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What Are The Rules Estimate Fraction Close To 0,1,1/2?

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Grade 7 Mathematics

Unit 2: Number Theory Fractions & Decimals Review

Concept of a Fraction | Simplest Form | Fractions and Decimals | Mixed Numbers as Improper Fractions | Improper Fractions as Mixed Numbers | Estimating Sums of Fractions | Whole Number Multiplied by a Fraction

 

2.1 The Concept of a Fraction



The denominator (bottom #) of a fraction tells us into how many parts one whole has been divided.



The numerator (top #) of a fraction tells us how many of those parts we are considering.



Example:  In this example the whole has been divided into 5 parts and we are considering 4 of those parts.



Equivalent fractions are fractions that have the same value but have different denominators and numerators.



Example:    These fractions are equivalent.



Note: We get the second fraction by simply multiplying both the numerator and denominator by 2.



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Writing Fractions in Simplest Form (AKA Lowest Terms)



A fraction is said to be in lowest terms (or simplest form) when the GCF of the numerator and the denominator is 1



To write a fraction in simplest form:

1. Find the GCF of the numerator and the denominator;

2. Divide both the numerator and denominator by their GCF.



Ex. Write  in simplest form.



Factors of 16: 1, 2, 4, 8, 16

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24



Common factors of 16 and 24: 1 ,2, 4, 8 Therefore the GCF of 16 and 24 is 8



So,



Since the GCF of 2 & 3 is 1 the fraction is now in simplest form (lowest terms)



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2.3 Fractions and Decimals



Fractions may easily be written as decimals since a fraction represents division.



To turn a fraction into a decimal we divide the numerator by the denominator.



Example: Means therefore by doing long division or using a calculator we get

= 0.8.



Note: Since we could easily have solved this question without using division.



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Writing Mixed Numbers as Improper Fractions



A mixed number is a number with a whole number part and a fraction. To write a mixed number as a fraction you do the following:







Example: Write  as an improper fraction.





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Writing an Improper Fractions as Mixed Numbers



An improper fraction is a fraction, which has a numerator larger than its denominator. To write an improper fraction as a mixed number we do the following:







The quotient is the whole number part of the mixed number while the remainder is the numerator of the fraction part and the denominator remains the same as the one in the improper fraction.

Example: Write the improper fraction as a mixed number.



              Therefore, 



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Estimating Sums of Fractions and Mixed Numbers



By estimating a fraction to be closest to 0 ,  or 1 we can easily estimate a sum of fractions or mixed numbers.



Example: Estimate .



Since is close to 0 and is close to and is close to 1 we would estimate the sum as follows: 





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Multiply Mentally A Whole Number by a Fraction (or vice versa)



When we multiply a fraction by a whole number, which is a multiple of the denominator we can solve as follows:



Means we have 4 halves which is 2 whole therefore,



means we have 1 third of 6 items therefore,     



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