# Free Fractions and Decimals 01 Practice Test - 7th grade

A fraction is ______.

A.

the ratio of the total number of parts to the number of parts considered.

B.

the ratio of the number of parts considered to the total number of parts.

C.

never a whole part

D.

always a whole part

#### SOLUTION

Solution : B

Consider the following example.

Suppose you have a pizza.
Divide the whole pizza into 4 parts.
Now, take 3 parts out of the 4 parts.

These 3 parts represent the fraction 3 out of 4, i.e., 34.

i.e., a fraction is the ratio of the number of divisions considered to the total number of divisions.

Which of the following is correct about improper fractions?

A.

In an improper fraction, the numerator is less than denominator and numerator is greater than 0.

B.

In an improper fraction, the numerator is always greater than the denominator.

C.

In an improper fraction, the numerator is greater than the denominator and denominator should not be equal to zero.

D.

In an improper fraction, the numerator is always equal to the denominator.

#### SOLUTION

Solution : C

In an improper fraction, the numerator is greater than the denominator and denominator should not be equal to zero.

e.g. 61576, 94,6621 etc

abc is called a/an ____ and is equal to ____.

A.

proper fraction, bc

B.

improper fraction, a÷bc

C.

mixed fraction, a×bc

D.

mixed fraction, a+bc

#### SOLUTION

Solution : D

abc is called a mixed fraction.
Here, 'a' is whole number part and bc is the fractional part.

e.g. 234, 516

abc=a+bc

e.g:  234= 2+34

Which of the given option is the simplest form of 1386018480 ?

A.

12

B.

34

C.

14

D.

32

#### SOLUTION

Solution : B

In order to reduce a fraction to its lowest terms, divide both numerator and denominator by their common factor.

13860101848010=13861848

1386318483=462616

4621161611=4256

427567=68=34

Convert 612, 14 and 63 into like fractions.

A.

512, 312, 2412

B.

612, 212, 2412

C.

612, 312, 2012

D.

612, 312, 2412

#### SOLUTION

Solution : D

In order to convert the fractions into like fractions, find the L.C.M of denominators of given fractions.

Then convert each fraction into an equivalent fraction having denominator as the L.C.M of the denominators of the given fractions.

L.C.M of [12, 4, 3] = 12

612=6×112×1=612

14=1×34×3=312

63=6×43×4=2412

Find the value of a if,

3a4=154

A.

3

B.

4

C.

1

D.

2

#### SOLUTION

Solution : A

3a4 is a mixed fraction.

3a4=  (3×4) +a4=  12 +a4

Given, (12+a)4154

Comparing the numerator gives, (12 + a) =15

Therefore, a = (15 - 12) = 3

Arrange the following fractions in ascending order,
fractions: 1216,49 and 610

A.

610, 49, 1216

B.

49, 610, 1216

C.

1216, 610, 49

D.

1216, 49, 610

#### SOLUTION

Solution : B

To compare the fractions, make the denominators equal.

For that, we have to find LCM of denominators 16,9,10

16=2×2×2×2

9=3×3

10=2×5

LCM of [16, 9, 10] = 2×2×2×2×3×3×5=720

1216=12×4516×45=540720

49=4×809×80=320720

610=6×7210×72=432720

Comparing numerators, 320720<432720<540720
49<610<1216

_____ is a fraction between 29 and 619

A.

1224

B.

610

C.

828

D.

3240

#### SOLUTION

Solution : C

One fraction exisiting between ab and cd is a +cb +d.

Here, we have to insert a fraction between 29 and 619.

a = 2, b = 9, c = 6 and d = 19

One fraction exisiting between them is: 2 +69 +19 = 828

Which of the following is a pair of like decimals?

A. 0.2010, 0.21159
B. 4.260, 4.9125
C. 4.19, 4.625
D. 9865.4946, 28.4900

#### SOLUTION

Solution : D

Decimal numbers having the same number of decimal places, i.e. decimals having the same number of digits on the right of the decimal point, are known as like decimals.

In the option with the numbers 9865.4946 and 28.4900, both decimal numbers have 4 digits in the decimal place.

Therefore, they are like decimals.

The rest of the options do not
have same number of decimal places.

Which of the following decimals are equal?

A. 10.0101, 10.01010
B. 10.101010, 01.010010
C. 0.1010, 0.1010000
D. 11.011011, 11.0101

#### SOLUTION

Solution : A and C

A very important property of decimals is that adding zeros after the last digit of the decimal part of any decimal number does not change the value of the decimal.

Hence,
10.0101, 10.01010 and
0.1010, 0.1010000 are the right options