Simplify :2 5/12 - 3/4 +1 7/8
Answers
Step-by-step explanation:
(i) 3/7 × 4/5
= (3 × 4)/(7 × 5)
= 12/35
(ii) 7/3 × 5/2
= (7 × 5)/(3 × 2)
= 35/6
(iii) 5 × 3/7
= 5/1 × 3/7
= (5 × 3)/(1 × 7)
= 15/7
(iv) 5/12 × 9
= 5/12 × 9/1
= (5 × 9)/(12 × 1)
= (5 × 3)/(4 × 1)
= 15/4
Sometimes for indicating multiplication of two fractions, we use the word ‘of ‘as follows:
(i) 1/2 of 8
= 1/2 × 8
= 1/2 × 8/1
= (1 × 8)/(2 × 1)
= 8/2
= 4
(ii) 1/5 of 20
= 1/5 × 20
= 1/5 × 20/1
= 20/5
= 4
(iii) 2/5 of 25
= 2/5 × 25
= 2/5 × 25/1
= (2 × 25)/(5 × 1)
= 50/5
= 10
(iv) 2/3 of 5/7
= 2/3 × 5/7
= (2 ×5)/(3 × 7)
= 10/21.
Examples on multiplication of fractions:
1. Multiply the fractions:
(i) 2/9 by 4/5
(ii) 3/5 by 12
(iii) 2¹/₃ by 2/5
(iv) 5³/₄ by 2³/₇
(i) 2/9 by 4/5
= 2/9 × 4/5
= (2 × 4)/(9 × 5)
= 8/45
(ii) 3/5 by 12
= 3/5 × 12
= 3/5 × 12/1
= (3 × 12)/(5 × 1)
= 36/5
= 7¹/₅
(iii) 2¹/₃ by 2/5
= 2¹/₃ × 2/5
= 7/3 × 2/5
= (7 × 2)/(3 × 5)
= 14/15
(iv) 5³/₄ by 2³/₇
= 5³/₄ × 2³/₇
= 23/4 × 17/7
= (23 × 17)/(4 × 7)
= 391/28
= 13²⁷/₂₈
2. Multiply and reduce to lowest form (if possible) :
(i) 2/5 × 5/4
(ii) 1/3 × 15/8
(iii) 4/5 × 12/7
(iv) 15/16 × 10/12
Solution:
(i) 2/3 × 5/4
= (2 × 5)/(3 × 4)
= (1 × 5)/(3 × 2)
= 5/6
(ii) 1/3 × 15/8
= (1 × 15)/(3 × 8)
= (1 × 5)/(1 × 8)
= 5/8
(iii) 4/5 × 12/7
= (4 × 12)/(5 × 7)
= 48/35
= 1¹³/₃₅
(iv) 15/16 × 10/12
= (15 × 10)/(16 × 12)
= (5 × 5)/(8 × 4)
= 25/32
3. Simplify the fractions:
(i) 5 × 3/20 × 2/15
(ii) 14/25 × 35/51 × 34/49
(i) 5 × 3/20 × 2/15
Solution:
5 × 3/20 × 2/15
= 5/1 × 3/20 × 2/15
= (5 × 3 × 2)/(1 × 20 × 15)
= 1/(2 × 5)
= 1/10
(ii) 14/25 × 35/51 × 34/49
Solution:
14/25 × 35/51 × 34/49
= (14 × 35 × 34)/(25 × 51 × 49)
= (2 × 1 × 2)/(5 × 3 × 1)
= 4/15
4. Which is greater? 2/7 of 3/4 or, 3/5 of 5/8.
Solution:
2/7 of 3/4
= 2/7 × 3/4
= (2 × 3)/(7 × 4)
= (1 × 3)/(7 × 2) = 3/14
and,
3/5 of 5/8
= 3/5 × 5/8
= (3 × 5)/(5 × 8)
= (3 × 1)/(1 × 8)
= 3/8
In order to compare these fractions, we convert them into equivalent fractions having same denominator equal to the LCM of 14 and 18.
LCM of 14 and 18 = 2 × 7 × 4 = 56
Therefore, 3/14
= (3 × 4)/(14 × 4)
= 12/56
and
3/8
= (3 × 7)/(8 × 7)
= 21/56
In numerator we clearly see i.e., 21 > 12
Therefore, 21/56 > 12/56 ⇒ 3/8 > 3/14
Hence, 3/5 of 5/8 is greater than 2/7 of 3/4.
5. Find:
(i) 3/5 of a dollar
(ii) 3/4 of a year
(iii) 2/3 of a day
(iv) 5/8 of a kilogram
(v) 2/3 of an hour
(vi) 7/25 of a litre
Solution:
(i) 1 dollar = 100 cents
Therefore, 3/5 of a dollar = 3/5 of 100 cents
Now, 3/5 of 100 = 3/5 × 100
= 3/5 × 100/1
= (3 × 100)/(5 × 1)
= (3 × 20)/(1 × 1)
= 60
Therefore, 3/5 of a dollar = 60 cents.
(ii) 1 year= 12 months
Therefore, 3/4 of a year = 3/4 of 12 months
Now, 3/4 of 12 = 3/4 ×12
= (3 × 12)/(4 × 1)
= (3 × 3)/(1 × 1) = 9
Therefore, 3/4 of a year = 9 months
(iii) 2/3 of a day
1 day = 24 hours
Therefore, 2/3 of a day = 2/3 of 24 hours
Now, 2/3 of 24
= 2/3 ×24
= 2/3 × 24/1
= (2 × 24)/(3 × 1)
= (2 × 8)/(1 × 1)
= 16
Therefore, 2/3 of a day = 16 hours
(iv) 5/8 of a kilogram
1 kilogram = 1000 grams
Therefore, 5/8 of a kilogram = 5/8 of 1000 grams = (5/8 × 1000) grams
Now, 5/8 × 1000 = 5/8 × 1000/1
= (5 × 1000)/(8 × 1)
= (5 × 125)/(1 × 1)
= 625
Therefore, 5/8 of a kilogram = 625 grams
(v) 2/3 of an hour
1 hour = 60 minutes
Therefore, 2/3 of an hour = (2/3 × 60) minutes
Now, 2/3 × 60
= 2/3 × 60/1
= (2 × 60)/(3 × 1)
= (2 × 20)/(1 × 1)
= 40
Therefore, 2/3 of an hour = 40 minutes
(vi) 7/25 of a litre
1 litre = 1000 ml
Therefore, 7/25 of a litre = (7/25 × 1000) ml
Now, 7/25 × l000 = 7/25 × 1000/1
= (7 × 1000)/(25 × 1)
= 7 × 40
= 280
Therefore, 7/25 of a litre = 280 ml.
In multiplying fractions word problems can arise in different situations. We will show you in details some examples step by step.
Examples on word problem on multiplication of fractions:
1. Sugar is sold at $ 17³/₄ per kg. Find the cost of 8¹/₂ kg of a sugar.
Solution:
Cost of 1kg of sugar = $ 17³/₄ = $ 71/4
Therefore, cost of 8¹/₂ kg of sugar = $ (71/4 × 8¹/₂)
= $ (71/4 × 17/2)
= $ (71 × 17)/(4 × 2)
= $ (1207/8)
= $ 150⁷/₈
Hence, the cost of 8¹/₂ kg of sugar is $ 150⁷/₈.
2.
Answer:
-19/24
Step-by-step explanation:
25/12 - 3/4 + 17/8
= (50 - 18 + 51) / 24
= (50 - 69 ) / 24
= -19 / 24