Download Fraction-3

Fraction - III
Look at the shaded parts in the figures below and fill in the equivalent fractions.
4
1
4
3
12
6
2
8
3
6
9
Use these rulers to find equivalent fractions.

1. ______
2. ______
3. ______
4. 3 
8
5. 5 
8
6.
8

2 4 8
 
4 8 16

2

8 16

6

8 16
16
16
14
16
Two equivalent fractions are defined as
represented by the same point on the
number line. How this works can be
illustrated with, for example, the
fractions
and
. We
divide the segment from 0 to 5 into 2 × 5
= 10 segments of equal length as the picture shows.
1
2

8 16
3
9

5 15
20 4

25 5
10 5

12 6
1
5

4 20
27
9

30 10
2 14

7 49
18 2

45 5
2 16

3 24
15 1

30 2
1
Comparing whole numbers and decimals
Like fractions have the same denominator. Unlike fractions have different denominators.
2/5 and 3/5 are like fractions. 2/5 and 3/7 are unlike fractions.
To compare like fractions, look at their numerators. 2/5 < 3/5
Practice A: Compare these fractions. Circle the smaller fraction.
1. 1
5
6
6
2. 4
9
2
9
3. 3
6
3
9
4. 5
8
5
11
5. 7
12
7
9
6. 2
6
12
3
To compare unlike fractions, express each using their least common denominator. Then, look at their
numerators.
Find an equivalent fraction for each with the same denominator 35, the least common multiple of 5 and
7. 2/5 = 14/35 and 3/7 = 15/35. Since 15/35 > 14/35, hence 3/7 > 2/5.
Practice B: Compare these fractions. Circle the larger fraction.
7. 2
3
4
3
8. 4
6
2
8
9. 2
7
1
9
10. 3
11
1
4
11. 5
8
2
4
12. 3
4
14
16
Another way to compare fractions is to use multiplication (cross-product).
Which is greater, 2/3 or 4/5?
Multiply each denominator by the numerator of the other fraction.
This makes a crisscross pattern, or X. Compare the products.
5 × 2 = 10
2
3
<
3 × 4 = 12
4
5
Practice C:
12 is greater than 10.
4
2
>
5
3
Practice D:
Practice C: 1. <, 2. >, 3. >, 4. <, 5. <, 6. >
Practice D: 1. >, 2. <, 3. <, 4. >, 5. <, 6. >
2
Decimal Fraction - It is a fraction whose denominator we do not write but we understand to be a power of 10.
The number of decimal digits indicates the number of zeroes in the denominator.
Decimal
Fraction
Tenth
0.1
1
10
Percent
Example 1.
=10-1
10%
Hundredth
0.01
1
100
Thousandth
0.001
=10-2
1%
=10-3
1
10000
0.1%
.8 =
8
10
One decimal digit; one 0 in the denominator.
.08 =
8
100
Two decimal digits; two 0's in the denominator.
.008 =
1
1000
Ten Thousandth
0.0001
=10-4
0.01%
8
Three decimal digits; three 0's in the denominator.
1000
And so on. The number of decimal digits indicates the power of 10.
614
100,000
(This example illustrates the inverse process of the above example)
Example 2.
Answer.
Write as a decimal:
614
= .00614
100,000
Five 0's in the denominator indicate five digits after the decimal point.
Alternatively, we can divide a whole number by a power of 10.
614
= 614 ÷ 100,000 = .00614
100,000
If the denominator is not a power of 10, we change the fraction to a decimal by making the
denominator a power of 10 by multiplying it or dividing it.
Example 3. Write
9
as a decimal.
25
Practice 1: Write as a decimal
a
11
20
c
1
8
= .55
= .125
b
8
200
= 0.04
d
7
250
= .028
3
Practice 2
4
2
3
3
1
1
3
2
1
4
1
4
2
2
2
4
1
1
3
4
3
4
3
1
2
Order the numbers from least to greatest.
7.
8.
1
3
2
4
9.
2
1
3
4
10.
2
1
3
4
4
2
1
3
4