9
Q:

# Karthik read $\frac{6}{13}$ th of a book in 1st week and $\frac{5}{9}$ th of the remaining book in 2nd week. If there were 100 pages unread after 2nd week, how many pages were there in the book ?

 A) 404 B) 415 C) 418 D) 420

Answer:   C) 418

Explanation:

Let the total book be 1

Then, in the 1st week $\frac{6}{13}$th of book is read

i.e remaining pages =  $1-\frac{6}{13}=\frac{7}{13}$

in 2nd week he read $\frac{5}{9}$th of it

i.e $\frac{5}{9}×\frac{7}{13}=\frac{35}{117}$
Remaining pages after 2nd week = $\frac{7}{13}-\frac{35}{117}=\frac{28}{117}$

But given remaining pages after 2nd week = 100

$\frac{28x}{117}=100$

--> x = 418

The total pages in the book are 418

Q:

2/3 as a decimal

 A) 0.47 B) 6.77 C) 0.67 D) 0.07

Answer & Explanation Answer: C) 0.67

Explanation:

To convert a fraction into decimal, just take the number on top which we called the numerator and divide it by the number at the bottom which we called the denominator.

2/3

How it comes :

÷ 0 bring down the decimal point.

20 ÷ 6 and carry the remainder 2 to make 20

20 ÷ 6 and carry the remainder 2 to make 20

20 ÷ 6 and carry the remainder 2 to make 20

etc...

This gives the recurring decimal 0.6666...

If we round off to two decimals , then it becomes 0.67.

Hence, decimal fraction of 2/3 = 0.67.

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0 51
Q:

3/8 as a decimal

 A) 1.375 B) 2.375 C) 0.375 D) 3.75

Answer & Explanation Answer: C) 0.375

Explanation:

Expressing 3/8 as a decimal fraction:

We can convert 3/8 into a decimal fraction by just dividing 3 by 8 or making 3 into 8 parts.

Then, it is 3/8 = 0.375 as a decimal fraction.

Other Method::

3/8 as a Decimal :

In this we should convert the denominator into 10, 100, 1000, 10000, 100000,... to make it simple.

Now to make 8 into 1000, we multiply numerator and denominator with 125

=> (3 x 125)/(8 x 125) = 375/1000 = 0.375.

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2 28
Q:

3/4 divided by 2 is

 A) 3/2 B) 2/3 C) 8/3 D) 3/8

Answer & Explanation Answer: D) 3/8

Explanation:

3/4 divided by 2

= 3/4/2

= 3/4x2

= 3/8.

Hence, 3/4 divided by 2 is equal to 3/8.

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1 47
Q:

1/8 as a decimal?

 A) 0.125 B) 0.225 C) 0.325 D) 0.425

Answer & Explanation Answer: A) 0.125

Explanation:

1/8 to convert into decimal,

Find an equivalent fraction with a denominator of a power of 10.

In this case, we will use 1000.

This can now be written as a decimal with 3 decimal places (because we have thousandths.

i.e, 0.125

Hence,

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2 231
Q:

What is $\frac{1}{5}$ as a decimal?

 A) 0.333 B) 0.666 C) 0.200 D) 0.452

Answer & Explanation Answer: C) 0.200

Explanation:

Here I converted the original fraction to a fraction with the denominator being 10, because decimals can be written in the tenths place.

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3 342
Q:

125 over 1000 in Simplest Form?

 A) 2/9 B) 1/8 C) 3/8 D) 4/7

Answer & Explanation Answer: B) 1/8

Explanation:

125 over 1000 in Simplest Form means $\frac{\mathbf{125}}{\mathbf{1000}}$ in its simple fraction form.

Now, to get the simplest form of 125/1000, find the HCF or GCD of both numerator and denominator i.e, 125 and 1000.

HCF of 125, 1000 = 125

Then, divide both numerator and denominator by 125

i.e,

Hence, $\frac{\mathbf{1}}{\mathbf{8}}$ is the simplest form of 125 over 1000.

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3 246
Q:

$\frac{\mathbf{1}}{\mathbf{8}}$ as a decimal?

 A) 0.375 B) 0.247 C) 0.214 D) 0.125

Answer & Explanation Answer: D) 0.125

Explanation:

Here  $\frac{\mathbf{1}}{\mathbf{8}}$ in decimal means 8th part in 1.

We know that $\frac{\mathbf{1}}{\mathbf{10}}$ = 0.1

Then,

=>

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3 333
Q:

Express 0.875 and 0.375 as a Fraction.

 A) 3/11 & 7/11 B) 7/9 & 9/13 C) 7/8 & 3/8 D) 7/9 & 9/11

Answer & Explanation Answer: C) 7/8 & 3/8

Explanation:

Given 0.875 and 0.375

0.875 ::

After decimal point there are 3 digits 875

Now, mutiply and divide 0.875 with 1000

Similarly,

0.375 ::

After decimal point there are 3 digits 375

Now, mutiply and divide 0.375 with 1000

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