Lesson Planning of Conversion of Decimal to Fraction and Fraction to Decimal
Students` Learning Outcomes
- Convert a given fraction to decimal if denominator of the fraction is 10 or power of 10.
- Convert fractions (up to three decimal places) into decimals.
Information for teachers
- To convert fraction into decimals we should have denominator 10 or power of 10. If the denominator is not 10 or power of 10 we can make them so by multiplying by suitable number, as; we can make for 2 power of 10 by multiplying it by 5, as;
- Convert decimal into fraction:-
- To convert decimal into fraction write the number as denominator and then simplify it to the lowest term, as;
Material / Resources
Writing board, chalk/marker, duster, pencil, pen, graph paper, ruler, textbook
- Who can explain what a fraction is?
- Who can explain what a decimal is?
- Do you remember the hundredth value we shaded on graph paper and presented as 0.01? (In the last class)
- We also said that it is a hundredth part of whole box. (1 / 100)
- This shows us that we can convert fractions into decimals and decimals into fractions.
- Share the objectives of the day.
- Ask them to find a decimal that is equivalent to 1 / 4?
- What method would you use to find this?
- Ask the students to highlight 1 / 100 on their graph paper.
- Once they are done ask the following: as;
- How many boxes (part) are there in one whole?
- Let them reply (100).
- What this single shaded box is called?
- Let them think and reply 1.01.
- Ask the students : as;
- Can we call it one out of hundred? (Expected answer would be as; Yes, as done before)
- Now ask them to shade 25 small boxes of their graph paper.
- Ask them what it would be as fraction and as decimal.
- Let them think on their own for five minutes.
- Now split them into groups and let the groups finalized how this shaded part would be presented as decimal, and as fraction.
- Allocate 15 minutes.
- Collect responses on board once the group discussion is done.
- Ask every group to give reason for whatever fraction and decimal they wrote. (you might get correct answer)
- Close the discussion on; as twenty five boxes are shaded out of hundred now we may call it 25 / 100 as a fraction.
- As we know each 10 small boxes is one tenth so we have one tenths + one tenths + five hundredths (as one small box is one hundredths)
- Hence, write on the board 0.1, + 0.1 + 0.05 = 0.25.
- Explain same logic for 33 / 100, 75 / 100.
- Conclude that any fraction which has 10 or multiple of 10 in the denominator can be represented as decimals.
- Give them time to discuss in pairs.
- Short cut: once it is clear that enough discussion is done on the fraction conversion. Announce the whole class that there is a short cut method too.
- This method is simply putting a decimal point in the numerator by looking at the denominator and leaving the denominator out.
- Phase one:
- When numerator is 10 then count “0”, suppose their power of strength is ‘n’ replace decimal point from right after ‘n’ of numerator.
- Explain the following with short cut method on board.
- Phase two:
- We know how to convert a fraction into a decimal if the decimator is 10 or power of 10.
- How about 1 / 4? And how can we convert this into fraction?
- Let student think and give responses.
- Write 1 / 4 in a bold format on the board.
- Ask what can I do to make 4 to 100? (let students think)
- One side of the board writes 4 x 10 = 40, 4 x 20 = 80, and 4 x 25 = 100.
- let student multiply both 1 and 4 by 25, as; (1 x 25 / 4 x 25)
- This will give us 25 / 100, and ask is this what we did on the graph paper?
- let them think and reply (yes)
- Ask what we called it as decimal?
- Let them reply (0.25).
- Ask any student to describe what step we took?
- The key is to find such a multiple that will convert denominator to 10 or power of 10.
- Let the students write the following step on their note books.
- Step 1: Find a number you can multiply by the bottom of the fraction to make it 10, or 100, or 1000, or any 1 followed by 0s.
- Step 2: Multiply both top and bottom by that number.
- Step 3: Then write down just the top number, putting the decimal place in the correct.
- Convert to an equivalent fraction whose denominator is a power of 10, such as 10, 100, 1000, 10000, and so on, and then write in decimal form, as;
1. 1 / 4 = (1 x 25) / (4 x 25) = 25 / 100 = 0.25
2. 3 / 20 = (3 x 5) / (20 x 5) = 15 / 100 = 0.15
3. 9 / 8 = (9 x 125) / (8 x 125) = 1125 / 1000 = 1.125
3 / 20 = (3 x 5) / (20 x 5) = 15 / 100 = 0.15
7 / 4 + (7 x 25) / (4 x 25) = 175 / 100 = 1.75
13 / 50 = (13 x 2) / (50 x 2) = 26 / 100 = 0.26
5 / 8 = ( 5 x 125) / (8 x 125) = 625 / 1000 = 0.625
1 / 250 = (1 x 4) / (250 x 4) = 4 / 1000 = 0.004
- Phase Three:
- Clean the board and write 0.25 on the board.
- Call any student to come and write its fraction.
- As there’re is lots of discussion taken places with graph paper student would find it easier to write 25 / 100.
- Ask if somebody would simplify the fraction. (25 ÷25 / 100 ÷ 25 = 1 /4)
- Announce now we will learn converting decimal to fraction.
- There are three steps:
- Take out your note books and ready to follow.
- Do as I say:
- Write a two – digit decimal number. Let it be 0.65.
- Convert 0.65 to a fraction, as; (65 / 100)
- Step 1: Note the number of place positions to the right of the decimal point. In this example, 0.65 is 65 hundredths, which is two places to the right of the decimal point.
- Step 2: Although we have now converted the decimal into a fraction, the fraction is not in its lowest terms. To reduce the new fraction into its lowest or simplest terms, both thee numerator and the denominator must be broken down into primes.
- Pair work:
- Working in pairs do the following:
- Convert 1.73 to a fraction.
- Convert 0.333 to a fraction.
- Allocate 15 minutes time to do this.
- Collect answers on the board.
- Appreciate the correct work.
- Allocate questions for pair work.
- Individual work:
- Write the following questions on board.
- Ask to give answer in simplified fractions.
- Allocate time or fix the time.
- Collect note book for assessment.
- 0.225, 0.21, 0.519, 0.86, 0.1, 0.9, 0.36, 0.75
- Appreciate the correct work.
- Textbook activity:
- Ask the students to practice pages given in their mathematics book.
- Draw a circle on the board.
- Ask what is the fraction for shaded part (1 / 4 or 25 / 100)?
- What is the decimal number for shaded part? (0.25)
- Ask what is the fraction for unshaded part? (3 / 4 or 75 / 100)
- What is the decimal number for unshaded part? (0.75)
- Let the students talk about all the phases done during the last three sessions.
Sum up / Conclusion
- To convert fractions into decimals we should have denominator 10 or power of 10. If the denominator is not 10 or power of 10 we can make them so by multiplying by suitable number.
- To convert decimals into fractions write the number as denominator and nominator then simplify it to the lowest term.
Follow up image