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प्रश्न
In the pattern `1/3 + 1/4 + 1/5 +` ..... which fraction makes the sum greater than 1 (first time)? Explain.
उत्तर
`1/3 + 1/4 + 1/5 = (20 + 15 + 12)/60`
= `47/60 < 1` ......[∵ Numerator < Denominator]
According to the pattern, next number will be `1/6`
∴ `1/3 + 1/4 + 1/5 + 1/6 = (40 + 30 + 24 + 20)/120`
= `114/120 < 1` .....[∵ Numerator < Denominator]
Now, according to the pattern, next number after `1/6` is `1/7`
∴ `1/3 + 1/4 + 1/5 + 1/6 + 1/7 = (280 + 210 + 168 + 140 + 120)/840`
= `918/840 > 1` .....[∵ Numerator > Denominator]
Hence, `1/7` makes the sum greater than 1 (first time).
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संबंधित प्रश्न
Find answers to the following. Write and indicate how you solved them.
Is `9/16` equal to `5/9`?
Find the difference between `8/9` and `2/7`
Which is smaller in the following fraction?
`10/42` and `21/42`
Six parts of a Rectangle
Rani has divided a green rectangle into six equal parts like this.
Now you divide each of these rectangles into six equal parts. Use a different way for each of the three rectangles.
[This game is to be played in groups of 4. Each player has to make a circle as shown. Each one has to make 15 tokens on slips on paper.
Write `1/2, 1/3, 1/4, 1/6, 1/12, 2/12, 3/12, 4/12,...11/12` to make your tokens.
Shuffle, the tokens and make a pile in the middle of the group. Now you are ready to start the game.
The first player takes a token from the pile, colours that part of the picture, and puts the token under the pile. The next player does the same, and so on. The winner is the one who first colours the circle completely.]
- Write the tokens you got.
Write the shaded portion as a fraction. Arrange them in ascending and descending order using the correct sign ‘<’, ‘=’, ‘>’ between the fractions:
Write the shaded portion as a fraction. Arrange them in ascending and descending order using the correct sign ‘<’, ‘=’, ‘>’ between the fractions:
How quickly can you do this? Fill appropriate sign.
`3/5 ☐ 6/5`
How quickly can you do this? Fill appropriate sign.
`5/7 ☐ 15/21`
Find answers to the following. Write and indicate how you solved them.
Is `1/15` equal to `4/30?`
