CONFIDENTIAL 1

Good Afternoon!Today we will be learning about Converting decimals to fractions

Let’s warm up :

Divide:

1) 57 ÷ 8

2) 35.93 ÷ 4

3) 13 ÷ 18

4) 86.76 ÷ 15

5) 94.42 ÷ 13

1) 7.125

2) 8.9825

3) 0.7222

4) 5.784

5) 7.263

CONFIDENTIAL 2

Let’s first review what we learnt in the previous session before proceeding further.

When we are given a long division to do, sometimes there will be numbers left over.

These are known as Remainders.

We can use the long division process to work out the answer to a number of decimal places.

Division with decimals is easier to understand if the divisor (the dividend is divided by the divisor) is a whole

number.

If the divisor has a decimal in it, we can make it a whole number by moving the decimal point the

appropriate number of places to the right.

CONFIDENTIAL 3

Review

Divide: 5 ÷ 12.Round to the nearest hundredths place.

Note: Since we must round to the hundredths place, we will carry the answer out 1 place beyond the

hundredths place.)

12 5 Place the numbers in the division equation format.

The dividend 5 is less than the divisor 12. Place a decimal point and bring it up to the

quotient.

12 5.00

0.4

- 4820

CONFIDENTIAL 4

12 5.000

0.416

- 4820

- 1280

Add a 0 onto the dividend. Start dividing. The remainder is not zero,

so add another zero to the dividend.

- 728

The remainder is still not zero. The remainder continues to be 8.

This is a repeating decimal. We need our answer rounded to the nearest hundredths place, so we are

ready to round.

0.416 rounded to the nearest hundredths place is 0.42

Review

CONFIDENTIAL 5

Review

4 233.4 Place the numbers in the division equation format.

Begin the division with 4 into 23 (since 4 cannot go into 2). This gives us 5 with a

remainder of 3.

4 233.4

5

- 203

Divide: 233.4 ÷ 4

We will saw another problem:

CONFIDENTIAL 6

Review

Now bring down the next 3, so we must divide 33 by 4. This gives us 8

with a remainder of 1. 4 233.4

58

- 2033

- 3214

Now bring down 4, so we must divide 14 by 4. Here, 4 occurs in the

dividend after the decimal , so we put a decimal in the quotient after 8. This

gives us 3 with a remainder of 2.

4 233.4

58.3

- 2033

- 3214

- 122

CONFIDENTIAL 7

Review

If after dividing you have a remainder, add a zero to the dividend and continue to

divide until there is no remainder or the decimals recur. Now bring down the next 0, so we must divide 20 by 4. This gives us 5

with a remainder of 0.

4 233.40

58.35

- 2033

- 3314

- 1220

- 2000

CONFIDENTIAL 8

Let’s start

Let us revise some terms before we proceed.

FRACTION : A number that names part of a whole or part of a group.

¼ means 1 part of 4 parts, where 4 parts is the whole or group.

DENOMINATOR: It is the number below the bar in a fraction.

NUMERATOR: It is the number above the bar in a fraction.

¼FRACTION

DENOMINATOR

NUMERATOR

MIXED NUMBERS : A number named by a whole number and a fraction.

CONFIDENTIAL 9

So we see that,A fraction is based on the number into which

the whole is divided (the denominator). The numerator (the top) is the PART,

the denominator (the bottom) is the WHOLE.

Count the decimal placesof the decimal starting from the decimal

point.

Step 1:

To convert a Decimal to a Fraction follow these steps:

CONFIDENTIAL 10

If there is one decimal place, place the number over 10.

If there are two decimal places,place the number over 100.

If there are three decimal places, place the number over 1000.

Simplify (or reduce) the fraction.

Step 2:

Step 3:

CONFIDENTIAL 11

Show the Decimal 0.45 with a model and express its equivalent

fraction.

Pink part: 45 NUMERATOR

Equal parts in all: 100

DENOMINATOR

So, 45 of the area is pink. 100

Here we see that,

Converting a Decimal to a Fraction with the help of a model

Decimal 0.45 is represented

by the pink portion shown

in the grid.

CONFIDENTIAL 12

Express 0.75 as a fraction

Step 1: Write down the decimal. 0.75

1

Step 2: Multiply both top and bottom by 100 (because there were 2 digits after the decimal place).

0.75 = 75 1 100

x 100

x 100

CONFIDENTIAL 13

Step 3: Reduce the fraction.

75 = 3 100 4

÷ 25

÷ 25Answer = 3 4

Note: 75 is called a decimal fraction and 3 is called a common fraction ! 100 4

Convert 0.235 to a simple fraction. 47 200

CONFIDENTIAL 14

Repeating decimal

Express 5.233233…… as a fraction

Step 1: Let x = 5.233233. Call this equation #1.

Step 2: Count how many numbers there are in the repeating part. In this example, the repeating part is 233. So there are 3 numbers in the repeating part.

Step 3: Multiply both sides by 1000, because 1000 has 3 zeroes. We get 1000x = 5233.233233... Call this equation #2.

CONFIDENTIAL 15

Step 4: Subtract equation #1 from equation #2.

Solving for x, we get x = 5228. 999

x = 5.233233

1000x = 5233.233233

999x = 5228

Convert 7.865865……… to a simple fraction. 7858 999

CONFIDENTIAL 16

BREAK

CONFIDENTIAL 17

GAME

Click on the link below for some exciting puzzle

http://www.thekidzpage.com/onlinejigsawpuzzles/kids-jigsaw-puzzles/12-piece-jigsaw/06-01-07-squirrel.html

CONFIDENTIAL 18

Assignments

Express the following decimals as a fraction:

1) 0.4 2) 1.55

3) 2.274 4) 0.4573

1) 2 5

2) 31 20

3) 1137500

4) 4573 10000

CONFIDENTIAL 19

Express the following repeating decimals as a fraction:

5) 245 33

5) 7.4242 6) 5.456456

7) 3.765765 8) 9.2323

6) 5451 999

7) 418 111 8) 914

99

CONFIDENTIAL 20

9) Show the Decimal 0.07 with a model and express its equivalent fraction.

Pink part: 7 NUMERATOR

Equal parts in all: 100

DENOMINATOR

9) So, 7 of the area is pink. 100

Here we see that,

Decimal 0.07 is represented

by the pink portion shown

in the grid.

CONFIDENTIAL 21

10) Express 1.392392…… as a fraction.

10) 1392 999

CONFIDENTIAL 22

Very Good!Let's Review

So we saw that,A fraction is based on the number into which

the whole is divided (the denominator). The numerator (the top) is the PART,

the denominator (the bottom) is the WHOLE.

Count the decimal places, of the decimal starting from the decimal point.

Step 1:

To convert a Decimal to a Fraction follow these steps:

If there is one decimal place, place the number over 10. If there are two decimal places, place the number over

100. If there are three decimal places, place the number over 1000.

Simplify (or reduce) the fraction.

Step 2:

Step 3:

CONFIDENTIAL 23

Show the Decimal 0.45 with a model and express its equivalent

fraction.

Pink part: 45 NUMERATOR

Equal parts in all: 100

DENOMINATOR

So, 45 of the area is pink. 100

Here we see that,

Converting a Decimal to a Fraction with the help of a model

Decimal 0.45 is represented

by the pink portion shown

in the grid.

Review

CONFIDENTIAL 24

Review

Express 0.75 as a fraction

Step 1: Write down the decimal. 0.75

1

Step 2: Multiply both top and bottom by 100 (because there were 2 digits after the decimal place).

0.75 = 75 1 100

x 100

x 100

CONFIDENTIAL 25

Review

Step 3: Reduce the fraction.

75 = 3 100 4

÷ 25

÷ 25Answer = 3 4

Note: 75 is called a decimal fraction and 3 is called a common fraction ! 100 4

CONFIDENTIAL 26

Review

Repeating decimal

Express 5.233233…… as a fractionStep 1: Let x = 5.233233. Call this equation

#1.

Step 2: Count how many numbers there are in the repeating part. In this example, the repeating part is 233. So there are 3 numbers in the repeating part.

Step 3: Multiply both sides by 1000, because 1000 has 3 zeroes. We get 1000x = 5233.233233... Call this equation

#2.

Solving for x, we get x = 5228. 999

x = 5.233233

1000x = 5233.233233

999x = 5228

Step 4: Subtract equation #1 from equation #2.

CONFIDENTIAL 27

You have done a nice job.See you in the next session.