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QUESTION: 1

A __________ is a fraction that represents a part of a whole.

Solution:

A **proper fraction **is a number representing a part of a whole. The whole may be a single object or a group of objects.

__ Example__: Consider the fraction 7/12. This fraction is read as ”seven-twelfth” which means that 7 parts out of 12 equal parts in which the whole is divided.

In the fraction 7/12, 7 is called the

QUESTION: 2

Three times the first of three consecutive odd integers is 3 more than twice the third. The third integer is:

Solution:

Let the three integers be: *x*, *x* + 2 and *x* + 4.

Then, 3*x* = 2(*x* + 4) + 3

*► x* = 11.

Third integer = *x* + 4 = 15.

QUESTION: 3

The product of two numbers is 2.0016. If one of them is 0.72, find the other number.

Solution:

Product of two numbers = 2.0016

One number = 0.72

Other number = (2.0016 ÷ 0.72)

Hence, the required number = 2.78

QUESTION: 4

If 299.4 ÷ 14.5 = 172, then 29.94 ÷ 1.45 = ?

Solution:

[ Here, Substitute 172 in the place of 2994/14.5 ]

QUESTION: 5

The price of commodity X increases by 40 paise every year, while the price of commodity Y increases by 15 paise every year. If in 2001, the price of commodity X was Rs. 4.20 and that of Y was Rs. 6.30, in which year commodity X will cost 40 paise more than the commodity Y ?

Solution:

Suppose commodity X will cost 40 paise more than Y after Z years. Then,

► (4.20 + 0.40Z) - (6.30 + 0.15Z) = 0.40

► 0.25Z = 0.40 + 2.10

► Z = (2.50 / 0.25) = 10

∴ X will cost 40 paise more than Y 10 years after 2001 i.e in 2011.

QUESTION: 6

A fraction acts as an operator ________.

Solution:

**Fraction as an operator ‘of ’.**

Fraction acts as an operator of 'of' represents multiplication.

** Example**: 1/3 of 90 = 1/3 × 90 = 30.

QUESTION: 7

The product of two proper fractions is ________ each of the fractions that are multiplied.

Solution:

When two proper fractions are multiplied, the product is **less than **both the fractions. Or, we say the value of the product of two proper fractions is **smaller **than each of the two fractions.

QUESTION: 8

In a class of 40 students 1/5 of the total number of students like to study English, 2/5 of the total number like to study mathematics and the remaining students like to study Science.

Q. How many students like to study English?

Solution:

Number of students who like english = 1/5 of 40

= 1/5 ×40

= 8 students

QUESTION: 9

What will be the vulgar fraction of 0.75

Solution:

► 0.75 = (75 / 100) = 3/4

QUESTION: 10

Find the average of 4.2, 3.8 and 7.6.

Solution:

Average = Sum of numbers / Total quantity of numbers

= (4.2 + 3.8 + 7.6) / 3

= 15.6 / 3

= 5.2

QUESTION: 11

(2 / 7) × 3 =_______

Solution:

► (2 / 7) × 3 = 6 / 7

QUESTION: 12

There is a tree between houses of A and B. If the tree leans on A’s House, the tree top rests on his window which is 12 m from ground. If the tree leans on B’s House, the tree top rests on his window which is 9 m from ground. If the height of the tree is 15 m, what is distance between A’s and B’s house?

Solution:

In ΔSTR, By Pythagoras theorem:

**RT ^{2} = ST^{2} + RS^{2}**

► ST^{2} = 152 - 92 = 144

► ST = 12m

In ΔTQP, By Pythagoras theorem:

**PT ^{2} = TQ^{2} + PQ^{2}**

► TQ^{2} = 15^{2} - 12^{2} = 81

► TQ = 9m

Distance between houses = SQ = ST + TQ = 12 + 9 = 21m

QUESTION: 13

What decimal of an hour is a second ?

Solution:

Required decimal =

QUESTION: 14

(2 / 5) ÷ 7 = ______.

Solution:

► (2 / 5) x (1 / 7) = (2 / 35)

QUESTION: 15

0.02 × 0.03 = ______

Solution:

0.02 × 0.03 = 0.0006

QUESTION: 16

In proper fraction, the numerator is ________ the denominator.

Solution:

In a proper fraction, the numerator is always less than the denominator.

**Examples of proper fractions include: **

1/2, 9/13 and 1/1001.

QUESTION: 17

Reciprocal of 7 / 2 is _____

Solution:

A reciprocal of a fraction a / b is created by changing places of numerator and denominator (it can only be done if the numerator of the original fraction a is different from zero), so it is b / a.

So, in the given example the reciprocal of 7/2 is 2 / 7.

QUESTION: 18

In a class 3/4^{th} of the students do not know either English or Hindi. But 1/6^{th} of the students know English. How much students know both English and Hindi if students who know Hindi are 1/8^{th} of total students in the class?

Solution:

3 / 4th do not know English or Hindi.

So, 1 / 4th know English or Hindi or both.

1/6th know English and 1/8th know Hindi .

Answer is 1 / 24.

QUESTION: 19

(1/3) of 3 is ____

Solution:

(⅓) of 3 means 1/3 * 3 = 1.

∵ 3 in numerator and denominator cancels out.

QUESTION: 20

Multiply 2.05 and 1.3.

Solution:

When you multiply 2.05 by 1.3 you get 2.665 , because there are three decimal places.

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