how do I arrange these fraction or mixed numbers in order from smallest to largest
1)5/6,5/7,-3/4,2/3,9/11,-3/7 and 2)2 1/2,
-7/2,-2 1/3,2 4/5,2 3/8.
You can either change them to equivalent fractions with a common denominator or change them to equivalent decimals.
To arrange these fractions or mixed numbers in order from smallest to largest, you can follow these steps:
1) Convert all the mixed numbers to improper fractions:
- For example, 2 1/2 can be converted to (2 × 2 + 1)/2 = 5/2.
2) Find a common denominator for all the fractions:
- In this case, the common denominator for all the given fractions will be 924, which is the least common multiple (LCM) of 2, 3, 4, 6, 7, 11, 8, and 5.
3) Convert all the fractions to have the common denominator:
- Multiply the numerator and denominator of each fraction by the appropriate factor to make the denominator equal to 924.
- For example, to convert 5/6, multiply both the numerator and denominator by 154: (5 × 154)/(6 × 154) = 770/924.
4) Arrange the fractions in ascending order based on their numerator values. If the fractions have the same numerator, compare their denominators:
- Start comparing the fractions from left to right, comparing numerators first.
- If two fractions have the same numerator, the one with the smaller denominator is considered smaller.
- Continue comparing until you have arranged all the fractions in the correct order.
Now, let's apply these steps to the given fractions:
1) Fractions:
- 5/6, 5/7, -3/4, 2/3, 9/11, -3/7
Convert them to have the common denominator of 924:
- (5 × 154)/(6 × 154) = 770/924
- (5 × 132)/(7 × 132) = 660/924
- (-3 × 231)/(4 × 231) = -693/924
- (2 × 308)/(3 × 308) = 616/924
- (9 × 84)/(11 × 84) = 756/924
- (-3 × 132)/(7 × 132) = -396/924
Arranged from smallest to largest:
- (-693/924), (-396/924), (616/924), (660/924), (756/924), (770/924)
2) Mixed numbers:
- 2 1/2, -7/2, -2 1/3, 2 4/5, 2 3/8
Convert them to improper fractions:
- (2 × 2 + 1)/2 = 5/2
- (-7 × 2)/2 = -7/2
- (-2 × 3 + 1)/3 = -5/3
- (2 × 5 + 4)/5 = 14/5
- (2 × 8 + 3)/8 = 19/8
Convert them to have the common denominator of 924:
- (5 × 462)/(2 × 462) = 2310/924
- (-7 × 462)/(2 × 462) = -3234/924
- (-5 × 308)/(3 × 308) = -1540/924
- (14 × 184)/(5 × 184) = 2576/924
- (19 × 231)/(8 × 231) = 4149/924
Arrange them from smallest to largest:
- (-3234/924), (-1540/924), (2310/924), (2576/924), (4149/924)
So, the fractions arranged from smallest to largest are:
1) (-693/924), (-396/924), (616/924), (660/924), (756/924), (770/924)
2) (-3234/924), (-1540/924), (2310/924), (2576/924), (4149/924)