Olympiad Test: Fractions and Decimals - Class 7 MCQ

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 numerator and 12 is called the denominator.

Let the three integers be: x, x + 2 and x + 4.
Then, 3x = 2(x + 4) + 3
Therfore, x = 11.
Third integer = x + 4 = 15.

Product of two numbers = 2.0016
One number = 0.72
Other number = (2.0016 ÷ 0.72)

Hence, the required number = 2.78

- Given that 2494 ÷ 14.5 = 172
- To find 24.94 ÷ 1.45, we need to move the decimal point one place to the right for both numbers
- This gives us 249.4 ÷ 14.5
- Dividing 249.4 by 14.5 gives us 17.2
- Therefore, the answer is 17.2

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.

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

Example: 1/3 of 90 = 1/3 × 90 = 30.

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.

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

= 1/5 ×40 
= 8 students 

► 0.75 = (75 / 100) = 3/4

Average = Sum of numbers / Total quantity of numbers

= (4.2 + 3.8 + 7.6) / 3
= 15.6 / 3
= 5.2

► (2 / 7) × 3 = 6 / 7

In ΔSTR, By Pythagoras theorem:
RT² = ST² + RS²

► ST² = 152 - 92 = 144
► ST = 12m

In ΔTQP, By Pythagoras theorem:
PT² = TQ² + PQ²

► TQ² = 15² - 12² = 81
► TQ = 9m

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

Required decimal =

► (2 / 5) x (1 / 7) = (2 / 35) 

0.02 × 0.03 = 0.0006 

In a proper fraction, the numerator is always less than the denominator.
Examples of proper fractions include: 
1/2, 9/13 and 1/1001.

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.

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.

(⅓) of 3 means 1/3 * 3 = 1.
∵ 3 in numerator and denominator cancels out.

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