Describe and compare fraction
Introduction :
Fractions:
A certain part of the whole is called as fractions. The fractions can be denoted as `a/b` , Where a, b are integers. We can multiply two or more fractions. There are three types of fractions in math,
1) Proper fraction
2) Improper fractions
3) Mixed fractions
Next we are going to describe what is proper fraction, improper fraction and compound fraction. Then we describe how to compare the fractions and give some problems on compare fractions.
Describe and compare fraction
Describe types of fractions:
Proper fraction:
A fraction is of the form a/b, where b > a
Improper fraction:
A fraction is of the form a/b, where a > b
Compound fraction:
A fraction is of the form a `b/c` . Here a = Quotient.
b = Remainder
c = Divisor.
Describe how to compare the fraction:
Step 1 : Rewrite the given input as the fraction if its needed.
Step 2: Find the least common denominator for the following fractions.
Step 3: Then rewrite the given fraction with the least common denominator.
Step 4: compare the fractions by using the numerator.
By using the above steps we can comparing the given fractions.
Problems on describe and compare fraction :
Problem 1:
Comparing the fractions `13/8` , `8/9`
Solution:
Step 1 : Rewrite the given input as the fraction if its needed.
`13/8 ` , `8/9`
Step 2: Find the least common denominator for the following fractions.
Multiples of 8 = 8 ,16, 24, 32, 40, 48, 56, 64, 72,80.....
Multiple of 9 = 9 , 18, 27, 36, 45, 54,63, 72 ......
72 is least common multiple.
So the least common denominator of the given fractions is 72.
Step 3: Then rewrite the given fraction with the least common denominator.
`13 / 9` = `( 13 * 9) / ( 8 * 9)` = `117 /72`
`8/9` = `( 8 * 8) / ( 9 * 8)` = `64 / 72`
Step 4: Compare the fractions by using the numerator.
`"117/72` > ` 64 / 72`
Answer: `117/72 ` > ` 64 / 72`
Problem 2:
Compare the following fractions and find the greatest fraction `-5/6` ,` -12/5` , `4/9` , `- 4/9`
Solution:
Given , ` -5/6` , `-12/5 ` , `4/9` , `- 4/9`
Step 1: Rewrite the given input as the fraction if its needed.
`"-5/6` , `-12/5` ,` 4/9` , ` - 4/9 `
Step 2: Find the least common denominator for the following fractions.
The least common denominator (LCD) is: 90
Step 3: Then rewrite the given fraction with the least common denominator
`-75/90, - 216/90 , 40/90, -40/90`
Step 4: Comparing the fractions by using the numerator.
`-216/90` < `-75/90` < `-40/90` < `40/90`
Answer: The greater fraction is `4/9`
Fractions:
A certain part of the whole is called as fractions. The fractions can be denoted as `a/b` , Where a, b are integers. We can multiply two or more fractions. There are three types of fractions in math,
1) Proper fraction
2) Improper fractions
3) Mixed fractions
Next we are going to describe what is proper fraction, improper fraction and compound fraction. Then we describe how to compare the fractions and give some problems on compare fractions.
Describe and compare fraction
Describe types of fractions:
Proper fraction:
A fraction is of the form a/b, where b > a
Improper fraction:
A fraction is of the form a/b, where a > b
Compound fraction:
A fraction is of the form a `b/c` . Here a = Quotient.
b = Remainder
c = Divisor.
Describe how to compare the fraction:
Step 1 : Rewrite the given input as the fraction if its needed.
Step 2: Find the least common denominator for the following fractions.
Step 3: Then rewrite the given fraction with the least common denominator.
Step 4: compare the fractions by using the numerator.
By using the above steps we can comparing the given fractions.
Problems on describe and compare fraction :
Problem 1:
Comparing the fractions `13/8` , `8/9`
Solution:
Step 1 : Rewrite the given input as the fraction if its needed.
`13/8 ` , `8/9`
Step 2: Find the least common denominator for the following fractions.
Multiples of 8 = 8 ,16, 24, 32, 40, 48, 56, 64, 72,80.....
Multiple of 9 = 9 , 18, 27, 36, 45, 54,63, 72 ......
72 is least common multiple.
So the least common denominator of the given fractions is 72.
Step 3: Then rewrite the given fraction with the least common denominator.
`13 / 9` = `( 13 * 9) / ( 8 * 9)` = `117 /72`
`8/9` = `( 8 * 8) / ( 9 * 8)` = `64 / 72`
Step 4: Compare the fractions by using the numerator.
`"117/72` > ` 64 / 72`
Answer: `117/72 ` > ` 64 / 72`
Problem 2:
Compare the following fractions and find the greatest fraction `-5/6` ,` -12/5` , `4/9` , `- 4/9`
Solution:
Given , ` -5/6` , `-12/5 ` , `4/9` , `- 4/9`
Step 1: Rewrite the given input as the fraction if its needed.
`"-5/6` , `-12/5` ,` 4/9` , ` - 4/9 `
Step 2: Find the least common denominator for the following fractions.
The least common denominator (LCD) is: 90
Step 3: Then rewrite the given fraction with the least common denominator
`-75/90, - 216/90 , 40/90, -40/90`
Step 4: Comparing the fractions by using the numerator.
`-216/90` < `-75/90` < `-40/90` < `40/90`
Answer: The greater fraction is `4/9`