Compound fraction tutor
Introduction :
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 fraction in math.
1) Proper fraction
2) Improper fraction
3) Compound fraction
The person who teach the education for a single or group of persons known as tutor. The tutors have the clear knowledge about their subjects and they can interact with the students and clear their doubts.
Compound fraction tutor :
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.
In the next section we are going to see how the tutor can solve the compound fraction problems.
Problems on compound fraction tutor
Problem 1:
Add the following two compound fractions `4 2/3 + 5 6/7 `
Solution:
Given , `4 2/3 + 5 6/7 `
We need to find the addition of given fraction,
4` 2/3 + 5 6/7` = `4 + 2 /3 + 5 + 6/7`
= `9 + 2/3 + 6/7`
We need to find the least common denominator,
lcd = 3 * 7 = 21
`9 + 2/3 + 6/7` = `189 / 21 + 14 / 21 + 18 / 21`
= `( 189 + 14 + 18 ) / 21`
= `221 / 21`
Answer: 4 `2/3` + 5 `6/7` = `221 / 21`
Problem 2:Dividing the compound fractions `8 5/12` ÷ `4 5/6`
Solution:
Given , two compound fractions `8 5/12` , `4 5/6`
We need to dividing the above fractions.
First we convert it into fractions.
`8 5/ 12` = `(( 12 * 8 ) + 5 ) / 12`
= `101 / 12`
`4 5/6` = `(( 4 * 6) + 5 ) / 6`
= `29 / 6`
`8 5/12` ÷` 4 5/6` = `101 / 12` ÷ `29 / 6`
Take a reciprocal for `29 / 6`
Reciprocal of `29 / 6` = `6 / 29`
Now multiply it with `101/12`
`8 5/12` ÷ `4 5/6` = `101 / 12` ÷ `29 / 6` = `101 / 12` * `6 / 29 `
`101 / 12 * 6 / 29` = `( 101 * 6) / ( 12 * 29)`
= `606 / 348 `
We can simplify it further.
Divide by 6 on both numerator and denominator,
`606 / 348` = `( 606 / 6 ) / ( 348 / 6)`
= `101 / 58`
Answer: `8 5/12` ÷ `4 5/6` = `101 / 58`
Problem 3:
Find two compound fractions equal to 7.5
Solution:
Given, decimal number 7.5
We need to find two mixed numbers,
Convert the given decimal number into two equal fraction.
Multiply and divide 7.5 by 10,
7.5 = `"7.5 * ( 10`
= `(7.5 * 10) / 10`
= `75 / 10`
Now divide 75 by 10 ,
____
10) 75 ( 7
70
5
The compound fraction of 7.5 = `75 / 10` is 7 `5/10`
To find another compound fraction, Consider the following,
Multiply and divide 7.5 by 20 ,
7.5 = `" 7.5 * ( 20`
= `(7.5 * 20) / 20`
= `150/ 20`
Now divide 150 by 20 ,
____
20) 150 ( 7
140
10
The compound fraction of 7.5 = `150 / 20` is 14 `10/20`
Answer: Twocompound fractions equal to 7.5 is 7` 5/10` and 7 `10/20`
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 fraction in math.
1) Proper fraction
2) Improper fraction
3) Compound fraction
The person who teach the education for a single or group of persons known as tutor. The tutors have the clear knowledge about their subjects and they can interact with the students and clear their doubts.
Compound fraction tutor :
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.
In the next section we are going to see how the tutor can solve the compound fraction problems.
Problems on compound fraction tutor
Problem 1:
Add the following two compound fractions `4 2/3 + 5 6/7 `
Solution:
Given , `4 2/3 + 5 6/7 `
We need to find the addition of given fraction,
4` 2/3 + 5 6/7` = `4 + 2 /3 + 5 + 6/7`
= `9 + 2/3 + 6/7`
We need to find the least common denominator,
lcd = 3 * 7 = 21
`9 + 2/3 + 6/7` = `189 / 21 + 14 / 21 + 18 / 21`
= `( 189 + 14 + 18 ) / 21`
= `221 / 21`
Answer: 4 `2/3` + 5 `6/7` = `221 / 21`
Problem 2:Dividing the compound fractions `8 5/12` ÷ `4 5/6`
Solution:
Given , two compound fractions `8 5/12` , `4 5/6`
We need to dividing the above fractions.
First we convert it into fractions.
`8 5/ 12` = `(( 12 * 8 ) + 5 ) / 12`
= `101 / 12`
`4 5/6` = `(( 4 * 6) + 5 ) / 6`
= `29 / 6`
`8 5/12` ÷` 4 5/6` = `101 / 12` ÷ `29 / 6`
Take a reciprocal for `29 / 6`
Reciprocal of `29 / 6` = `6 / 29`
Now multiply it with `101/12`
`8 5/12` ÷ `4 5/6` = `101 / 12` ÷ `29 / 6` = `101 / 12` * `6 / 29 `
`101 / 12 * 6 / 29` = `( 101 * 6) / ( 12 * 29)`
= `606 / 348 `
We can simplify it further.
Divide by 6 on both numerator and denominator,
`606 / 348` = `( 606 / 6 ) / ( 348 / 6)`
= `101 / 58`
Answer: `8 5/12` ÷ `4 5/6` = `101 / 58`
Problem 3:
Find two compound fractions equal to 7.5
Solution:
Given, decimal number 7.5
We need to find two mixed numbers,
Convert the given decimal number into two equal fraction.
Multiply and divide 7.5 by 10,
7.5 = `"7.5 * ( 10`
= `(7.5 * 10) / 10`
= `75 / 10`
Now divide 75 by 10 ,
____
10) 75 ( 7
70
5
The compound fraction of 7.5 = `75 / 10` is 7 `5/10`
To find another compound fraction, Consider the following,
Multiply and divide 7.5 by 20 ,
7.5 = `" 7.5 * ( 20`
= `(7.5 * 20) / 20`
= `150/ 20`
Now divide 150 by 20 ,
____
20) 150 ( 7
140
10
The compound fraction of 7.5 = `150 / 20` is 14 `10/20`
Answer: Twocompound fractions equal to 7.5 is 7` 5/10` and 7 `10/20`