# 2.3 Recognise and represent decimal fractions  (Page 2/2)

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With a calculator:

2. Make decimal fractions from the following:

2.1 $\frac{3}{4}$ = 3  4 = 0, ____

 2.2 $\frac{2}{5}$ = 25 = 2.3 $\frac{3}{5}$ = 2.4 $\frac{4}{5}$ = 2.5 $\frac{5}{5}$ = 2.6 $\frac{1}{4}$ =

We can convert any ordinary fraction to decimals in that way.

3. Make one-third into a decimal: $\frac{1}{3}$ = 1  3 =_____

Can you think of a reason why the answer is the way it is?

Without a calculator:

4. Write down equivalent fractions for each of the following and then write them as decimal fractions:

 Fraction Fraction as tenths Decimal fraction half one third Can’t
 Fraction Fraction as tenths Decimal fraction two-thirds Can’t one-quarter three-quarters one-fifth two-fifths three-fifths four-fifths one-sixth Can’t one-eighth

(Some of the above have more than one decimal place but it is good to know about them.)

5. What about the thirds and sixths and others that cannot be made into tenths? Use division.

• one-third = 1  3 =
• two-thirds = 2  3 =

Use your own method for the division or use a calculator. $\frac{1}{3}$ = 1  3

Or one way: ? x 3 = 1

0 x 3 = 0,0

0,3 x3 = 0,9

0,03 x 3 = 0,09

0,99 (which is nearly 1)

so: (0 x 3) + ( 0,3 x 3) + ( 0,03 x 3)

0 + 0,3 + 0,03

= 0,333

(and the calculator will go on dividing: 0,333)

We say: 0,3 recurring or 0,3֯(The dot means recurring.)

1. Solve without a calculator:

1.1 17 × 26

1.2 153  9

2. Share 11 sausage rolls equally amongst 10 boys. How much sausage roll will each boy receive?

3. Share 12 sausage rolls equally amongst 10 boys. How much sausage roll will each boy receive?

4. Mike drinks $1\frac{1}{2}$ mugs of milk for breakfast. His sister, Sharon, drinks $\frac{3}{4}$ of a mug of milk. How much milk have they drunk altogether?

5. Write the following in expanded notation:

 5.1 64,8 = 5.2 341,2 =

6. Write as decimals:

• Three and four-fifths = ………………………
• One and three-tenths = ………………….
• Five and one-quarter = …………………
• $4\frac{1}{2}$ = ………………….

7. From<;>; = write down the correct sign to make the following true:

• 2,4 ____ 4,2
• 1,7 _____2,1

8. Write down the number that is:

 Answer one tenth more than 45,9 one tenth less than 10

## Assessement

 Learning outcomes(LOs) LO 1 Numbers, Operations and RelationshipsThe learner will be able to recognise, describe and represent numbers and their relationships, and to count, estimate, calculate and check with competence and confidence in solving problems. Assessment standards(ASs) We know this when the learner: 1.1 counts forwards and backwards in a variety of intervals; 1.3 recognises and represents the following numbers in order to describe and compare them: common fractions with different denominators, common fractions in diagrammatic form, decimal fractions and multiples of single-digit numbers; 1.3.2 common fractions with different denominators, including halves, thirds, quarters, fifths, sixths, sevenths and eighths; 1.3.3 common fractions in diagrammatic form; 1.3.4 decimal fractions of the form 0,5; 1,5 and 2,5; etc., in the context of measurement; 1.3.6 multiples of single-digit numbers to at least 100; 1.5 recognises and uses equivalent forms of the numbers including common fractions and decimal fractions; 1.5.1 common fractions with denominators that are multiples of each other; 1.5.2 decimal fractions of the form 0,5; 1,5 and 2,5, etc., in the context of measurement; 1.7 solves problems that involve comparing two quantities of different kinds (rate); 1.7.1 comparing two or more quantities of the same kind (ratio); 1.8 estimates and calculates by selecting and using operations appropriate to solving problems that involve addition of common fractions, multiplication of at least whole 2-digit by 2-digit numbers, division of at least whole 3-digit by 1-digit numbers and equal sharing with remainders; 1.8.3 addition of common fractions in context; 1.8.6 equal sharing with remainders; 1.9 performs mental calculations involving: 1.9.2 multiplication of whole numbers to at least 10 x 10; 1.12 recognises, describes and uses:, and 1.12.1 the reciprocal relationship between multiplication and division (e.g. if 5 x 3 = 15 then 15 ÷ 3 = 5 and 15 ÷ 5 = 3; 1.12.2 the equivalence of division and fractions (e.g. 1 ÷ 8 = ⅛); 1.12.3 the commutative, associative and distributive properties with whole numbers. Learning outcomes(LOs) LO 2 Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills. Assessment standards(ASs) We know this when the learner: 2.1 investigates and extends numeric and geometric patterns looking for a relationship or rules; 2.1.1 represented in physical or diagrammatic form; 2.1.2 not limited to sequences involving constant difference or ratio; 2.1.3 found in natural and cultural contexts; 2.1.4 of the learner’s own creation; 2.2 describes observed relationships or rules in own words; 2.3 determines output values for given input values using verbal descriptions and flow diagrams; 2.3.1 verbal descriptions; 2.3.2 flow diagrams.

## Memorandum

ACTIVITY 1: recognising and representing decimal fractions

1.1 Missing numbers: 10; 1; one-tenth

1.2 Calculator answers: 10; 1; 0,1

0,1 means one-tenth

2.1

 x 1 000 x 100 x 10 x 1 x 0,1 (a) 1 4 5 6 3 (b) 4 6 0 1 9 (c) 8 5 (d) 3 1 7 (e) 4 5 6 2

2.2 (b) 4 x 1 000 + 6 x 100 + 0 x 10 + 1 x 1 + 9 x 0,1

(c) 0 x 1 000 + 0 x 100 + 0 x 10 + 8 x 1 + 5 x 0,1 or just: 8 x 1 + 5 x 0,1

(d) 0 x 1 000 + 0 x 100 + 3 x 10 + 1 x 1 + 7 x 0,1 or just: 3 x 10 + 1 x 1 + 7 x 0,1

(e) 0 x 1 000 + 4 x 100 + 5 x 10 + 6 x 1 + 2 x 0,1 or just: 4 x 100 + 5 x 10 + 6 x 1 + 2 x 0,1

ACTIVITY 2: comparing decimal fractions

1.1<

1.2 

1.3<

1.4<

1.5 

1.6<

2. Encircled number: 49,1

3.1 10,9

3.2 5,4

3.3 5,9

3.4 8,2

3.5 7

3.6 99,1

3.7 5,9

3.8 9,9

ACTIVITY 3: converting from fractions to decimal fractions and vice versa

1. Discussion

2. With a calculator

• 0,75
• 2.2 0,4
• 2.3 0,6
• 2.4 0,8

2.5 0,8

2.6 0,25

3. 0,33333

4.

 Fraction Fraction as tenths Decimal fraction half Five tenths 0,5 One-third Can’t 0,3333 Two-thirds Can’t 0,6666 One-quarter Can’t; 0,25 Three-quarters Can’t; 0,75 One-fifth Two-tenths 0,2 Two-fifths Four-tenths 0,4 Three-fifths Six-tenths 0,6 Four-fifths Eight-tenths 0,8 One-sixth Can’t 0,1666 One-eighth Can’t; 0,125
• 0,333
• 0,666

1.1 442

1.2 17

2. one and one-tenth or 1,1 sausage rolls

3. one and two-tenths or 1 and a fifth sausage rolls (or 1,2)

4. two and a quarter mugs

• 6 x 10 + 4 x 1 + 8 x 0,1
• 3 x 100 + 4 x 10 + 1 x 1 + 2 x 0,1
• 3,8
• 1,3
• 5,25
• 4,5
• <
• <
• 46
• 9,9

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