[25-(-2){7-(6-3)}]\[3+{5-(-3)x(-2)
Answers
Multiplying fractions
To multiply fractions, we multiply the numerators and then multiply the denominators.
Example 1: Fractions
\phantom{=}\dfrac{5}{6} \times \dfrac{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
= \dfrac{5 \times 5}{6 \times 7}=
6×7
5×5
equals, start fraction, 5, times, 5, divided by, 6, times, 7, end fraction
= \dfrac{25}{42}=
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\dfrac{2}{3} \times 1\dfrac352
3
2
×1
5
3
2, start fraction, 2, divided by, 3, end fraction, times, 1, start fraction, 3, divided by, 5, end fraction
= ~\dfrac{8}3 \times \dfrac{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 \qquad[How do we write a mixed number as a fraction?]
=\dfrac{8\times 8}{3 \times5}=
3×5
8×8
equals, start fraction, 8, times, 8, divided by, 3, times, 5, end fraction
=\dfrac{64}{15}=
15
64
equals, start fraction, 64, divided by, 15, end fraction
We can also write this as 4\dfrac4{15}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
\phantom{=} \dfrac{3}{10} \times \dfrac16=
10
3
×
6
1
empty space, start fraction, 3, divided by, 10, end fraction, times, start fraction, 1, divided by, 6, end fraction
=\dfrac{3\times1}{10\times6}=
10×6
3×1
equals, start fraction, 3, times, 1, divided by, 10, times, 6, end fraction
=\dfrac{\stackrel{1}{\cancel{3}} \times ~1 }{ 10\times \underset{2}{\cancel{6}}} \qquad=
10×
2
6
3
1
× 1
equals, start fraction, start cancel, 3, end cancel, start superscript, 1, end superscript, times, space, 1, divided by, 10, times, start cancel, 6, end cancel, start subscript, 2, end subscript, end fraction [Explain]
=\dfrac{1}{20}=
20
1