Respuesta :
To multiply fractions, we multiply the numerators and then multiply the denominators.
Example 1: Fractions
5
6
×
5
7
=
6
5
×
7
5
empty space, start fraction, 5, divided by, 6, end fraction, times, start fraction, 5, divided by, 7, end fraction
=
5
×
5
6
×
7
=
6×7
5×5
equals, start fraction, 5, times, 5, divided by, 6, times, 7, end fraction
=
2
5
4
2
=
42
25
equals, start fraction, 25, divided by, 42, end fraction
Example 2: Mixed numbers
Before multiplying, we need to write the mixed numbers as improper fractions.
2
2
3
×
1
3
5
2
3
2
×1
5
3
2, start fraction, 2, divided by, 3, end fraction, times, 1, start fraction, 3, divided by, 5, end fraction
=
8
3
×
8
5
=
3
8
×
5
8
equals, space, start fraction, 8, divided by, 3, end fraction, times, start fraction, 8, divided by, 5, end fraction
spaceHow do we write a mixed number as a fraction?
Here is how we rewrite
2
2
3
2
3
2
2, start fraction, 2, divided by, 3, end fraction as
8
3
3
8
start fraction, 8, divided by, 3, end fraction :
2
2
3
=
1
+
1
+
2
3
2
3
2
=1+1+
3
2
start color purple, 2, end color purple, start color blue, start fraction, 2, divided by, 3, end fraction, end color blue, equals, start color purple, 1, end color purple, plus, start color purple, 1, end color purple, plus, start color blue, start fraction, 2, divided by, 3, end fraction, end color blue
=
3
3
+
3
3
+
2
3
2
3
2
=
3
3
+
3
3
+
3
2
empty space, equals, start color purple, start fraction, 3, divided by, 3, end fraction, end color purple, plus, start color purple, start fraction, 3, divided by, 3, end fraction, end color purple, plus, start color blue, start fraction, 2, divided by, 3, end fraction, end color blue
=
3
+
3
+
2
3
2
3
2
=
3
3+3+2
empty space, equals, start fraction, start color purple, 3, end color purple, plus, start color purple, 3, end color purple, plus, start color blue, 2, end color blue, divided by, 3, end fraction
=
8
3
2
3
2
=
3
8
empty space, equals, start fraction, 8, divided by, 3, end fraction
Here is how we rewrite
1
3
5
1
5
3
1, start fraction, 3, divided by, 5, end fraction as
8
5
5
8
start fraction, 8, divided by, 5, end fraction :
1
3
5
=
1
+
3
5
1
5
3
=1+
5
3
start color purple, 1, end color purple, start color blue, start fraction, 3, divided by, 5, end fraction, end color blue, equals, start color purple, 1, end color purple, plus, start color blue, start fraction, 3, divided by, 5, end fraction, end color blue
=
5
5
+
3
5
1
5
3
=
5
5
+
5
3
empty space, equals, start color purple, start fraction, 5, divided by, 5, end fraction, end color purple, plus, start color blue, start fraction, 3, divided by, 5, end fraction, end color blue
=
5
+
3
5
1
5
3
=
5
5+3
empty space, equals, start fraction, start color purple, 5, end color purple, plus, start color blue, 3, end color blue, divided by, 5, end fraction
=
8
5
1
5
3
=
5
8
empty space, equals, start fraction, 8, divided by, 5, end fraction
=
8
×
8
3
×
5
=
3×5
8×8
equals, start fraction, 8, times, 8, divided by, 3, times, 5, end fraction
=
6
4
1
5
=
15
64
equals, start fraction, 64, divided by, 15, end fraction
We can also write this as
4
4
1
5
4
15
4
4, start fraction, 4, divided by, 15, end fraction .
Want to learn more about multiplying fractions? Check out this video.
Cross-reducing
Cross-reducing is a way to simplify before we multiply. This can save us from dealing with large numbers in our product.
Example
3
1
0
×
1
6
=
10
3
×
6
1
empty space, start fraction, 3, divided by, 10, end fraction, times, start fraction, 1, divided by, 6, end fraction
=
3
×
1
1
0
×
6
=
10×6
3×1
equals, start fraction, 3, times, 1, divided by, 10, times, 6, end fraction
=
1
×
1
1
0
×
2
=
10×
2
6
3
1
× 1
Hide explanation
Instead of simplifying our answer at the end, we can divide the numerator and denominator by a common factor before multiplying. This makes multiplying easier!
We can divide the
3
33 in the numerator and the
6
66 in the denominator by their common factor of
3
3start color pink, 3, end color pink:
1
×
1
1
0
×
2
10×
2
6÷3
3÷3
1
× 1
=
1
2
0
=
20
1
equals, start fraction, 1, divided by, 20, end fraction
Prefer a visual understanding of fraction multiplication? Check out one of these videos:
Multiplying 2 fractions: fraction model
Multiplying 2 fractions: number line
Practice
PROBLEM 1
5
8
×
7
8
8
5
Example 1: Fractions
5
6
×
5
7
=
6
5
×
7
5
empty space, start fraction, 5, divided by, 6, end fraction, times, start fraction, 5, divided by, 7, end fraction
=
5
×
5
6
×
7
=
6×7
5×5
equals, start fraction, 5, times, 5, divided by, 6, times, 7, end fraction
=
2
5
4
2
=
42
25
equals, start fraction, 25, divided by, 42, end fraction
Example 2: Mixed numbers
Before multiplying, we need to write the mixed numbers as improper fractions.
2
2
3
×
1
3
5
2
3
2
×1
5
3
2, start fraction, 2, divided by, 3, end fraction, times, 1, start fraction, 3, divided by, 5, end fraction
=
8
3
×
8
5
=
3
8
×
5
8
equals, space, start fraction, 8, divided by, 3, end fraction, times, start fraction, 8, divided by, 5, end fraction
spaceHow do we write a mixed number as a fraction?
Here is how we rewrite
2
2
3
2
3
2
2, start fraction, 2, divided by, 3, end fraction as
8
3
3
8
start fraction, 8, divided by, 3, end fraction :
2
2
3
=
1
+
1
+
2
3
2
3
2
=1+1+
3
2
start color purple, 2, end color purple, start color blue, start fraction, 2, divided by, 3, end fraction, end color blue, equals, start color purple, 1, end color purple, plus, start color purple, 1, end color purple, plus, start color blue, start fraction, 2, divided by, 3, end fraction, end color blue
=
3
3
+
3
3
+
2
3
2
3
2
=
3
3
+
3
3
+
3
2
empty space, equals, start color purple, start fraction, 3, divided by, 3, end fraction, end color purple, plus, start color purple, start fraction, 3, divided by, 3, end fraction, end color purple, plus, start color blue, start fraction, 2, divided by, 3, end fraction, end color blue
=
3
+
3
+
2
3
2
3
2
=
3
3+3+2
empty space, equals, start fraction, start color purple, 3, end color purple, plus, start color purple, 3, end color purple, plus, start color blue, 2, end color blue, divided by, 3, end fraction
=
8
3
2
3
2
=
3
8
empty space, equals, start fraction, 8, divided by, 3, end fraction
Here is how we rewrite
1
3
5
1
5
3
1, start fraction, 3, divided by, 5, end fraction as
8
5
5
8
start fraction, 8, divided by, 5, end fraction :
1
3
5
=
1
+
3
5
1
5
3
=1+
5
3
start color purple, 1, end color purple, start color blue, start fraction, 3, divided by, 5, end fraction, end color blue, equals, start color purple, 1, end color purple, plus, start color blue, start fraction, 3, divided by, 5, end fraction, end color blue
=
5
5
+
3
5
1
5
3
=
5
5
+
5
3
empty space, equals, start color purple, start fraction, 5, divided by, 5, end fraction, end color purple, plus, start color blue, start fraction, 3, divided by, 5, end fraction, end color blue
=
5
+
3
5
1
5
3
=
5
5+3
empty space, equals, start fraction, start color purple, 5, end color purple, plus, start color blue, 3, end color blue, divided by, 5, end fraction
=
8
5
1
5
3
=
5
8
empty space, equals, start fraction, 8, divided by, 5, end fraction
=
8
×
8
3
×
5
=
3×5
8×8
equals, start fraction, 8, times, 8, divided by, 3, times, 5, end fraction
=
6
4
1
5
=
15
64
equals, start fraction, 64, divided by, 15, end fraction
We can also write this as
4
4
1
5
4
15
4
4, start fraction, 4, divided by, 15, end fraction .
Want to learn more about multiplying fractions? Check out this video.
Cross-reducing
Cross-reducing is a way to simplify before we multiply. This can save us from dealing with large numbers in our product.
Example
3
1
0
×
1
6
=
10
3
×
6
1
empty space, start fraction, 3, divided by, 10, end fraction, times, start fraction, 1, divided by, 6, end fraction
=
3
×
1
1
0
×
6
=
10×6
3×1
equals, start fraction, 3, times, 1, divided by, 10, times, 6, end fraction
=
1
×
1
1
0
×
2
=
10×
2
6
3
1
× 1
Hide explanation
Instead of simplifying our answer at the end, we can divide the numerator and denominator by a common factor before multiplying. This makes multiplying easier!
We can divide the
3
33 in the numerator and the
6
66 in the denominator by their common factor of
3
3start color pink, 3, end color pink:
1
×
1
1
0
×
2
10×
2
6÷3
3÷3
1
× 1
=
1
2
0
=
20
1
equals, start fraction, 1, divided by, 20, end fraction
Prefer a visual understanding of fraction multiplication? Check out one of these videos:
Multiplying 2 fractions: fraction model
Multiplying 2 fractions: number line
Practice
PROBLEM 1
5
8
×
7
8
8
5
