Circle the pairs of rational numbers in at are equivalent.
75/100 ; 3/4
Answers
Answer:
Given (7/9) and (8/13)
Taking LCM for 9 and 13 we get,
9 × 13 = 117
Now we convert the given fractions into its equivalent fractions, then it becomes
(7 × 13)/ (9 × 13) and (8 × 9)/ (13 × 9)
Therefore (91/117) > (72/117)
Hence (7/9) > (8/13)
(ii) Given (11/9) and (5/9)
As the denominator is equal, they form equivalent fractions.
But we know that 11 > 5
Hence (11/9) > (5/9)
(iii) Given (37/41) and (19/30)
Taking LCM for 41 and 30 we get,
30 × 41 = 1230
Now we convert the given fractions into its equivalent fractions, then it becomes
(37 × 30)/ (41 × 30) and (19 × 41)/ (30 × 41)
Therefore (1110/1230) > (779/1230)
Hence (37/41) > (19/30)
(iv) Given (17/15) and (119/105)
Taking LCM for 15 and 105 we get, 5 × 3 × 7 = 105
Now we convert the given fractions into its equivalent fractions, then it becomes
(17 × 7)/ (15 × 7) and (119/105)
Therefore (119/105) = (119/105)
Hence (17/15) = (119/105)
2. Arrange the following fractions in ascending order:
(i) (3/8), (5/6), (6/8), (2/4), (1/3)
(ii) (4/6), (3/8), (6/12), (5/16)
Solution:
(i) Given (3/8), (5/6), (6/8), (2/4), (1/3)
Now we have to arrange these in ascending order, to arrange these in ascending order we have to make those as equivalent fractions by taking LCM’s.
LCM of 8, 6, 4 and 3 is 24
Equivalent fractions are
(9/24), (20/24), (18/24), (12/24), (8/24)
We know that 8 < 9 < 12 < 18 < 20
Now arranging in ascending order
(8/24) < (9/24) < (12/24) < (18/24) < (20/24)
Hence (1/3) < (3/8) < (2/4) < (6/8) < (5/6)
(ii) Given (4/6), (3/8), (6/12), (5/16)
Now we have to arrange these in ascending order, to arrange these in ascending order we have to make those as equivalent fractions by taking LCM’s.
LCM of 8, 6, 12 and 16 is 48
Equivalent fractions are
(32/48), (15/48), (18/48), (15/48)
We know that 12 < 15 < 18 < 32
Now arranging in ascending order
(12/48) < (15/48) < (18/48) < (32/48)
(6/12) < (5/16) < (3/8) < (4/6)
3. Arrange the following fractions in descending order:
(i) (4/5), (7/10), (11/15), (17/20)
(ii) (2/7), (11/35), (9/14), (13/28)
Solution:
(i) Given (4/5), (7/10), (11/15), (17/20)
Now we have to arrange these in descending order, to arrange these in descending order we have to make those as equivalent fractions by taking LCM’s.
LCM of 5, 10, 15 and 20 is 60
Equivalent fractions are
(48/60), (42/60), (44/60), (51/60)
We know that 51 > 48 > 44 > 42
Now arranging in descending order
Hence (17/20) > (4/5) > (11/15) > (7/10)
(ii) Given (2/7), (11/35), (9/14), (13/28)
Now we have to arrange these in descending order, to arrange these in descending order we have to make those as equivalent fractions by taking LCM’s.
LCM of 7, 35, 14 and 28 is 140
Equivalent fractions are
(40/140), (44/140), (90/140), (65/140)
We know that 90 > 65 > 44 > 40
Now arranging in descending order
Hence (9/14) > (13/28) > (11/35) > (2/7)
4. Write five equivalent fraction of (3/5).
Solution:
Given (3/5)
By multiplying or dividing both the numerator and denominator so that it keeps the same value by this we can get the equivalent fractions.
(3 × 2)/ (5 × 2), (3 × 3)/ (5 × 3), (3 × 4)/ (5 × 4), (3 × 5)/ (5 × 5), (3 × 6)/ (5 × 6)
Equivalent fractions are
(6/10), (9/15), (12/20), (15/25), (18/30)
5. Find the sum:
(i) (5/8) + (3/10)
(ii) 4 3/4 + 9 2/5
(iii) (5/6) + 3 + (3/4)
(iv) 2 3/5 + 4 7/10 + 2 4/15
Solution:
(i) Given (5/8) + (3/10)
Taking LCM for 8 and 10 we get 40
Now we have to convert the given fractions into equivalent fractions with denominator 40
(5/8) + (3/10) = (5 × 5)/ (8 × 5) + (3 × 4)/ (10 × 4)
= (25/40) + (12/40)
= (37/40)
(ii) Given 4 3/4 + 9 2/5
First convert given mixed fractions into improper fractions.
4 3/4 + 9 2/5 = (19/4) + (47/5)
Taking LCM for 4 and 5 we get 20
Now we have to convert the given fractions into equivalent fractions with denominator 20
4 3/4 + 9 2/5 = (19/4) + (47/5) = (19 × 5)/ (4 × 5) + (47 × 4)/ (5 × 4)
= (95/20) + (188/20)
= (283/20)
(iii) Given (5/6) + 3 + (3/4)
Taking LCM for 6, 1 and 4 we get 12
Now we have to convert the given fractions into equivalent fractions with denominator 12
(5/6) + 3 + (3/4) = (5 × 2)/ (6 × 2) + (3 × 12)/ (1 × 12) + (3 × 3)/ (4 × 3)
= (10/12) + (36/12) + (9/12)
= (55/12)
(iv) Given 2 3/5 + 4 7/10 + 2 4/15
First convert given mixed fractions into improper fractions
2 3/5 + 4 7/10 + 2 4/15 = (13/5) + (47/10) + (34/15)
Taking LCM for 5, 10 and 15 we get 30
Now we have to convert the given fractions into equivalent fractions with denominator 30
2 3/5 + 4 7/10 + 2 4/15 = (13/5) + (47/10) + (34/15) = (13 × 6)/ (5 × 6) + (47 × 3)/ (10 × 3) + (34 × 2)/ (15 × 2)
= (78/30) + (141/30) + (68/30)
= (287/30)
6. Find the difference of:
(i) (13/24) and (7/16)
(ii) 6 and (23/3)
(iii) (21/25) and (18/20)
(iv) 3 3/10 and 2 7/15
Solution:
(i) Given (13/24) and (7/16)
To find the difference we have to make it equivalent fractions.
LCM of 24 and 16 is 48.
Now converting the given fractions into equivalent fractions with denominator 48.
(13/24) – (7/16) = (26/48) – (21/48)
= (26 – 21)/48
= (5/48)
(ii) Given 6 and (23/3)
To find the difference we have to make it equivalent fractions.
LCM of 3 and 1 is 3.