|
|
|
Improper fraction to Mixed number |
|
|
|
Method
|
|
|
|
|
|
|
|
|
|
|
|
Solution
|
Solution provided by AtoZmath.com
|
|
|
|
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)`
|
|
|
|
|
|
|
|
|
|
