Maharashtra Board Class 6 Maths part 1 Chapter 5 Decimal Fractions PDF Download

Decimal Fractions: Addition and Subtraction

Nandu went to a shop to buy a pen, notebook, eraser and paintbox. The shopkeeper told him the prices. A pen costs four and a half rupees, an eraser one and a half, a notebook six and a half and a paintbox twenty-five rupees and fifty paise. Nandu bought one of each article. Prepare his bill.

If Nandu gave a 100 rupee note, how much money does he get back?

100 - =

Nandu will get ................ rupees back.

While solving problems with the units rupees-paise, metres-centimetres, we have used fractions with up to two decimal places. When solving problems with the units kilogram-gram, kilometre-metre, litre-millilitre, we have to use fractions with up to three decimal places.

Example

Reshma bought some vegetables. They included three-quarter kilo potatoes, one kilo onions, half a kilo cabbage and a quarter kilo tomatoes. What is the total weight of the vegetables in her bag?

We know: 1 kg = 1000 g, half kg = 500 g, three-quarter kg = 750 g, quarter kg = 250 g

Teacher's Note

When you go shopping with your mother at the market, you see many different weights and prices. We use decimal numbers every day when we buy things.

Exam Trick

Remember: Decimal point separates rupees from paise. Just like 4.50 rupees means 4 rupees and 50 paise. Count carefully from the right side.

Points to Remember

Decimal fractions have a dot called a decimal point.
The decimal point separates whole numbers from parts of numbers.
Two decimal places are used for money (rupees-paise).
Three decimal places are used for weight (kilogram-gram).
Always line up decimal points when adding or subtracting.

Now to find out the total weight of the vegetables, let us add using both units, kilograms and grams, in turn.

Note the similarity between the addition of integers and the addition of decimal fractions.

Total weight of vegetables is 2500 g, that is \(\frac{2500}{1000}\) kg, that is 2.500 kg

We know that, 2.500 = 2.50 = 2.5

The weight of vegetables in Reshma's bag is 2.5 kg.

Teacher's Note

Take a pen and notebook when you go shopping with your parents. Write down the weight of each vegetable. This helps you learn maths in real life.

Exam Trick

Remember: Zeros after the last digit after a decimal point do not change the value. So 2.500 = 2.50 = 2.5. All three are the same.

Points to Remember

When adding decimals, line up the decimal points.
Add from right to left, just like whole numbers.
Trailing zeros do not change the value.
Grams, kilograms, metres and centimetres use decimals.
Always check your answer by estimating first.

Practice Set 14

1. In the table below, write the place value of each of the digits in the number 378.025

2. Solve

(1) 905.5 + 27.197

(2) 39 + 700.65

(3) 40 + 27.7 + 2.451

3. Subtract

(1) 85.96 - 2.345

(2) 632.24 - 97.45

(3) 200.005 - 17.186

4. Avinash travelled 42 km 365 m by bus, 12 km 460 m by car and walked 640 m. How many kilometres did he travel altogether? (Write your answer in decimal fractions)

5. Ayesha bought 1.80 m of cloth for her salwaar and 2.25 m for her kurta. If the cloth costs 120 rupees per metre, how much must she pay the shopkeeper?

6. Sujata bought a watermelon weighing 4.25 kg and gave 1 kg 750g to the children in her neighbourhood. How much of it does she have left?

7. Anita was driving at a speed of 85.6 km per hour. The road had a speed limit of 55 km per hour. By how much should she reduce her speed to be within the speed limit?

Teacher's Note

Subtraction with decimals is like subtraction with whole numbers. Just remember to line up the decimal points carefully, just like you line up the ones and tens places.

Exam Trick

Remember: Borrow from the next place value if needed, just like in whole number subtraction. The decimal point stays in the same column.

Points to Remember

Line up decimal points before subtracting.
Subtract from right to left like whole numbers.
You can borrow from the next place value.
Regroup if the digit on top is smaller.
Write the decimal point in the answer below the other decimal points.

Showing Decimal Fractions on the Number Line

Example: Observe how the numbers 0.7 and 6.5 are marked on the number line.

In the same way, show the following numbers on the number line

(1) 3.5

(2) 0.8

(3) 1.9

(4) 4.2

(5) 2.7

Teacher's Note

A number line helps you see where decimal numbers are placed. It makes understanding decimals easier because you can see them on a line like points on a ruler.

Exam Trick

Remember: On a number line, 0.7 is between 0 and 1, closer to 1. Count the small lines to place decimal numbers correctly.

Points to Remember

Decimal numbers sit between whole numbers on a number line.
0.5 is always in the middle between two whole numbers.
0.1, 0.2, 0.3 are one-tenth, two-tenths, three-tenths.
The number line helps you compare decimals.
Larger decimals are further to the right on the number line.

Converting a Common Fraction into a Decimal Fraction

You know that if the denominator of a common fraction is 10 or 100, it can be written as a decimal fraction.

Can you recall how to convert the fractions \(\frac{1}{2}\), \(\frac{1}{4}\), \(\frac{2}{5}\) into decimal fractions?

A fraction whose denominator is 1000 can also be written as a decimal fraction. Let us see how.

If the denominator of a common fraction is 10, 100, 1000, then:

(1) If there are more digits in the numerator than zeros in the denominator, then count as many digits from the right as the number of zeros, and place the decimal point before those digits.

Examples

\(\frac{723}{10} = 72.3\)

\(\frac{51250}{100} = 512.50\)

\(\frac{5138}{1000} = 5.138\)

(2) If there are as many digits in the numerator as zeros in the denominator, place the decimal point before the number in the numerator and a zero in the integers' place.

Examples

\(\frac{7}{10} = 0.7\)

\(\frac{54}{100} = 0.54\)

\(\frac{725}{1000} = 0.725\)

(3) If there are fewer digits in the numerator than the zeros in the denominator, place zeros before the digits in the numerator to make the total number of digits equal to the number of zeros in the denominator. Place a decimal point before them and a zero in the integers' place.

Examples

\(\frac{8}{100} = \frac{08}{100} = 0.08\)

\(\frac{8}{1000} = \frac{008}{1000} = 0.008\)

Teacher's Note

Converting fractions to decimals is like changing rupees to paise or metres to centimetres. Both are just different ways to write the same amount.

Exam Trick

Remember: Count the zeros in the denominator. That tells you how many decimal places you need. For example, 1000 has three zeros, so you need three decimal places.

Points to Remember

Count the zeros in the denominator first.
Move the decimal point to the left by that many places.
Add zeros in front if needed to make enough decimal places.
Always put a zero before the decimal point if there is no whole number.
The denominator tells you how many decimal places to use.

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