Tìm a, để:

a) \(1 = \frac{a}{5}\)

b) \(\frac{{24}}{{36}} = \frac{a}{{54}}\)

c) \(\frac{{21}}{a} = \frac{{15}}{{20}}\)

d) \(\frac{{48}}{{208}} = \frac{a}{{13}}\)

e) \(\frac{{13}}{4} = \frac{{585}}{a}\)

a) \(1 = \frac{a}{5}\)

Phân số có giá trị bằng 1 khi tử số bằng mẫu số.

Vậy a = 5

b) \(\frac{{24}}{{36}} = \frac{a}{{54}}\)

\(\frac{{24}}{{36}} = \frac{{24:6}}{{36:6}} = \frac{4}{6}\)

\(\frac{4}{6} = \frac{{4 \times 9}}{{6 \times 9}} = \frac{{36}}{{54}}\)

Do đó: \(\frac{{36}}{{54}} = \frac{a}{{54}}\)

Vậy: a = 36

c) \(\frac{{21}}{a} = \frac{{15}}{{20}}\)

\(\frac{{15}}{{20}} = \frac{{15:5}}{{20:5}} = \frac{3}{4}\)

\(\frac{3}{4} = \frac{{3 \times 7}}{{4 \times 7}} = \frac{{21}}{{28}}\)

Do đó: \(\frac{{21}}{a} = \frac{{21}}{{28}}\)

Vậy: a = 28

d) \(\frac{{48}}{{208}} = \frac{a}{{13}}\)

\(\frac{{48}}{{208}} = \frac{{48:16}}{{208:16}} = \frac{3}{{13}}\)

Do đó: \(\frac{3}{{13}} = \frac{a}{{13}}\)

Vậy: a = 3

e) \(\frac{{13}}{4} = \frac{{585}}{a}\)

\(\frac{{13}}{4} = \frac{{13 \times 45}}{{4 \times 45}} = \frac{{585}}{{180}}\)

Do đó: \(\frac{{585}}{{180}} = \frac{{585}}{a}\)

Vậy: a = 180