FRACTIONS 5

We already know what fractions are. Let’s review some important concepts before we carry on with the unit.

Equivalent fractions

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Review the concept of equivalent fractions.

Two fractions are equivalent when they express the same portion of a unit. 5

Two equivalent fractions have the same numerical value.

Remember b a d c = 5 a · d = b · c

How can we recognise equivalent fractions?

In equivalent fractions, the cross products are the same.

If we multiply the two parts of a fraction by the same number, we get an equivalent fraction.

➜ simPliFYing Fractions

As a result of the above property, we can say that:

If we divide the two parts of a fraction by the same number, we get an equivalent fraction.

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This transformation is called simplifying fractions. A fraction that cannot be fimplified is called an irreducible fraction.

Practise simplifying fractions.

Let's practise!

UNDERSTAND AND APPLY IN THE CHALLENGE

1 On average, a person sleeps seventy-five thousand hours before they reach the age of 20, one hundred and twenty-five thousand hours between the ages of 20 and 60 and fifty thousand hours after the age of 60. Write the portion of the hours of sleep for each stage of life as an irreducible fraction

2 Divide, express in decimal form and check that the fractions , 4 1 8 2 12 3 and are equivalent.

3 Find the irreducible fraction of: a) 18 15 b) 54 30 c)

Remember

To calculate the lowest common multiple of several numbers:

• We decompose them into prime factors.

• We take the common and noncommon prime factors with the highest exponent.

Reducing fractions to a common denominator

Comparing, adding and subtracting fractions is very simple when they all have the same denominator. When they do not, we substitute them for equivalent fractions which have the same denominator. The example below demonstrates the process that we should follow.

Example

We want to order the fractions ,and 12 7 14 9 21 11 from lowest to highest. To do so, we first reduce them to a common denominator.

• We take the lowest common multiple of the denominators as the denominator:

• In each fraction, we multiply the numerator and denominator by the same number to get 84 in the denominator: anayaeducacion.es

Reduce to a common denominator and compare.

Let's practise!

Now, we can put the fractions in order: 21 11 12 7 14 9 <<

To reduce fractions to a common denominator:

• We calculate the lowest common multiple of the denominators.

• We multiply the two parts of each fraction by the number that we get from dividing the lowest common multiple by the corresponding denominator.

4 Copy and complete to get equivalent fractions with the same denominator. 2, 4 3 , 10 7 8 · 20 220 , · 20 3 4 , · 20 7 4 a) 2 1 , 1 4 , 1 8 8 Common denominator: 8 b) 3 2 , 6 1 , 9 5 8 Common denominator: 18 c) 4 3 , 6 5 , 2 9 8 Common denominator: 36 d) 4 1 , 5 3 , 10 3 8 Common denominator: 20

5 Reduce to the common denominator indicated in each case.

6 Reduce to a common denominator.

7 Reduce to a common denominator. Then, order the fractions from lowest to highest.