Maths-
General
Easy
Question
Find 10 rational numbers between
𝑎𝑛𝑑 ![3 over 4](data:image/png;base64,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)
Hint:
Make the denominators same for the two given rational numbers and thus get
10 national numbers between them.
The correct answer is: 10 rational numbers
Given rational numbers are
and ![3 over 4](data:image/png;base64,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)
Let us make the denominators the same , say 80
So,
and ![fraction numerator 3 cross times 20 over denominator 4 cross times 20 end fraction equals 60 over 80](data:image/png;base64,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)
So 10 national numbers between
and
are same as
and
.
∴ 10 rational numbers between
and
are ![49 over 80 comma 50 over 80 comma 51 over 80 comma 52 over 80 comma 53 over 80 comma 54 over 80 comma 55 over 80 comma 56 over 80 comma 57 over 80 58 over 80](data:image/png;base64,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)
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By what rational number
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Maths-
Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal:![59 over 8](data:image/png;base64,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)
Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal:![59 over 8](data:image/png;base64,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)
Maths-General
Maths-
A sim earns Rs. 40000 per month. He spends
of his income on food,
of the remaining on education of children and
of the remainder on the house rent. How much money is still left with him?
A sim earns Rs. 40000 per month. He spends
of his income on food,
of the remaining on education of children and
of the remainder on the house rent. How much money is still left with him?
Maths-General
Maths-
Find the cost of 3
m of cloth at Rs 36
. per meter.
Find the cost of 3
m of cloth at Rs 36
. per meter.
Maths-General
Maths-
Find the area of circular ring whose external and internal radii are 10cm and 3 cm respectively
Find the area of circular ring whose external and internal radii are 10cm and 3 cm respectively
Maths-General