1 ESO - UNIT 07 - FRACTIONS.

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:

Axel Cotón Gutiérrez Mathematics 1º ESO 7.1

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.


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.


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.


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.


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:


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.


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.


Unit 07 February

MATH VOCABULARY: Equivalent Fraction, Simplest Fraction, Cross-Product, Cancelling

Fractions.


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:


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.


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:


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.


Unit 07 February

If we have mixed numbers, firstly we rewrite then as improper fractions:

MATH VOCABULARY: Unlike Denominators, Multiplicative Inverse.


1 ESO - UNIT 07 - FRACTIONS.

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Transcript of 1 ESO - UNIT 07 - FRACTIONS.