.
How to think about it
Put every fraction on a number line before operating on it. Ask two questions in order: how many parts is the whole cut into, and how many do I have? Then ask whether the answer should be more or less than one, and keep that expectation to check against.
Worked example
In 3/4 the 4 cuts one whole into four equal parts, and you take 3Equal is the word doing the work. Four unequal pieces are not quarters.
3/4 is also 3 divided by 4, which is 0.75The fraction bar is a division sign that never got written out.
7/4 is more than one: four quarters make a whole, and there are three leftAn improper fraction is not an error, it is a number above one.
7/4 as a mixed number is 1 and 3/4Same number, different clothes. Neither is more correct than the other.
Your turn
Name the part of a fraction that says how many equal pieces the whole was cut into.
The says how many equal parts the whole became
Solve one, graded on the server
The trap
Believing a bigger denominator means a bigger fraction. One tenth is smaller than one half, because cutting the same whole into more pieces makes each piece smaller. The digits say the opposite of the sizes.