Lesson Presentation Decimal Equivalents

Success Criteria
Aim
I can calculate decimal fraction equivalents.

Fraction Spinners
Click the button to spin the two hexagons to generate a fraction at the place where the edges meet.
Perform the actions relating to the fraction created.
Spin to generate fraction

Fractions and Division
Fractions are another way of writing division.
Because of this, every fraction has a decimal number equivalent which we calculate by doing the division.

Fractions and Division
Some decimal number equivalents we can learn as facts:

However, some decimal number equivalents need to be calculated:
Fractions and Division

Calculating a Decimal Equivalent
When we want to calculate a decimal equivalent of a fraction, we use the written method of short division:
Step 1: Calculate 70 ÷ 8
0
0
7
0
8
8
6
Step 2: Calculate 60 ÷ 8
7
4
Step 3: Calculate 40 ÷ 8
5
We add the decimal point and the zeros to the calculation because we know the answer will be a decimal number less than one.
0
The multiple of 8 that comes immediately before 70 is 64, 64 = 8 × 8, so 70 ÷ 8 = 8 remainder 6
The multiple of 8 that comes immediately before 60 is 56, 56 = 7 × 8, so 60 ÷ 8 = 7 remainder 4
40 is a multiple of 8, 40 = 5 × 8, so 40 ÷ 8 = 5

Calculating a Decimal Equivalent
Have a go at using the written method of short division to find the decimal equivalent of this fraction:
0
0
2
0
7
2
6
8
4
5
This decimal equivalent has a very long string of decimal numbers. When this happens, we want to round the decimal number to the nearest thousandth.
To do this, we need to calculate the value of the next digit.
0
0
5
7
6
Step 1: Calculate 20 ÷ 7
Step 2: Calculate 60 ÷ 7
Step 3: Calculate 40 ÷ 7
The multiple of 7 that comes immediately before 20 is 14, 14 = 2 × 7, so 20 ÷ 7 = 2 remainder 6
The multiple of 7 that comes immediately before 60 is 56, 56 = 8 × 7, so 56 ÷ 7 = 8 remainder 4
The multiple of 7 that comes immediately before 40 is 35, 35 = 5 × 7, so 35 ÷ 7 = 5 remainder 5
Step 3: Calculate 50 ÷ 7
The multiple of 7 that comes immediately before 50 is 49, 49 = 7 × 7, so the next digit after the thousandths is a 7.

Calculating a Decimal Equivalent
When we want to calculate a decimal equivalent of a fraction, we use the written method of short division:
Step 1: Calculate 50 ÷ 6
0
0
5
0
6
8
2
Step 2: Calculate 20 ÷ 6
3
2
Step 3: Calculate 20 ÷ 6
3
This decimal equivalent is recurring. This means that the same digit will repeat for infinity! To show this, we place a dot over the recurring digit.
0
The multiple of 6 that comes immediately before 50 is 48, 48 = 8 × 6, so 50 ÷ 6 = 8 remainder 2
The multiple of 6 that comes immediately before 20 is 18, 18 = 3 × 6, so 20 ÷ 6 = 3 remainder 2
The multiple of 6 that comes immediately before 20 is 18, 18 = 3 × 6, so 20 ÷ 6 = 3 remainder 2

Decimal Equivalents

Tarsia Domino Puzzle
Match the edges of the triangles and squares together by calculating the decimal fraction equivalents.

Success Criteria
Aim
I can calculate decimal fraction equivalents.