3
Fractions and Decimals
Quick Review
1.Fraction
a
Fractions（分數）are numbers written in the form .
b
(a) Proper fraction（真分數）
2 6
E.g., ,
5 11
(b) Improper fraction（假分數）
4 23
E.g., ,
3 7
(c) Mixed fraction（帶分數）
1 1
E.g., 1 , 2
3 7
Determine whether each of the following
is true (1 – 5).
6
72
.
is the simplest form of
7
84
65
5
2.
=6 7
7
7
8
3. is greater than .
8
9
2 5 7
4. + = 3 6 9
5.3.15 - 2.01 + 11.2 = 12.34
1.
T/F
T/F
T/F
T/F
T/F
Ans: 1.T 2.F 3.F 4.F
5.T
2. Simplification of Fraction
E.g., Concept Check
48 48 ÷ 24 2
=
= (2 and 3 have no common factors other than 1)
72 72 ÷ 24 3
3.Decimal
integral part
decimal point
tenths
3.125
hundredths
thousandths
4. Conversion between Fractions and Decimals
(a) Decimals（小數）to fractions(b) Fractions to decimals
1
25 1
E.g., E.g., 0.25 =
=
= 0.05
20
100 4
55
11
13
3.55 = 3
=3
= 0.52
100
20
25
Fractions and Decimals
11
5. Arithmetic Operations of Fraction
Addition(b) Subtraction
(a) 2 3
1
5
E.g., +
E.g., 2 - 1
5 4
4
6
8 15
9 11 (Change the mixed fractions
(L.C.M. of 5 and 4 is 20.)
=
+
= 20 20
4 6 to improper fractions.)
23
27 22
(L.C.M. of 4 and 6 is 12.)
=
=
20
12 12
5
3 (Change the improper fraction
=1
=
12
20 to mixed fraction.)
Multiplication(d) Division
(c) 2
2
1 5
E.g., 2 × 1
E.g., ÷
5
3
4 6
4 12 5 (Change the mixed fractions
1 6 3 (Interchange the numerator
×
=
= ×
5 3 to improper fractions.)
and denominator.)
24 5
3
=4
=
10
6. Arithmetic Operations of Decimal
Addition(b) Subtraction
(a) E.g., 0.23 + 1.592
E.g., 4.27 - 1.95
0.23
= 1.822
+ 1.592
1.822
= 2.32
Multiplication(d) Division
(c) 1.3
E.g., 1.3 × 2.4
E.g., 12 ÷ 2.4
= 3.12
2.4
2 6 0 52
3.1 2
Mistake Hunt
1. Calculate 2.34 - 1.6.
Solution:
2.3 4
−
1.6
2.1 8
\2.34 - 1.6 = 2.18
12
➥
➥
Level-up Practice Q. 12
Train Up Mathematics: A Foundation Course (P6 to S1)
= 120 ÷ 24
=5
4.27
− 1.95
2.32
5
24 120
120
!!
We must match the place value of each digit
before adding or subtracting the numbers.
Hence the correct solution is as follows:
2.34
− 1.6
0.74
\2.34 - 1.6 = 0.74
2. Calculate 1
Solution:
1
➥
!!
1
1
÷2 .
6
3
We have to reverse both the numerator and the
denominator of the fraction. Hence the correct
solution is as follows:
1
1 7 7
÷2 = ÷
6
3 6 3
49
×3
=
6
49
=
2
➥
1
1
1 7 7
÷2 = ÷
6
3 6 3
7 3
= ×
6 7
1
=
2
Level-up Practice Q. 11
What's Wrong?
Study each of the following and determine whether the solution of each question is correct. If it is not,
correct the solution.
2. Calculate
1. Calculate 4.22 - 1.4.
Solution:
Solution:
4.22
− 1.4
4.08
\4.22 - 1.4 = 4.08
8÷
5
8
= ×
5
=6
8 4
÷ .
5 15
4
15
15
4
Level-up Practice
Translation Exercise
In each of the following, fill in the alphabet that represents the correct Chinese term.
A. 小數 B.
分母 C.
分數 D.
假分數
E. 帶分數 F. 分子 G.
H.
真分數
最簡形式
(a) Convert the following improper fractions to mixed fractions.
化為
把下列
。
(b) Reduce the following fractions to the simplest form.
把下列
化簡為
。
(c) Convert the following decimals to fractions.
把下列
化為
(d) In the fraction
在分數
。
3
, the denominator is 5 and the numerator is 3.
5
3
中，
5
是 5，
是 3。
Fractions and Decimals
13
Multiple-choice Questions
1. Which of the following is an improper fraction?
19
16
4
2
2 D.
A.B. C.
14
36
9
3
54
to a mixed fraction.
4
27
4
104
1
A. B. C.
13 D.
2
54
8
2
2. Convert
3. Which of the following fractions are arranged in ascending order?
1 1 1
5 7 8
A., , B., , 3 4 5
6 8 9
C.
11 7 15
5 5 5
, , D., ,
12 8 16
7 9 8
5
=
16
A.
0.3125B.
0.3C.
0.35D.
0.625
4.
1
=
4
A.
1B.
4C.
8D.
16
5. 4 ÷
Basic Questions
6. What fraction of the whole figure is shaded?
7. Reduce each of the following fractions to its simplest form.
(a) 54
=
72
(b) 45
=
250
(c) 255
=
195
8. Convert the following decimals to the simplest fractions.
14
0.35(b)
0.375(c)2.45
(a)
=
=
35
= =
100
Train Up Mathematics: A Foundation Course (P6 to S1)
9. Convert the following fractions to decimals.
27
9
3
20 9
(b) 8 27
(c)3 8
20
16
= = =
(a) )
)
)
10. Calculate the following expressions.
5
7 5
5
3
7
1
(b) 2 - 1 (c) + - 1
+ 8 6
12 18
16
24
12
= = =
(a) 11. Calculate the following expressions.
27
7
8
2 9
2
(b) 1 ÷ (c) × 2 ÷ 7
× 2 4
18
18
7 14
3
= = =
(a) 12. Calculate the following expressions.
(a)0.17 + 0.48(b) 1.2 × 2.3(c) 0.96 ÷ 0.8
= = =
Enhanced Questions
13. Calculate the following expressions.
(a) 1
1
1
2
3
÷ 2 × 2 × 1 6
3
5
4
(b) 1
5
1
1
3
-3 ×1 ÷3
8
3
2
4
Fractions and Decimals
15
14.(a) Calculate 2
1 1
1
2
- 1 .(b)Calculate - .
3 4
3
3
(c) Hence, calculate
2
1
2
-1
3
3
.
1 1
3 4
15. Calculate the following expressions.
(a)2.17 + 0.4 × 2.5(b) 2.72 × 5 + (6.6 - 3.8) ÷ 1.4
1
of it. Betty
3
2
drinks 0.25 L. Then Cindy drinks of the remaining soft drink. How much soft
5
drink does Cindy drink?
16. There is a bottle of soft drink with a volume of 1.5 L. Amy drinks
Self-assessment
1. Fill in the correct number:
16
18
=
3
2
Train Up Mathematics: A Foundation Course (P6 to S1)
2. What fraction of the whole figure
is shaded?
3. Calculate the following expressions.
(a)2.42 × 5(b)14.74 ÷ (4.3 - 2.96)
Knowledge Extension Corner
1
to a decimal, we get 0.3333... We call the decimal a recurring decimal and
3
write it as 0.3 . The dot on the top of 3 means 3 is repeated. Sometimes, there is more than one
When we convert
repeating digit, for example
repeated are 037.
1
  . It means the digits
= 0.037 037 037... and we write it as 0.037
27
Work it out
Convert the following fractions to recurring decimals (1 – 2).
1.
2
1
2.
11
9
Internet Adventure
Converting a Recurring Decimal to a Fraction
Can you express 0.44444... to a fraction? Let’s see the following website for
more details.
http://www.quickermaths.com/how-to-convert-recurring-decimal-tofraction/
Fractions and Decimals
17