In the pattern 1-3 -1-4- 1-5 -which fraction makes the sum greater than 1 first time- explain-

1/3 + 1/4 + 1/5 = 20+15+12/60 = 47/60 lt;1 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 lt;1 Now ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VI

Mathematics

Addition of Fractions

In the patter...

Question

Question 125

In the pattern $\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + . . .,$ which fraction makes the sum greater than 1 (first time)? explain.

Open in App

Solution

$\frac{1}{3} + \frac{1}{4} + \frac{1}{5} = \frac{20 + 15 + 12}{60} = \frac{47}{60} < 1$
According to the pattern, next number will be $\frac{1}{6}$
$∴ \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} = \frac{40 + 30 + 24 + 20}{120} = \frac{114}{120} < 1$
Now according to the pattern, next number after $\frac{1}{6} i s \frac{1}{7} ∴ \frac{1}{3} + \frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{7} = \frac{280 + 210 + 168 + 140 + 120}{840} = \frac{918}{840} > 1$
Hence $\frac{1}{7}$ makes the sum greater than 1(first time)

Suggest Corrections

Similar questions

Question 64

Will the quotient $7 \frac{1}{6} \div 3 \frac{2}{3}$ be a fraction greater than 1.5 or less than 1.5? Explain.

Q. Study the following pattern.

1 = 1^{2}

1 + 3 = 2^{2}

1 + 3 + 5 = 3^{2}

1 + 3 + 5 + 7 = 4^{2}

and so on.
What is the sum of the first 10 odd numbers?

Question 109 (i)

Observe the following patterns and fill in the blanks to make the statements true:
$- 5 \times 4 = - 20$
$- 5 \times 3 = - 15 = - 20 - (- 5)$
$- 5 \times 2$ =____ = -15 – (-5)
$- 5 \times 1 =$ ____=____
$- 5 \times 0 = 0 =$ ____
$- 5 \times (- 1) = 5 =$ ____
$- 5 \times (- 2) =$ _____=_____

Question 4
Starting from (−1) $\times$ 5 ,write various products showing a pattern to show (−1) $\times$ (−1)=1.

Q. Question 3 (i)
Multiply the following fractions

\frac{2}{5} \times 5 \frac{1}{4}

Join BYJU'S Learning Program

Question 125 In the pattern 13+14+15+...,which fraction makes the sum greater than 1 (first time)? explain.

13+14+15=20+15+1260=4760<1 According to the pattern, next number will be 16 ∴13+14+15+16=40+30+24+20120=114120<1 Now according to the pattern, next number after16is17∴13+14+15+16+17=280+210+168+140+120840=918840>1 Hence 17makes the sum greater than 1(first time)

Question 125

In the pattern $\frac{1}{3} + \frac{1}{4} + \frac{1}{5} + . . .,$ which fraction makes the sum greater than 1 (first time)? explain.