# PUT RATIONAL NUMBERS IN ORDER

## About "Put rational numbers in order"

Put rational numbers in order :

• Convert integers and mixed numbers to improper fractions.
• Find the least common denominator LCD of all the fractions.
• Rewrite fractions as equivalent fractions using the GCD.
• Order the new fractions by the numerator.
• In case we have decimals, we have to convert it into fraction.

Let us see some examples to understand the above concept.

Example 1 :

Write the following rational numbers in order from greatest to least.

 19/25 is already a fraction, so we can leave it as it is. =  19/25 For converting the second number 0.33 into fraction, we have to multiply both numerator and denominator by 100. 0.33 x (100/100)=  33/100 68% can be written as 68/100 =  68/100 Since 14/20 is already in fractional form, we don't have to convert this 14/20 50% can be written as 50/100 50/100

The denominators of the above fractions are 25, 100, 100, 20 and 100.

Since the denominators are different, we have to find least common multiple.

L.C.M = 100

19/25 (1)  ==> (19/25) x (4/4)  =  76/100

0.33 (2)  ==> (33/100)

68% (3)  ==> (68/100)

14/20 (4)  ==> (14/20) x (5/5)  =  70/100

50% (5)  ==> (50/100)

The rational numbers from greatest to least is 76/100, 70/100, 68/100, 50/100, 33/100

Hence the required order is 19/25, 14/20, 68%,  50%, 0.33

Example 2 :

Write the following rational numbers in order from greatest to least.

 5/6 is already a fraction, so we can leave it as it is. =  5/6 For converting the second number 0.121 into fraction, we have to multiply both numerator and denominator by 1000. 0.121 x (1000/1000)=  121/1000 8/9 is already a fraction, so we can leave it as it is. =  8/9 70% can be written as 70/100 70/100 11/12 is already a fraction, so we can leave it as it is. 11/12

The denominators of the above fractions are 6, 1000, 9, 100 and 12.

Since the denominators are different, we have to find least common multiple.

L.C.M = 3 x 2 x 5 x 2 x 5  x 10 x 3  =  9000

5/6 (1)==> (5/6) x (1500/1500)  =  7500/9000 (3)

0.121 (2)==> 0.121 x (1000/1000)  = 121/1000 (5)

8/9 (3)==> (8/9) (1000/1000)  = 8000/9000 (2)

70% (4)==> (70/100) x (90/90)  =  6300/9000 (4)

11/12 (5)==> (11/12) x (750/750)  =  8250/9000 (1)

The rational numbers from greatest to least is 8250/9000, 8000/9000, 7500/9000, 6300/9000, 121/9000

Hence the required order is 11/12, 8/9, 5/6, 70%, 0.121

Example 3 :

Write the following rational numbers in order from least to greatest.

 3/4 is already a fraction, so we can leave it as it is. =  3/4 13/17 is already a fraction, so we can leave it as it is. =  13/17 To convert 0.888 as fraction, we have to multiply both numerator and denominator by 1000 0.888 x (1000/1000) =  888/1000 11/15 is already a fraction, so we can leave it as it is. 11/15 77.7% can be written as 77.7/100. In order to convert this into fraction, we have to multiply both numerator and denominator by 10. (77.7/100) x (10/10) =  777/1000

The denominators of the above fractions are 4, 17, 1000, 15 and 1000.

Since the denominators are different, we have to find least common multiple.

L.C.M = 5 x 2 x 2 x 5 x 17 x 10 x 3 x 10  =  510000

3/4 (1)==>(3/4)x(127500/127500) = 382500/510000 (3)

13/17 (2)==>(13/17)x(30000/30000)=390000/510000 (4)

0.888(3)==>

(8/1000)x(510/510)=4080/510000 (1)

11/15 (4)==>

(11/15)x(34000/34000)=374000/510000 (2)

77.7 (5)==>

(777/1000) x (510/510)  =  396270/510000 (5)

The rational numbers from greatest to least is 8250/9000, 8000/9000, 7500/9000, 6300/9000, 121/9000

Hence the required order is 0.888, 11/15, 3/4, 13/17, 77.7%

After having gone through the stuff given above, we hope that the students would have understood "Put rational numbers in order".

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6