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Fractions & Decimals

Objectives

To understand that fractions and decimals are different ways of showing part of a whole.

To use the visual aids to reinforce this concept.

To make a connection between fractions and decimals.

Resources

Abacus 4 Textbook 1 | Squared paper | Fraction and Equivalent Decimals (MyMaths)

Today's Lesson

Main Activity

Talk about English money with your student. If there are 100 pence to one English pound, ask your child what half a pound is in terms of pence (Answer: 50p). We can represent this as £0.50. When we are talking about English money, there are always two digits after the decimal point. (We always write £0.50 and never £0.5) However, when we are using decimals more generally, we would not need the ‘0’ after the ‘5’. We would say that ½ is equivalent to 0.5

Think about how you would find ¼ or a quarter of £1.00. (Answer: 25p). This is written as £0.25; ¼ is equivalent to the decimal 0.25

Run through activities 5 and 6 on Fraction and Equivalent Decimals (MyMaths)

Turn to page 57 in Abacus 4 Textbook 1.

Look at the number line and draw attention to the fractions on top and the decimals underneath at the exact same points. Explain to your student that 1/10 is the same as saying 0.1 – you could remind them of the place value columns that we have looked at before, wh

ere to the right of the decimal point we have the ‘tenths’ column. For example:

Ask your student to fill in the missing numbers on the line, using the numbers before and after to help.

Look at the second section of divisions by 10. Remind your child that when you divide something, you break it up into even sized pieces, or groups. When you divide by 10, you are finding 1/10 of that number. To do this, we use our place value columns and move all the digits one place to the right. (We can remember how many places to move as there is one ‘0’ in ‘10’; this becomes relevant later on when we divide by 100 or 1000.)

For example 34 ÷ 10 =

Remember our columns, and imagine or write 34 in the correct place:

Now we move both digits of our number one place to the right, not forgetting to include the digital point, which will now be necessary:

So we can see that 34 ÷ 10 = 3.4

Conversely, when we multiply a number by 10, we move each digit one place to the left. For example:

4.2 x 10 =

4.2 x 10 = 42

If you forget which way the digits should move, check your answer to see if it makes sense. When we multiply one number by a whole number, our answer will be greater that the number we started with. When we divide a number by a whole number, our answer will be less than our original number. For example, if we made a mistake and moved our number 4.2 in the answer above to the right instead of the left, we would have the answer 0.42 which is smaller than the number we started with, so does not make sense.

Citations

[1] app.mymaths.co.uk