2. Introduction
Oto's tablet and cell phone are
running out of battery, but they only
have one cable to charge both
devices. Oto wants to charge the one
with the least battery first. The tablet
indicates that it has 2/5 of battery,
and the mobile phone 3/7. But since
these fractions do not have the
same denominator, he does not
know which of the two has less
2
5
3
7
3. Represents the fraction
To represent two fifths, we will have to divide
the rectangle into 5 parts and keep 2
2
5
10. Explanation
Dividing the rectangle on the left
in the same way the rectangle on
the right was divided, for each of
the colored parts we have 7 parts.
How many colored parts do we
have in the rectangle?
2
5
=
2x7
5x7
?
?
11. Explanation
Indeed! We have 14 colored
parts since 7 +7 is 14 and 2 times
7 as well. And how many parts are
there in the square?
2
5
=
2x7
5x7
14
?
13. Explanation
In this square, instead of having it
divided into 7 parts, we have it
divided into 7 by 5 parts. How
many colored parts do we have?
3
7
=
3x5
7x5
?
?
14. Explanation
That is! We have 15 colored
parts since 3 times 5 is 15. So,
how many parts are there in the
square?
3
7
=
3x5
7x5
15
?
16. Activity 1
What has happened?
The two complete figures have been colored
The figures are divided into the same number of parts
The figures have been transformed into triangles
17. Activity 1
Very good! They are divided into 35 parts each
The two complete figures have been colored
The figures are divided into the same number of parts
The figures have been transformed into triangles
20. Explanation
To compare two fractions with different denominators, we
can reduce the denominators of both fractions to a
common one. We multiply the numerator and denominator
of each fraction by the denominator of the other. In this
way, both fractions have the same denominator. Therefore
now we only look at the new numerators. The fraction that has
the smallest numerator is the smallest fraction
21. Explanation
To compare two fractions with
different denominators, we can
reduce the denominators of both
fractions to a common one. We
multiply the numerator and
denominator of each fraction by
the denominator of the other
2
5
2
5
7
7
x
x
3
7
3
7
5
5
x
x
22. Explanation
In this way, both fractions have the
same denominator. Therefore now
we only look at the new
numerators. The fraction that has
the smallest numerator is the
smallest fraction 15
35
14
35
<
2
5
3
7
23. Example
Which of the two fractions is the largest? Multiply the numerator of the first by the denominator
of the second
8
11
7
9
?
?
=
x
32. Explanation
Comparing two fractions with different denominators is very easy since we only have
to multiply the numerator of each fraction by the denominator of the other and
compare the resulting quantities. This method is called the cross product
method
72 77
<
8
11
7
9
<
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