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Fraction Calculator
1.1
Reduced terms
Find Reduced terms of `(30)/(20)`
Solution:
`30/20 = (2 xx 3 xx 5)/(2 xx 2 xx 5) = 3/2`
1.2
Improper Fraction to Mixed Number
Find Improper Fraction to Mixed Number of `(30)/(20)`
Solution:
`30/20=(30 -: 10)/(20 -: 10)=3/2=1 (1)/(2)`
Step by step solution :
Find the Greatest Common Factor (GCF) of `30` and `20`, and reduce the fraction by dividing both numerator and denominator by GCF = 10
`=(30 -: 10)/(20 -: 10)=3/2`
First Divide the numerator (`3`) by the denominator (`2`)
`3 -: color{red}{2} = color{green}{1}` with remainder of `color{blue}{1}`
The mixed number can be created by using the quotient `color{green}{1}` as the whole number, the remainder `color{blue}{1}` as the numerator and the `color{red}{2}` as the denominator.
So `30/20 = color{green}{1} (color{blue}{1})/(color{red}{2})`
1.3
Fraction to decimal
Find Fraction to decimal of `(30)/(20)`
Solution:
`30/20 = (10 × 3)/(10 × 2) = (3)/(2) = 1.5`
Or using division of 2 numbers
1
.
5
20
3
0
.
0
−
2
0
= 20 × 1
1
0
0
−
1
0
0
= 20 × 5
0
20 table
20
×
1
=
20
20
×
2
=
40
20
×
3
=
60
20
×
4
=
80
20
×
5
=
100
20
×
6
=
120
20
×
7
=
140
20
×
8
=
160
20
×
9
=
180
20
×
10
=
200
2.
Mixed Number to Improper Fraction
1. Find Mixed Number to Improper Fraction of `3 (4)/(5)`
Solution:
`3 (4)/(5) = ((3 xx 5) + 4)/5 = (15 + 4)/5 = 19/5`
Step by step solution :
Step 1 :
Multiply the denominator by the whole number
`3 xx 5 = 15`
Step 2 :
Now Add the answer to the numerator
`15 + 4 = 19`
Step 3 :
Now Write answer over the denominator
`=19/5`
3.
Compare Two Fraction
3. Compare two fractions `(3)/(4)` and `(5)/(6)`
Solution:
Step-1 :
Find the LCD of denominators
Here, LCD of 4 and 6 = 12
Step-2 :
Convert each fraction into its equivalent with the LCD in the denominator
For `3/4`, multiply numerator and denominator by 3 to have LCD = 12 in the denominator.
`3/4 = 3/4 xx 3/3 = 9/12`
For `5/6`, multiply numerator and denominator by 2 to have LCD = 12 in the denominator.
`5/6 = 5/6 xx 2/2 = 10/12`
Step-3 :
Compare fractions: If denominators are the same, we can compare the numerators.
Here 9 < 10,
`:. 9/12 < 10/12`
So, we conclude `3/4 < 5/6`
4.
Ascending and descending order of fractions
1. Arrange the fractions `1/2,3/4,5/6` in Ascending order
Solution:
Step-1 :
Find the LCD of denominators
Here, LCD of 2, 4, 6 = 12
Step-2 :
Convert each fraction into its equivalent with the LCD in the denominator
For `1/2`, multiply numerator and denominator by 6 to have LCD = 12 in the denominator.
`1/2 = 1/2 xx 6/6 = 6/12`
For `3/4`, multiply numerator and denominator by 3 to have LCD = 12 in the denominator.
`3/4 = 3/4 xx 3/3 = 9/12`
For `5/6`, multiply numerator and denominator by 2 to have LCD = 12 in the denominator.
`5/6 = 5/6 xx 2/2 = 10/12`
Step-3 :
Arrange fractions: If denominators are the same, then we can arrange the numerators.
Here 6 < 9 < 10
`:. 6/12 < 9/12 < 10/12 `
So, we conclude `1/2< 3/4< 5/6`
5.
Addition, Subtraction, Multiplication and Division of Fraction Numbers
Find `3/4 + 4/5 + 5/6`
`=(3)/(4)+(4)/(5)+(5)/(6)`
`=(3 * 15 + 4 * 12 + 5 * 10)/(60)`
`=(45 + 48 + 50)/(60)`
`=(143)/(60)`