To express the fraction [tex]\(\frac{-4}{-7}\)[/tex] with different denominators, we first observe that both the numerator and the denominator are negative, which means the fraction is positive. Thus, [tex]\(\frac{-4}{-7} = \frac{4}{7}\)[/tex].
Now let's re-express this positive fraction with the given denominators.
### Part (i): Rewriting with denominator -28
To change the denominator from 7 to -28, we start by finding the equivalent fraction. This involves determining what factor you need to multiply 7 by to get -28:
[tex]\[ 7 \times (-4) = -28 \][/tex]
Similarly, we need to multiply the numerator by the same factor [tex]\( -4 \)[/tex]:
[tex]\[
4 \times (-4) = -16
\][/tex]
Thus, the fraction [tex]\(\frac{4}{7}\)[/tex] when expressed with a denominator of -28 becomes:
[tex]\[
\frac{4}{7} = \frac{-16}{-28}
\][/tex]
### Part (ii): Rewriting with denominator 35
Next, we need to change the denominator from 7 to 35. We begin by figuring out what factor we need to multiply 7 by to get 35:
[tex]\[ 7 \times 5 = 35 \][/tex]
We then multiply the numerator by the same factor [tex]\(5\)[/tex]:
[tex]\[
4 \times 5 = 20
\][/tex]
Thus, the fraction [tex]\(\frac{4}{7}\)[/tex] when expressed with a denominator of 35 becomes:
[tex]\[
\frac{4}{7} = \frac{20}{35}
\][/tex]
### Conclusion
From the calculations above, we have rewritten the fraction [tex]\(\frac{4}{7}\)[/tex] as:
- With denominator [tex]\(-28\)[/tex]: [tex]\(\frac{-16}{-28}\)[/tex]
- With denominator [tex]\(35\)[/tex]: [tex]\(\frac{20}{35}\)[/tex]
And consequently:
[tex]\[
\frac{-4}{-7} = \frac{-16}{-28} = \frac{20}{35}
\][/tex]
