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Here are a few recommended readings before getting started with this lesson.
In order to state what part of the pizza each person will eat, a certain type of numbers should be used.
The set of rational numbers, represented by the symbol Q, is formed by all numbers that can be expressed as the ratio between two integers, ab, where b≠ 0. - 3, 13, 5, 3145 All four of these examples are rational numbers. Note that integers are also rational because they can always be written as fractions with a denominator of 1. -3 = -31, 5= 51 In other words, integer numbers is a subset of rational numbers.
In the definition of rational numbers, the word fraction
showed up but was not explained in detail. To clarify any doubts, its definition will now be presented.
Fractions are a specific type of ratio that compares a part to a whole. Fractions are rational numbers written in the form ab, where the numerator a is the part and the denominator b is the whole.
l part→ whole→ a/b l←numerator ←denominator
a over b.Fractions where a is less than b are called proper fractions. Fractions where a is greater than or equal to b are called improper fractions.
Split into factors
Cross out common factors
Cancel out common factors
Consider a bar that is split into different parts. Find the fraction that describes the relationship between the shaded parts and the bar as a whole. Any shaded parts on the right-hand side indicate that the fraction is an improper fraction. Do not simplify the fractions.
Fractions that have different numerators and denominators but represent the same value are called equivalent fractions. For example, the following fractions are equivalent because they are all equal to the same value, even though they look different. 1/2=3/6=5/10 Imagine two friends, Emily and Maya, who have two identical cakes. Emily divided her cake into four parts and ate one. Maya divided her cake into eight slices and ate two.
Emily and Maya ate the same amount of cake. Therefore, 14 and 28 are equivalent fractions. 1/4=2/8 Equivalent fractions can be formed by multiplying or dividing the numerator and denominator by the same number.
When a fraction has a large numerator and denominator, it can be hard to estimate its value. Simplifying such a fraction and finding an equivalent fraction with a smaller numerator and denominator can be helpful.
To determine whether the given fraction can be simplified, split the numerator and denominator into prime factors and see if there are any common factors other than 1. 18 &= 2* 3* 3 66 &= 2* 3* 11 The numerator and denominator share factors 2 and 3. Therefore, the fraction can be simplified. If the numerator and denominator did not have common factors other than 1, the fraction would be said to be simplified or written in its simplest form.
The greatest common factor (GCF) of the numbers 18 and 66 can be found by multiplying all their common factors. GCF(18,66) = 2* 3= 6 If the numerator and denominator share only one common factor, then that factor is their GCF.
Finally, to reduce the fraction, divide its numerator and denominator by their GCF. 18/66=18/ 6/66/ 6=3/11 As a result, an equivalent fraction of 311 was obtained. It is the simplest form of the given fraction 1866.
After having a lot of fun with her friends on Saturday, Jordan woke up rested and energized the next day and decided to do her math homework. When she finished, she texted her answers to her friend Emily and asked if she got the same results.
Find the greatest common factor (GCF) of the numerator and denominator of a fraction, then use it to simplify the fraction.
Notice that Emily's fractions are written in their simplest form, but Jordan's fractions are not simplified. Therefore, to find the equivalent fractions, each of Jordan's fractions will be analyzed and simplified, one at a time.
Consider the given fraction. Can it be simplified? If yes, write the given fraction in its simplest form. If the fraction is already simplified, write it as it is.
On top of the topics mentioned in this lesson, there are many other real-life applications of fractions. Here are some of them.