Q.2 ] Subtopic : - Addition and subtraction of rational numbers . Description : write fractions in mixed form and find out the hidden word. 1] 5 6 + 8 6 2] 3 4 − 9 4 3] −5 8 − 2 7 4] 2 5 −3 7 5] 3 7 + ( −6 11 ) + ( −8 21 ) + 5 22 6]−3 − 7 2 7] −9 2 + 5 12 8] −1 12 − ( −4 9 ) 1 2 3 4 5 6 7 8 Answers : - A = 1 1 2 I = −6 35 N = 6 1 2 L = 13 36 R = 2 1 6 A = 1 1 12 O = −125 462 T = −51
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Step-by-step explanation:
Answers : - A = 1 1 2 I = −6 35 N = 6 1 2 L = 13 36 R = 2 1 6 A = 1 1 12 O = −125 462 T = −51
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Answer:
- five sixths plus eight sixths is thirteen sixths.
- three quarters minus nine quarters is minus three halfs.
- minus five eighths minus two sevenths is minus fifty-one fifty-sixths.
- two fifths minus three sevenths is minus one thirty-fifth.
- minus one hundred fifteen two-hundred thirty-firsts plus five twenty-seconds is minus one hundred twenty-five four-hundred sixty-seconds.
- minus three minus seven halfs is minus thirteen halfs.
- minus nine halfs plus five twelfths is minus forty-nine twelfths.
- minus one twelfth minus minus four ninths is thirteen thirty-sixths.
Step-by-step explanation:
It is a form of a fraction which is defined as the ones having a fraction and a whole number.
Example: 2(1/7), where 2 is a whole number and 1/7 is a fraction.
1)Add: 5/6 +8/6 = 5 + 8/6
= 13/6
= 2 1/6 ≅ 2.1666667
The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 6) = 6.
In other words - five sixths plus eight sixths is thirteen sixths.
2)Subtract: 3/4 - 9/4
= 3 - 9/4
= -6/4
= 2 · -3/2 · 2
= -3/2
The common denominator you can calculate as the least common multiple of both denominators - LCM(4, 4) = 4.
In other words - three quarters minus nine quarters is minus three halfs.
3) Unary minus: -5/8
= -5/8
Subtract: the result of step No. 1 - 2/7
= -5/8 - 2/7
= -5 · 7/8 · 7
- 2 · 8/7 · 8
= -35/56 - 16/56
= -35 - 16/56
= -51/56
The common denominator you can calculate as the least common multiple of both denominators - LCM(8, 7) = 56.
In other words - minus five eighths minus two sevenths is minus fifty-one fifty-sixths.
4.Subtract: 2/5 - 3/7 = 2 · 7/5 · 7 - 3 · 5/7 · 5 = 14/35 - 15/35
= 14 - 15/35
= -1/35
The common denominator you can calculate as the least common multiple of both denominators - LCM(5, 7) = 35.
In other words - two fifths minus three sevenths is minus one thirty-fifth.
5.Add: 3/7 + (-6/11) = 3 · 11/7 · 11 + (-6) · 7/11 · 7
= 33/77 + (-42/77) = 33 + (-42)/77
= -9/77===>the result of step No. 1
The common denominator you can calculate as the least common multiple of both denominators - LCM(7, 11) = 77.
In other words - three sevenths plus minus six elevenths is minus nine seventy-sevenths.
Add: the result of step No. 1 + (-8/21) = -9/77 + (-8/21) = -9 · 3/77 · 3 + (-8) · 11/21 · 11
= -27/231 + (-88/231) = -27 + (-88)/231
= -115/231===>the result of step No. 2
The common denominator you can calculate as the least common multiple of both denominators - LCM(77, 21) = 231.
In other words - minus nine seventy-sevenths plus minus eight twenty-firsts is minus one hundred fifteen two-hundred thirty-firsts.
the result of step No. 2 + 5/22 = -115/231 + 5/22 = -115 · 2/231 · 2 + 5 · 21/
22 · 21 = -230/462 + 105/462
= -230 + 105/462
= -125/462
The common denominator you can calculate as the least common multiple of both denominators - LCM(231, 22) = 462.
In other words - minus one hundred fifteen two-hundred thirty-firsts plus five twenty-seconds is minus one hundred twenty-five four-hundred sixty-seconds.
6).Subtract: -3 - 7/2 = -3/1 - 7/2
= -3 · 2/1 · 2 - 7/2
= -6/2 - 7/2
= -6 - 7/2
= -13/2
The common denominator you can calculate as the least common multiple of both denominators - LCM(1, 2) = 2.
In other words - minus three minus seven halfs is minus thirteen halfs.
7. Unary minus: -9/2 = -9/2
Add: the result of step No. 1 + 5/12 = -9/2 +5/12
= -9 · 6/2 · 6 + 5/12
= -54/12 + 5/12
= -54 + 5/12
= -49/12
The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 12) = 12.
In other words - minus nine halfs plus five twelfths is minus forty-nine twelfths.
8.Unary minus: -1/12
= -1/12
Subtract: the result of step No. 1 - (-4/9) = -1/12 - (-4/9) = -1 · 3/12 · 3 - (-4) · 4/9 · 4 = -3/36 - (-16/36) = -3 - (-16)/36
= 13/36
The common denominator you can calculate as the least common multiple of both denominators - LCM(12, 9) = 36.
In other words - minus one twelfth minus minus four ninths is thirteen thirty-sixths.
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