Fractions And Decimals

The two fractions are equivalent if a × d = c × b .
A.

⇒ 40 × 5 = 200 and 4 × 50 = 200

⇒ 4× 50 = 5 × 40

B.

⇒ 12 × 5 = 60 and 4 × 15 = 60

⇒ 12 × 5 = 4 × 15

C.

⇒ 16 × 5 = 80 and 20 × 4 = 80

⇒ 16 × 5 = 20 × 4

D.

⇒ 9 × 5 = 45 and 15 × 4 = 60

⇒ 9 × 5 ≠ 15 × 4

Here numerator (5) is less than the denominator (7), ∴ its value is less than 1. Hence it lies between 0 and 1.

For denominator 4 to be equal to 12, we need to multiply by 3.
⇒ , Thus numerator is 3.

A. can be further divided.
B.
C. cannot be further divided.
D. cannot be further divided.

Two fractions ( ) will be equivalent if a × d = b × c

For

⇒ 5 × p = 20 × 8

⇒ p = 32

Simplifying each of the above option,
A.

B.

C.

D.

Here in all the fraction numerators are same. Thus smaller the denominator greater the fraction.
⇒ 6 is the smallest in all the denominators,

∴ is the greatest
fraction.

All the fractions are like fractions. Thus smaller the numerator smaller the fraction.
⇒ 3 is the smallest in all the numerators,

∴ is the smallest
fraction.

All the fractions are like fractions.

Thus sum .

All the fractions are like fractions.

Thus subtraction .

Since, 0.7499 is greater than 0.749 and less than 0.75.
Thus it lies between 0.749 and 0.75.

Since, 0.023 is greater than 0.02 and less than 0.03.
Thus it lies between 0.02 and 0.03.

On dividing 11 by 7, we get quotient as 1 and remainder as 4.
⇒ 1 whole and or _, ∴ =

_{Converting all the decimals to like decimals 0.07 = 0.070 and 0.008}
Sum = 0.070 + 0.008 = 0.078

Since the whole part is same, We compare the tenth part of each decimal.

⇒ 0.29 have the greatest tenth part. Thus 0.29 is the greatest decimal.

On comparing the whole part we get that 0 is the smallest. On comparing the tenth part of those whose whole part is 0. We get,
0.082 has the smallest tenth part i.e. 0. Thus 0.082 is the smallest.

Only option B and D have the same whole part as 13.
Now rounding the thousand part of 13.572 we get 13.57. Now rounding off hundred part we get 13.6.

Converting given decimals into like decimals we get 15.8 as 15.80 and 6.73 as 06.73.
⇒ 15.80 – 06.73 = 9.07

whole

is a fraction

proper

is a proper fraction as 5(Numerator)<9(Denominator)

like

and are like fraction as they have the same denominator(15)

mixed

A mixed fraction is a whole number and fraction combined. Example- 1 where 1 is the whole number and is fraction

improper

Because numerator is greater than the denominator. (18>5)

Proper

Because numerator is less than the denominator.( 7<19 )

like

Because denominator is same in both fraction.

unlike

Because denominator is different in both fraction.

we can write 6 = 2×3 and 15 = 3×5

If we put this in fraction we get

34 can be written as 34 = 17×2

Then we get

different

as we know converting mixed fraction into improper fraction, first we multiply denominator in whole part of fraction then add it with numerator.

In this case –

2×8 +7 =23

So this become

For converting into mixed fraction the Quotient (12) goes to the whole number part , Remainder (3)on the numerator and the denominator is same as 7.

for solving this , follow the steps given below

for converting this into fraction we can multiply and divide both numerator and denominator by 100.

Now we can write 1625 =65×25 and 100 =25×4

So we get fraction

0.28

As they are like fractions only numerators will get added-

see the steps below –

As they are like fractions only numerators will get subtracted -

The addition is done after converting the mixed fraction into improper fraction –

As they are like fractions only numerators will get added -

The substraction is done after converting the mixed fraction into improper fraction –

Now we do substraction-

As they are like fractions only numerators will get subtracted -

The value will be

50 paisa coins add 50 time .

That is 50+50+50+50+50………………..50times..

Simplest form of this will be

50×50 =2500 paisa .

As we all know that 100 paisa = 1Rs.

So we divide our total value in paisa by 100 to get value in Rs.

3 Hundredths =300

3 tenths =30

3 Hundredths + 3 tenths

300 + 30 =330.

False

Like fractions are those fractions that have the same denominator. It does not matter what the numerator is as long as the denominator is same.

False

18 = 2 × 3 × 3

30 = 3 × 13

Hence, HCF of 18 and 39 = 3

Dividing both numerator and denominator of by 3

∴ is the lowest form.

True

Equivalent fractions are those which are obtained by multiplying or dividing both numerator and denominator by same number.

Dividing numerators and denominators,

Fraction 2 to fraction 1

∴

Also,

As both numerator and denominator is multiplied by same number, they are equivalent fractions.

True

When 2 fractions are added, the result in most cases will be a fraction (), but in some case if it does happen to be just a integer, it can always be written with denominator 1 (hence)

Hence, converting it to a fraction.

True

When 2 fractions are subtracted, the result in most cases will be a fraction (), but in some case if it does happen to be just a integer, it can always be written with denominator 1 (hence).

Hence, converting it to a fraction.

True

If a whole is divided into let’s suppose n parts, then each fraction represents part, hence a fraction.

When all n parts are joined together,

∴

Hence, a whole is formed.

True

Let ‘a’ be the same digit at ones and tens place in a number.

Place value of digit at ones’ place = 1 × a = a

Place value of digit at tens place = 10 × a = 10a

Hence,

The place value of a digit at the tenths place is 10 times the same digit at the ones place.

False

Let ‘a’ be the same digit at tens and hundreds place in a number.

Place value of digit at tens place = 10 × a = 10a

Place value of digit at hundreds place = 100 × a = 100a

Hence,

The place value of a digit at the hundreds place is 10 times the same digit at the tens place.

True

When an even decimal (or any even number) is followed by 5, it is

round down. When an odd decimal is followed by a 5, it is round up.

Here, in 3.725,

2 is even number

Hence, since 2(a even number) is followed by 5, it is round down.

∴ The decimal 3.725 is equal to 3.72 correct to two decimal places.

True,

_False

_{= 23 + 0.4}

_{= 23.4 (Decimal expansion gives 0.4)}

True

In the figure, there are total 8 parts.

Out of these 8 parts, 3 are shaded.

Hence, fraction represented =

False

Number of unshaded parts = 4

Total number of parts = 9

Fraction represented by unshaded portion =

_False

are both like fractions (fractions with same denominators)

For like fractions, for both addition and subtraction numerators can directly be added/subtracted with same denominators.

Hence,

_False

_{LCM of 18 and 15 is}

_{LCM = 2 × 3 × 3 × 5 = 90}

Therefore,

_True

are both like fractions (fractions with same denominators)

For like fractions, for both addition and subtraction numerators can directly be added/subtracted with same denominators.

Hence,

False

Writing both the numbers, one below the other and adding additional zeroes to required places, we get

True

Writing both the numbers, one below the other and adding additional zeroes to required places, we get

True

are both like fractions (fractions with same denominators)

To compare like fractions, they can directly be compared with their numerators.

As 16>13

∴

False

For decimal numbers, if integer part is same, then the comparison is done by checking digits starting from the right of decimal point to the extreme right.

Checking the first digit right of decimal,

2>0

∴ 19.25>19.053

True

If zeroes are added after the last non-zero digit of a decimal number, it does not make any change to the number.

we can convert given fractions in to decimal then

So

we can convert given fractions in to decimal then

So, as we see 0.5 <6.7857

we can convert given fractions in to decimal then

So

3.25 <3.4

we can convert given fractions in to decimal then

So

we can convert given fractions in to decimal then

So

IT represent the area =

there are 15 boxes out of which 4 are unshaded so, the fraction is

one fruit is divided among 6 person, so one person will get

12.104 <12.124 <12.142 <12.214<12.401

for largest decimal number using this numbers will be –

Less then zero means – 0.8531

for smallest four digit decimal number will be –

2.345

as we know converting mixed fraction into improper fraction, first we multiply denominator in whole part of fraction then add it with numerator.

In this case –

6×3 +2 = 20

So this become

as we know converting mixed fraction into improper fraction, first we multiply denominator in whole part of fraction then add it with numerator.

In this case –

5×3 +2 = 17

So this become

for converting this into fraction we can multiply and divide both numerator and denominator by 1000.

we can write 6.03 as

And we know that 603 = 6×100 +3

So the mixed function wee be

as we know 1 kg = 1000gm

So, 5201 gm will be =

as we know 100 paise = 1Rs.

So, 2009 paise =

Its can be converted into mixed fraction – we can write the numerator 2009 = 20×100+ 9

So the mixed fraction become

As we know 100 cm = 1m

So 1537 cm will be =

As an improper fraction

As we know 1km = 1000m

2435 m =

Can be written as

The 487 divided by 200 can be written as 487 = 200×2 +87

We can write mixed fraction will be

for arrangement of this we have to make the denominator same for all fraction

For this we multiply denominators and numerator by different values =

So we can now this fractions in ascending order-

For arranging this in descending order we have to convert it into decimal points

So we can write this in descending order-

for making denominator 44 we multiply denominator and numerator by 11.

So we get

for making numerator 60 we multiply numerator and denominator by 12

So we get

we can write the 129 as

129 = 16×8 +1

So we write it as mixed fraction =

For round off 20.83 to nearest tenths we will look at next one digit after decimal point

That is 8, so it will round off to 10 .

So the digit become 20.83 = 21.

For round off 75.195 to nearest hundredths we will look at hundredth place after decimal point

That is 9, so it will round off to 10

So the number become 75.195 = 75.20

For round off 27.981 to nearest tenths we will look at next one digit after decimal point

That is 9, so it will round off to 10 .

So the digit become 27.981 = 28.

for adding fraction we have to make denomination of both fraction equal (like fractions)

For this we make both denominator equal to 24.

So we get,

The addition is done after converting the mixed fraction into improper fraction –

Also we make denominator equal to 8

So,

As they are like fractions only numerators will get added -

For subtraction we have to make both denominator equal so we can do it by this

The subtraction is done after converting the mixed fraction into improper fraction –

Now we have to make both fractions like fractions so we multiply above fraction by 3

So we get

Now we do subtraction-

As they are like fractions only numerators will get subtracted -

The subtraction is done after converting the mixed fraction into improper fraction –

Now we have to make both fractions like fractions so we multiply above fraction by 2

So we get

Now we do subtraction-

As they are like fractions only numerators will get subtracted -

The subtraction is done after converting the mixed fraction into improper fraction –

Now we have to make both fractions like fractions so we multiply above fraction by 2

So we get

Now we do subtraction-

As they are like fractions only numerators will get added -

Bicycle travelled by Katrina in the morning = km

Bicycle travelled by Katrina in the evening = km

Now, total distance travelled by Katrina = distance travelled in the morning + distance travelled in the evening

Total distance travelled =

∴ total distance travelled by Katrina is km.

of the rectangle is has 16 parts

whole rectangle is considered 1.

Now the number of parts the whole rectangle will have = 16 × 4= 64 parts

Size of tennis racquet

Representing the above in improper fraction we get

The numerator = 80 × 11 + 9

=880 + 9

=889

and the denominator remains same = 80

∴ the improper fraction

Lets consider the total amount of food consumed = 1

Amount of food available for next level

Now the amount of not available for next level will be

Age at which Mr. Rajan got a job = 24yrs

Age at which he got retired = 60 yrs

No. Of years Mr. Rajan worked = 60 – 24

= 36years

Fraction of his job till the age of retirement

Total number of hours in a day = 24 hours

Number of hours the food remains in our stomach = 4 hours

Fraction of hours the food remains in our stomach in a day

First we need to subtract 25.5 from 50

we get = 50 – 25.5 = 24.5

∴ this is the number we should add to 25.5 to get 50

Weight of potatoes purchased = 1kg 200g

Converting 200g in kg = 0.2kg

∴ weight of potatoes = 1.2kg

Weight of Dhaniya = 250g

Converting 250g in kg

Weight of onion purchased = 5kg 300g

Converting 300g in kg

∴ total weight of onions = 5.3kg

weight of palak purchased = 500g

converting 500g to kg

weight of tomatoes purchased = 2kg 600g

converting 600g in kg

∴ total weight of tomatoes = 2.6kg

∴ total weight in kg = 1.2kg + 0.25kg + 5.3kg + 0.5kg + 2.6kg

=9.85kg

0.011

0.101

0.110

1.001

Lets write the numbers as below and add

∴ the solution is 22.022

Quantity of CNG saved = 33000 tonnes

Quantity of Diesel saved = 3300 tonnes

Quantity of Petrol saved = 21000 tonnes

Fraction of the quantity of diesel saved to the quantity of petrol saved

Fraction of the quantity of diesel saved to the quantity of CNG saved

From the chart given we can see rice is contains 5.3 Joules which is maximum compared to all and milk contains 3.0 Joules which is the least compared to others.

∴ rice provides the max energy and milk provides the least energy

Now, fraction of the least energy to maximum energy

Lets consider the full cup as 1.

Part of the cup filled

Now part of the cup still to be filled = full cup – part of the cup filled

Length of lace bought by Mary

Length of lace Mary used

Length of lace left with Mary = length of lace bought by Mary – length of lace used

Sunita Weight Earlier =

Weight Gained=

Total Weight Gained by Sunita on Monday=

46 +

= +

=

=

=

Quantity of juice purchased on Monday

Quantity of juice purchased on Tuesday

Total quantity of juice purchased = juice purchased on Monday + juice purchased on Tuesday

Quantity of juice she purchased

Quantity of juice she gave her friend

Quantity of juice she is left with = quantity she purchased – quantity she gave her friend

Total Length of wood given to carpenter

Length of wood sawed off

Hence, length of remaining wood = total length of wood – length of wood sawed off

Distance travelled by Nasir in a bus

Distance travelled by Nasir by walk

∴ total distance travelled by Nasir = distance travelled in bus + distance travelled by walk

Weight of Neetu’s Fish

Weight of Narendra’s fish

So we can see that Neetu’s fish weighs more than Narendra’s fish

Difference between Neetu’s fish and Narendra’s fish

= weight of Neetu’s fish – weight of Narendra’s fish

Length of cloth needed for shirt

Length of cloth needed for scarf

∴ total length of cloth needed = length of shirt +length of scarf

a) When we add

We get

∴ we cannot directly add the numerators and denominators we need to take LCM and solve it.

b) When we add

We get

∴ we cannot directly add the numerators and denominators we need to take LCM and solve it.

1 metre = 100 centimetre

Now we have 1 metre 40centimetre + 60 centimetre

we have 40 cm + 60 cm =100cm 1metre

∴ we have 1metre + 1metre = 2metres

and the other value is given as 2.6metres

∴ we can see that 2.6metres is greater than 1metre 40centimetre + 60centimetre.

(i) = D

As we can see in the figure, there are two circles, when we divide the circles into two halves we get 4 parts. Therefore both the circles are divided into 4 halves.

Now when we divide these 4 parts again we will get 8 parts as we can see in the figure.

Now we can see that 6 sub parts are shaded out of 4 intitial half of the circle therefore we get the fraction as

(ii) = A

As we can see in the figure from 0 to 2 it is sub divided into 10 parts. Out of these 10 parts 6 parts are shaded so we get the fraction as

(iii) = E

As we can see in the figure there are 6 boxes and all the 6 boxes are shaded therefore we get the fraction as

(iv) = B

As we can see in the figure there are 16 boxes and out of the 16 boxes only 6 are shaded therefore we get the fraction as

Total numbers we have 0, 1, 2, 3, 4, 5 which is 6 numbers

As we know Natural numbers start from 1

∴ total natural numbers in the collection = 5 (1, 2, 3, 4, 5)

Hence the fraction will be

As we know Whole number starts from 0

∴ total whole numbers in the collection = 6 (0, 1, 2, 3, 4, 5)

Hence the fraction will be

-3, -2, -1, 0, 1, 2, 3

There are 7 numbers

As we know Natural numbers start from 1

∴ total natural numbers in the collection = 3 (1, 2, 3)

Hence the fraction will be

As we know Whole number starts from 0

∴ total whole numbers in the collection = 4 (0, 1, 2, 3, 4, 5)

Hence the fraction will be

Let the two numbers be x and y

Now sum of two numbers will be

…eqn 1

Difference of two numbers will be

…eqn 2

Now subtracting equation 2 from 1 we get

Now substituting in eqn 1

We get

⇒ 22x + 5 = 14

⇒ 22x = 14 – 5

A right angle is 90°

A straight line is 180°

Now fraction of right angle to straight line

(i) in Bag I, as the fraction is less than 1 that is numerator is smaller than denominator which is a proper fraction.

(ii) in Bag II, as the fraction is equal to 1that is both numerator and denominator are same resulting as 1.

(iii) in Bag III, as the fraction is greater than 1 that is numerator is greater than denominator which is improper fraction.

(iv) in Bag I, as the fraction is less than 1 that is numerator is smaller than denominator which is a proper fraction.

(v) in Bag I, as the fraction is less than 1 that is numerator is smaller than denominator which is a proper fraction.

(vi) in Bag I, as the fraction is less than 1 that is numerator is smaller than denominator which is a proper fraction.

(vii) in Bag II, as the fraction is equal to 1that is both numerator and denominator are same resulting as 1.

(viii) in Bag I, as the fraction is less than 1 that is numerator is smaller than denominator which is a proper fraction.

(ix) in Bag I, as the fraction is less than 1 that is numerator is smaller than denominator which is a proper fraction.

(x) in Bag I, as the fraction is less than 1 that is numerator is smaller than denominator which is a proper fraction.