Year 4: Halves, quarters and three quarters

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. A hundred square has 100 small squares. Each is one hundredth. Count the shaded squares, then write the decimal.

1. Count the small squares in the whole. There are 10 rows of 10 small squares. Each small square is one hundredth.
   10 × 10 = 100 squares
2. Count the shaded squares. Count the full rows first (10 squares each), then the extra squares.
   2 full rows = 20 squares
   20 + 5 = 25 squares
3. Write the fraction. The top number is the shaded squares.
   25100
4. Write it as a decimal. Tenths are the first column after the point and hundredths are the second column.

   	ones		tenths	hundredths
   0.25	0	.	2	5

   
   25 hundredths = 0 ones, 2 tenths and 5 hundredths, so 0.25

Check. Go back: 0.25 is 25100. ✓

Watch out. Each row of 10 squares is one tenth (0.1). Count in tens to be quick.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. A hundred square has 100 small squares. Each is one hundredth. Count the shaded squares, then write the decimal.

1. Count the small squares in the whole. There are 10 rows of 10 small squares. Each small square is one hundredth.
   10 × 10 = 100 squares
2. Count the shaded squares. Count the full rows first (10 squares each), then the extra squares.
   5 full rows = 50 squares
3. Write the fraction. The top number is the shaded squares.
   50100
4. Write it as a decimal. Tenths are the first column after the point and hundredths are the second column.

   	ones		tenths	hundredths
   0.50	0	.	5	0

   
   50 hundredths = 0 ones and 5 tenths, so 0.5

Check. Go back: 0.5 is 50100. ✓

Watch out. Each row of 10 squares is one tenth (0.1). Count in tens to be quick.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. A hundred square has 100 small squares. Each is one hundredth. Count the shaded squares, then write the decimal.

1. Count the small squares in the whole. There are 10 rows of 10 small squares. Each small square is one hundredth.
   10 × 10 = 100 squares
2. Count the shaded squares. Count the full rows first (10 squares each), then the extra squares.
   7 full rows = 70 squares
   70 + 5 = 75 squares
3. Write the fraction. The top number is the shaded squares.
   75100
4. Write it as a decimal. Tenths are the first column after the point and hundredths are the second column.

   	ones		tenths	hundredths
   0.75	0	.	7	5

   
   75 hundredths = 0 ones, 7 tenths and 5 hundredths, so 0.75

Check. Go back: 0.75 is 75100. ✓

Watch out. Each row of 10 squares is one tenth (0.1). Count in tens to be quick.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 2 equal parts.
   100 ÷ 2 = 50 squares in each part
2. Find how many squares are in 12. 1 part of 50 squares.
   1 part = 50 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   12 = 50100
4. Write it as a decimal. 50 hundredths is 0 ones, 5 tenths and 0 hundredths. A trailing 0 in the hundredths column can be left out: 0.50 = 0.5.
   50100 = 0.5  (0.50)

Check. 50 × 2 = 100, so 2 equal parts of 50 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. A half is 0.5 (5 tenths), which is the same as 0.50 (50 hundredths).

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
   100 ÷ 4 = 25 squares in each part
2. Find how many squares are in 34. 3 parts of 25 squares.
   3 × 25 = 75 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   34 = 75100
4. Write it as a decimal. 75 hundredths is 0 ones, 7 tenths and 5 hundredths.
   75100 = 0.75

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
   100 ÷ 4 = 25 squares in each part
2. Find how many squares are in 14. 1 part of 25 squares.
   1 part = 25 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   14 = 25100
4. Write it as a decimal. 25 hundredths is 0 ones, 2 tenths and 5 hundredths.
   25100 = 0.25

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
   100 ÷ 4 = 25 squares in each part
2. Find how many squares are in 24. 2 parts of 25 squares.
   2 × 25 = 50 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   24 = 50100
4. Write it as a decimal. 50 hundredths is 0 ones, 5 tenths and 0 hundredths. A trailing 0 in the hundredths column can be left out: 0.50 = 0.5.
   50100 = 0.5  (0.50)

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Look at the bottom number: 10 means tenths and 100 means hundredths. Put the digits in a place-value table and write the decimal point after the ones.

1. Look at the bottom number. 10 means tenths. Tenths go in the first column after the decimal point.
   510 is 5 tenths.
2. Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.

   	ones		tenths
   0.5	0	.	5

3. Write the decimal.
   510 = 0.5

Check. Go back to a fraction: 0.5 = 510. ✓

Watch out. The bottom number tells you how many digits come after the point: 10 gives one digit, 100 gives two digits.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Look at the bottom number: 10 means tenths and 100 means hundredths. Put the digits in a place-value table and write the decimal point after the ones.

1. Look at the bottom number. 100 means hundredths. Tenths go in the first column after the point and hundredths in the second column.
   25100 is 25 hundredths.
2. Split the hundredths into tenths and hundredths. 10 hundredths make 1 tenth.
   25 hundredths = 2 tenths and 5 hundredths
3. Write the digits in the place-value table. Put each digit in its column. The decimal point goes after the ones.

   	ones		tenths	hundredths
   0.25	0	.	2	5

4. Write the decimal.
   25100 = 0.25

Check. Go back to a fraction: 0.25 = 25100. ✓

Watch out. The bottom number tells you how many digits come after the point: 10 gives one digit, 100 gives two digits.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
   50 hundredths = 50100
2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
   50 and 100 both divide by 50.
3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
   50 ÷ 50 = 1 and 100 ÷ 50 = 2
   50100 = 12
4. Write the fraction.
   0.5 = 12

Check. Go back to a decimal: 12 of 100 is 50, which is 50 hundredths = 0.50. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
   25 hundredths = 25100
2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
   25 and 100 both divide by 25.
3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
   25 ÷ 25 = 1 and 100 ÷ 25 = 4
   25100 = 14
4. Write the fraction.
   0.25 = 14

Check. Go back to a decimal: 14 of 100 is 25, which is 25 hundredths = 0.25. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
   75 hundredths = 75100
2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
   75 and 100 both divide by 25.
3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
   75 ÷ 25 = 3 and 100 ÷ 25 = 4
   75100 = 34
4. Write the fraction.
   0.75 = 34

Check. Go back to a decimal: 34 of 100 is 75, which is 75 hundredths = 0.75. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Count the digits after the point to find the bottom number (10 or 100). Write those digits as the top number. Put any whole number in front.

1. Count the digits after the decimal point. One digit after the point means tenths. Two digits mean hundredths.
   0.1 has 1 digit after the point, so the bottom number is 10.
2. Read the digits after the point as one number. This is the top number. Ignore any 0 at the front.
   The digits after the point are 1, which is 1.
3. Write the fraction.
   0.1 = 110   (1 tenth)

Check. Go back: 110 written as a decimal is 0.1. ✓

Watch out. The number of digits after the decimal point matches the number of zeros in the bottom number.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Count the digits after the point to find the bottom number (10 or 100). Write those digits as the top number. Put any whole number in front.

1. Count the digits after the decimal point. One digit after the point means tenths. Two digits mean hundredths.
   0.01 has 2 digits after the point, so the bottom number is 100.
2. Read the digits after the point as one number. This is the top number. Ignore any 0 at the front.
   The digits after the point are 01, which is 1.
3. Write the fraction.
   0.01 = 1100   (1 hundredth)

Check. Go back: 1100 written as a decimal is 0.01. ✓

Watch out. For 0.05 the top number is 5, not 05. The bottom number is 100 because there are two digits after the point.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
   50 hundredths = 50100
2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
   50 and 100 both divide by 50.
3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
   50 ÷ 50 = 1 and 100 ÷ 50 = 2
   50100 = 12
4. Write the fraction.
   0.5 = 12

Check. Go back to a decimal: 12 of 100 is 50, which is 50 hundredths = 0.50. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 2 equal parts.
   100 ÷ 2 = 50 squares in each part
2. Find how many squares are in 12. 1 part of 50 squares.
   1 part = 50 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   12 = 50100
4. Write it as a decimal. 50 hundredths is 0 ones, 5 tenths and 0 hundredths. A trailing 0 in the hundredths column can be left out: 0.50 = 0.5.
   50100 = 0.5  (0.50)
5. Add the whole number. The whole number goes in front of the point.
   2 + 0.5 = 2.5

Check. 50 × 2 = 100, so 2 equal parts of 50 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. A half is 0.5 (5 tenths), which is the same as 0.50 (50 hundredths).

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
   100 ÷ 4 = 25 squares in each part
2. Find how many squares are in 34. 3 parts of 25 squares.
   3 × 25 = 75 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   34 = 75100
4. Write it as a decimal. 75 hundredths is 0 ones, 7 tenths and 5 hundredths.
   75100 = 0.75
5. Add the whole number. The whole number goes in front of the point.
   3 + 0.75 = 3.75

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
   100 ÷ 4 = 25 squares in each part
2. Find how many squares are in 14. 1 part of 25 squares.
   1 part = 25 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   14 = 25100
4. Write it as a decimal. 25 hundredths is 0 ones, 2 tenths and 5 hundredths.
   25100 = 0.25
5. Add the whole number. The whole number goes in front of the point.
   1 + 0.25 = 1.25

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 2 equal parts.
   100 ÷ 2 = 50 squares in each part
2. Find how many squares are in 12. 1 part of 50 squares.
   1 part = 50 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   12 = 50100
4. Write it as a decimal. 50 hundredths is 0 ones, 5 tenths and 0 hundredths. A trailing 0 in the hundredths column can be left out: 0.50 = 0.5.
   50100 = 0.5  (0.50)
5. Add the whole number. The whole number goes in front of the point.
   6 + 0.5 = 6.5

Check. 50 × 2 = 100, so 2 equal parts of 50 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. A half is 0.5 (5 tenths), which is the same as 0.50 (50 hundredths).

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
   50 hundredths = 50100
2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
   50 and 100 both divide by 50.
3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
   50 ÷ 50 = 1 and 100 ÷ 50 = 2
   50100 = 12
4. Put the whole number in front.
   2 and 12 = 212
5. Write the fraction.
   2.5 = 212

Check. Go back to a decimal: 12 of 100 is 50, which is 50 hundredths = 0.50. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
   75 hundredths = 75100
2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
   75 and 100 both divide by 25.
3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
   75 ÷ 25 = 3 and 100 ÷ 25 = 4
   75100 = 34
4. Put the whole number in front.
   4 and 34 = 434
5. Write the fraction.
   4.75 = 434

Check. Go back to a decimal: 34 of 100 is 75, which is 75 hundredths = 0.75. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
   25 hundredths = 25100
2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
   25 and 100 both divide by 25.
3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
   25 ÷ 25 = 1 and 100 ÷ 25 = 4
   25100 = 14
4. Put the whole number in front.
   1 and 14 = 114
5. Write the fraction.
   1.25 = 114

Check. Go back to a decimal: 14 of 100 is 25, which is 25 hundredths = 0.25. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
   50 hundredths = 50100
2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
   50 and 100 both divide by 50.
3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
   50 ÷ 50 = 1 and 100 ÷ 50 = 2
   50100 = 12
4. Put the whole number in front.
   7 and 12 = 712
5. Write the fraction.
   7.5 = 712

Check. Go back to a decimal: 12 of 100 is 50, which is 50 hundredths = 0.50. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Write the decimal as hundredths. Then divide the top and the bottom by the same number to make it simpler.

1. Write the part after the point as hundredths. Two digits after the point mean the bottom number is 100. If there is only one digit, write a 0 after it first: 0.5 = 0.50.
   25 hundredths = 25100
2. Find a number that divides into the top and the bottom. The biggest one makes the fraction as simple as possible.
   25 and 100 both divide by 25.
3. Divide the top and the bottom by it. Dividing both by the same number does not change the value.
   25 ÷ 25 = 1 and 100 ÷ 25 = 4
   25100 = 14
4. Put the whole number in front.
   3 and 14 = 314
5. Write the fraction.
   3.25 = 314

Check. Go back to a decimal: 14 of 100 is 25, which is 25 hundredths = 0.25. ✓

Watch out. Do not forget to simplify: 0.75 is 3/4, and 75/100 is the same amount written in a longer way.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Work out what one gap is worth. Then count on from the left end.

1. Find the two numbers at the ends and count the gaps. All the gaps on a number line are the same size.
   The line goes from 0 to 1 in 4 equal gaps.
2. Work out what one gap is worth. Share the distance between the ends equally.
   1 ÷ 4 = 0.25
3. Count the gaps from the left end to the point. Count the gaps, not the tick marks.
   The point is 1 gap after 0.
4. Work out the number. Start at the left end and add the gaps.
   0 + 1 × 0.25 = 0 + 0.25 = 0.25

Check. Count back from 1: 3 gaps back is 1 − 0.75 = 0.25. ✓

Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Work out what one gap is worth. Then count on from the left end.

1. Find the two numbers at the ends and count the gaps. All the gaps on a number line are the same size.
   The line goes from 0 to 1 in 4 equal gaps.
2. Work out what one gap is worth. Share the distance between the ends equally.
   1 ÷ 4 = 0.25
3. Count the gaps from the left end to the point. Count the gaps, not the tick marks.
   The point is 2 gaps after 0.
4. Work out the number. Start at the left end and add the gaps.
   0 + 2 × 0.25 = 0 + 0.50 = 0.50

Check. Count back from 1: 2 gaps back is 1 − 0.50 = 0.50. ✓

Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.

Key words. A decimal is a number with a decimal point. The digits after the point are parts of one whole: the first column is tenths and the second column is hundredths.

Method. Work out what one gap is worth. Then count on from the left end.

1. Find the two numbers at the ends and count the gaps. All the gaps on a number line are the same size.
   The line goes from 0 to 1 in 4 equal gaps.
2. Work out what one gap is worth. Share the distance between the ends equally.
   1 ÷ 4 = 0.25
3. Count the gaps from the left end to the point. Count the gaps, not the tick marks.
   The point is 3 gaps after 0.
4. Work out the number. Start at the left end and add the gaps.
   0 + 3 × 0.25 = 0 + 0.75 = 0.75

Check. Count back from 1: 1 gap back is 1 − 0.25 = 0.75. ✓

Watch out. Do not just read the nearest number on the line. Count the small gaps to find the exact value.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 2 equal parts.
   100 ÷ 2 = 50 squares in each part
2. Find how many squares are in 12. 1 part of 50 squares.
   1 part = 50 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   12 = 50100
4. Write it as a decimal. 50 hundredths is 0 ones, 5 tenths and 0 hundredths. A trailing 0 in the hundredths column can be left out: 0.50 = 0.5.
   50100 = 0.5  (0.50)
   12 m = 0.5 m

Check. 50 × 2 = 100, so 2 equal parts of 50 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. A half is 0.5 (5 tenths), which is the same as 0.50 (50 hundredths).

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
   100 ÷ 4 = 25 squares in each part
2. Find how many squares are in 34. 3 parts of 25 squares.
   3 × 25 = 75 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   34 = 75100
4. Write it as a decimal. 75 hundredths is 0 ones, 7 tenths and 5 hundredths.
   75100 = 0.75
   34 kg = 0.75 kg

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
   100 ÷ 4 = 25 squares in each part
2. Find how many squares are in 14. 1 part of 25 squares.
   1 part = 25 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   14 = 25100
4. Write it as a decimal. 25 hundredths is 0 ones, 2 tenths and 5 hundredths.
   25100 = 0.25
5. Add the whole number. The whole number goes in front of the point.
   1 + 0.25 = 1.25
   114 litres = 1.25 litres

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 2 equal parts.
   100 ÷ 2 = 50 squares in each part
2. Find how many squares are in 12. 1 part of 50 squares.
   1 part = 50 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   12 = 50100
4. Write it as a decimal. 50 hundredths is 0 ones, 5 tenths and 0 hundredths. A trailing 0 in the hundredths column can be left out: 0.50 = 0.5.
   50100 = 0.5  (0.50)
5. Add the whole number. The whole number goes in front of the point.
   2 + 0.5 = 2.5
   212 km = 2.5 km

Check. 50 × 2 = 100, so 2 equal parts of 50 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. A half is 0.5 (5 tenths), which is the same as 0.50 (50 hundredths).

Key words. Pence (p) are small amounts of money. 100 pence make 1 pound.

Method. Change the money into pence. Find a fraction of it: divide by the bottom number, then multiply by the top number. Change back to pounds.

1. Change the pounds into pence. 1 pound is 100 pence, so we can divide the pence exactly.
   £1 = 1 × 100 = 100p
2. Find one part: divide by the bottom number, 2. The bottom number says how many equal parts.
   100p ÷ 2 = 50p
3. Change back to pounds and pence. 100p = £1, so divide by 100. Always show two decimal places.
   50p = £0.50

Check. 50p × 2 = 100p, so 2 parts make the whole amount. ✓

Watch out. Write money with two decimal places: £3.50, not £3.5.

Key words. Pence (p) are small amounts of money. 100 pence make 1 pound.

Method. Change the money into pence. Find a fraction of it: divide by the bottom number, then multiply by the top number. Change back to pounds.

1. Change the pounds into pence. 1 pound is 100 pence, so we can divide the pence exactly.
   £2 = 2 × 100 = 200p
2. Find one part: divide by the bottom number, 4. The bottom number says how many equal parts.
   200p ÷ 4 = 50p
3. Change back to pounds and pence. 100p = £1, so divide by 100. Always show two decimal places.
   50p = £0.50

Check. 50p × 4 = 200p, so 4 parts make the whole amount. ✓

Watch out. Write money with two decimal places: £3.50, not £3.5.

Key words. Pence (p) are small amounts of money. 100 pence make 1 pound.

Method. Change the money into pence. Find a fraction of it: divide by the bottom number, then multiply by the top number. Change back to pounds.

1. Change the pounds into pence. 1 pound is 100 pence, so we can divide the pence exactly.
   £4 = 4 × 100 = 400p
2. Find one part: divide by the bottom number, 4. The bottom number says how many equal parts.
   400p ÷ 4 = 100p
3. Multiply by the top number, 3. The top number says how many parts we take.
   100p × 3 = 300p
4. Change back to pounds and pence. 100p = £1, so divide by 100. Always show two decimal places.
   300p = £3.00

Check. 100p × 4 = 400p, so 4 parts make the whole amount. ✓

Watch out. Write money with two decimal places: £3.50, not £3.5.

Key words. Pence (p) are small amounts of money. 100 pence make 1 pound.

Method. Change the money into pence. Find a fraction of it: divide by the bottom number, then multiply by the top number. Change back to pounds.

1. Change the pounds into pence. 1 pound is 100 pence, so we can divide the pence exactly.
   £5 = 5 × 100 = 500p
2. Find one part: divide by the bottom number, 2. The bottom number says how many equal parts.
   500p ÷ 2 = 250p
3. Change back to pounds and pence. 100p = £1, so divide by 100. Always show two decimal places.
   250p = £2.50

Check. 250p × 2 = 500p, so 2 parts make the whole amount. ✓

Watch out. Write money with two decimal places: £3.50, not £3.5.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
   100 ÷ 4 = 25 squares in each part
2. Find how many squares are in 14. 1 part of 25 squares.
   1 part = 25 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   14 = 25100
4. Write it as a decimal. 25 hundredths is 0 ones, 2 tenths and 5 hundredths.
   25100 = 0.25
   14 litre = 0.25 litre

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
   100 ÷ 4 = 25 squares in each part
2. Find how many squares are in 34. 3 parts of 25 squares.
   3 × 25 = 75 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   34 = 75100
4. Write it as a decimal. 75 hundredths is 0 ones, 7 tenths and 5 hundredths.
   75100 = 0.75
   34 litre = 0.75 litre

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Key words. A hundred square has 100 small squares. Each small square is 1 hundredth. A half is 1 of 2 equal parts and a quarter is 1 of 4 equal parts.

Method. Use a hundred square. Cut it into equal parts to find how many hundredths the fraction is worth. Then write it as a decimal.

1. Think of a hundred square. It has 100 small squares, and each is 1 hundredth. Cut it into 4 equal parts.
   100 ÷ 4 = 25 squares in each part
2. Find how many squares are in 34. 3 parts of 25 squares.
   3 × 25 = 75 squares
3. Write it as hundredths. The bottom number is 100 because the square has 100 squares.
   34 = 75100
4. Write it as a decimal. 75 hundredths is 0 ones, 7 tenths and 5 hundredths.
   75100 = 0.75
5. Add the whole number. The whole number goes in front of the point.
   2 + 0.75 = 2.75
   234 m = 2.75 m

Check. 25 × 4 = 100, so 4 equal parts of 25 squares fill the whole hundred square. Known facts: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75. ✓

Watch out. 1/4 is 0.25, not 0.4 and not 0.14. A quarter is 25 hundredths.

Key words. Lengths, masses and capacities can be written as decimals: 2.5 m is two and a half metres, 1.75 kg is 1 and 3/4 kilograms. Line up the decimal points to add or subtract.

Method. Take the 1 m away from the whole number part. The 0.75 stays the same.

1. Split 2.75 m. 2.75 = 2 + 0.75
   2.75 m = 2 m + 0.75 m
2. Take away 1 m from the whole metres. Only the 2 changes.
   2 − 1 = 1
3. Put the parts together. The 0.75 is not changed.
   1 + 0.75 = 1.75 m

Check. 1.75 + 1 = 2.75. ✓

Watch out. Only subtract from the whole metres.