Fractions represent numbers less than zero. Just like decimals, they represent a part of a whole number. Fractions are also DIVISION PROBLEMS.
Fractions are division problems
Yes, fractions are division problems. If you share 2 pies between 3 people it is the same as dividing the 2 pies by 3. You divide the 2 pies into 3 equal parts. The answer is less than 1 since 3 is more than 2. What about improper fractions? 4/2 is the same as 4 divided by 2, which is 2. You divide 4 into 2 parts. Each part is 2. Explore and try to fit this into your concept of fractions.
Fractions on a Numberline
You should be able to represent and place fractions on a numberline. Remember-a fraction is a part of a whole.
Fraction Models
Equivalent Fractions
Equivalent Fractions have the same value, even though they may look different. Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps its value.
Remember-
Whatever you do to the top, you have to do the bottom.
Remember-
Whatever you do to the top, you have to do the bottom.
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Simplifying/Reducing Fractions
The numerator and denominator of a fraction are called its terms. If we simplify a fraction, then we are reducing it to lowest terms. Reducing a fraction to lowest terms will not change its value; the reduced fraction will be an equivalent fraction. All we need to do is divide the numerator and the denominator by the same number. I put this in the equivalent fractions section because all you're doing is finding an equivalent fraction by making BOTH terms the lowest they can be.
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Practice/Assessment
Estimating Sums and Differences
A good strategy to use when adding and subtracting fractions is to estimate in order to see if your answer is reasonable. We use benchmark fractions to help us round fractions.
Once you know which benchmark fraction you are rounding to, all you need to do is add or subtract those benchmark fractions.