The document discusses various topics relating to fractions, including: 1) The different ways fractions can be interpreted and represented, such as parts of a unit, mathematical operators, and divisions. 2) Converting between mixed numbers, improper fractions, and proper fractions. 3) The concept of equivalent fractions and how to determine if two fractions are equivalent. 4) Methods for comparing, adding, subtracting, multiplying, and dividing fractions, including using common denominators or least common multiples.

1. Unit 07 February
1. THE MEANING OF FRACTIONS.
A Fraction can be seen as a part of a unit, as a mathematical operator or as
division.
1.1. FRACTIONS AS A PART OF A UNIT.
A Whole is a Unit, and then we divided this whole in equal-sized parts.
In a fraction:
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2. Unit 07 February
1.2. FRACTIONS AS A MATHEMATICAL OPERATOR.
A fraction is a number that operate an amount and transforms it. To calculate
the Fraction of a Number, we divide the number by the Denominator and the result
must be multiplied by the Numerator.
1.3. FRACTIONS AS DIVISIONS.
A fraction is also the quotient of the numerator between the denominator.
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3. Unit 07 February
1.4. COMPARING FRACTIONS USING DECIMAL NUMBERS.
To compare fractions using decimal numbers we just do the divisions and we
compare the decimal numbers we get.
1.5. FROM EXACT DECIMAL TO FRACTION.
The exact decimals can be converted in fractions with denominators of 10, 100,
1,000, and so on.
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4. Unit 07 February
MATH VOCABULARY: Numerator, Denominator.
2. MIXED NUMBERS. PROPER AND IMPROPER FRACTIONS.
When we convert numbers bigger than 1 to fractions we use Mixed Numbers.
But we can rewrite a mixed number as a fraction called Improper Fraction. To
convert mixed numbers to improper fractions, multiply the whole number by the
denominator and then add to the numerator.
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5. Unit 07 February
We also can rewrite an improper fraction as a mixed number. To convert a
improper fraction to a mixed number we use the division proof rule:
The fractions smaller than unit are called Proper Fractions.
MATH VOCABULARY: Mixed Number, Improper Fraction, Proper Fraction.
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6. Unit 07 February
3. EQUIVALENT FRACTIONS.
You can write the same fraction in different ways. For example, these fractions
are exactly the same, but because the larger shape is split into a different number of
segments in each case:
When two fractions are Equivalent, this means they are the same in terms of
shape and size, but are expressed using different numbers.
3.1. FUNDAMENTAL PROPERTY OF FRACTIONS.
If the numerator is multiplied or divided by a number the denominator must
also be multiplied or divided by the same number, for example:
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7. Unit 07 February
The fractions that we obtain multiplying or dividing are equivalent each other.
That is means that if we divide numerator by denominator we will obtain the same
quotient and the same remainder.
3.2. SIMPLEST FRACTION BY CANCELLING FRACTIONS.
When we multiply we can obtain infinite equivalent fractions, but when we
divide there are a finite number of equivalent fraction, the smallest one is called
Simplest Fraction.
To obtain the Simplest Fraction we divide the numerator and denominator by
their HCF. When we obtain the simplest fraction we are Cancelling Fractions.
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8. Unit 07 February
3.3. CHECKING FRACTIONS.
To check if two fractions are equivalent we have to use the Cross-Multiplying
Product. This is also called Taking the Cross-Product.
3.4. FINDING THE UNKNOWN TERM.
Using the cross-product we can find an unknown term in an equality of
fractions.
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9. Unit 07 February
MATH VOCABULARY: Equivalent Fraction, Simplest Fraction, Cross-Product, Cancelling
Fractions.
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10. Unit 07 February
4. COMPARING FRACTIONS.
Sometimes we have to compare fractions to see which is greater or smaller.
There are two ways of comparing fractions. We have seen the Decimal Method of
comparing fractions in point 1.4. Now we are going to focus in the Same Denominator
Method.
4.1. THE SAME DENOMINATOR METHOD.
If two fractions have the same denominator they are very easy to compare:
But to compare two fractions with different denominators, first we have to find
equivalent fractions from the original fractions with the same denominator. There are
some steps to follow:
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11. Unit 07 February
5. ADDING AND SUBTRACTING FRACTIONS.
To add or subtract fractions we need to have the same denominator. If we
have the same denominator we add or subtract the numerators and the denominator
remains.
If we have unlike denominators, firstly we need to find equivalent fractions to
the originals using the LCM as when we are comparing fractions, and then proceed as
above.
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12. Unit 07 February
If we have mixed fractions, firstly we rewrite then as improper fractions, and
then proceed as above.
6. MULTIPLYING AND DIVIDING FRACTIONS.
6.1. MULTIPLYING FRACTIONS.
The diagram shows the multiplication:
To multiply fractions, multiply the numerators and then multiply the
denominators, then cancel any common factors:
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13. Unit 07 February
6.2. DIVIDING FRACTIONS.
To divide two fractions, multiply the first fraction by the Multiplicative Inverse
of the second. This is the same as cross-multiplying their numerators and
denominators.
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14. Unit 07 February
If we have mixed numbers, firstly we rewrite then as improper fractions:
MATH VOCABULARY: Unlike Denominators, Multiplicative Inverse.
Axel Cotón Gutiérrez Mathematics 1º ESO 7.14