Page 32 - Start Up Mathematics_7

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Example 4: Vani wants to put a picture in a frame. The picture is 5 cm wide. To fit in the
4
1
frame the picture cannot be more than 5 cm wide. How much should the picture
2
be trimmed?

3 23
Solution: Width of the picture = 5 cm = cm
4 4
1 11
Width of the frame = 5 cm = cm
2 2
23 11
Width of the picture to be trimmed = – cm
4 2
23 22 1
= – cm = cm
4 4 4
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Example 5: Ritu ate part of an apple and the remaining apple was eaten by her brother Somu.
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How much part of the apple did Somu eat? Who had the larger share? By how
much? (NCERT)
Solution: Let the apple be considered as 1.
Part of the apple Ritu ate = 3 Extension
5
3 5 – 3 2 Decimal fractions are those in which
∴ Somu ate = 1 – = = apple
5 5 5 the denominator is some power of
3 2 10, e.g., 3 or 15 .
 3 > 2 ∴ > 10 100
5 5

Hence, Ritu had a larger share.
By how much:
3 2 1
– =
5 5 5
1
i.e., Ritu ate part more than Somu.
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Example 6: Mr John, a school principal, drives from his residence to school. It takes him
about 40 minutes to travel a distance of 30 km everyday. One day after travelling
20 km, his car encountered a snag (fault) which took 10 minutes to repair.
(a) What fraction of the total distance had Mr John travelled before his car
encountered a fault?
(b) What fraction of total time was spent in repairing the car?
20 2
Solution: (a) Fraction of distance travelled before the fault is detected = 30 = 3

10 1
(b) Fraction of the total time spent to repair the car = =
50 5
EXERCISE 2.1

1. Compare the following:

3 4 2 2 9 11 3 5
(a) and (b) and (c) and (d) and
4 5 9 3 10 15 5 7

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