Simplify: 13/11 × (-14/5) + 13/11 × (-7/5) + (-13/11) × 34/5
Solution:
We have to simplify the given numbers.
13/11 × (-14/5) + 13/11 × (-7/5) + (-13/11) × 34/5 = [(13/11) × (-14/5)] + [(13/11) × (-7/5)] + [(-13/11) ×(34/5)]
Taking (13/11) × (-14/5),
(13/11) × (-14/5) = 13 × (-14) / (11 × 5)
If the signs of the factors are different, the product is negative.
= -182/55
Taking (13/11) × (-7/5),
(13/11) × (-7/5) = 13 × (-7) / (11 × 5)
If the signs of the factors are different, the product is negative.
= -91/55
Taking (-13/11) × (34/5),
(-13/11) × (34/5) = (-13) × 34 / (11 × 5)
If the signs of the factors are different, the product is negative.
= -442/55
Now, [(13/11) × (-14/5)] + [(13/11) × (-7/5)] + [(-13/11) × (34/5)] = -182/55 + (-91/55) + (-442/55)
Since the numbers have same denominator, we get
= (-182 - 91 - 442)/55
= -(182 + 91 + 442)/55
= -715/55
On dividing the numerator and denominator by 11,
= -(715/11) / (55/11)
= -65/5
= -13
Therefore, the required value is -13.
✦ Try This: Simplify: 3/13 × (-6/5) + 3/13 × (-3/5)
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 9
NCERT Exemplar Class 7 Maths Chapter 8 Problem 81(i)
Simplify: 13/11 × (-14/5) + 13/11 × (-7/5) + (-13/11) × 34/5
Summary:
The simplified value of 13/11 × (-14/5) + 13/11 × (-7/5) + (-13/11) × 34/5 is -13
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