2 bài tập So sánh các phân số (có lời giải)

a) $\frac{3}{5}$ < 1 b) $\frac{7}{6}\,\, > 1$ c) $\frac{4}{5}$ < 1 d) $\frac{9}{{14}}$ < 1

e) $\frac{8}{3}$ > 1 f) $\frac{{14}}{3}\, > \frac{{10}}{3}$ g) $\frac{5}{7} > \frac{3}{7}$ h) $\frac{7}{5} < \frac{9}{5}$

i) $\frac{{218}}{{376}} < \frac{{218}}{{367}}$ j) $\frac{{721}}{{218}} < \frac{{721}}{{215}}$

k)

Vì: $\frac{{1999}}{{2003}} < 1 < \frac{9}{8}$ Nên: $\frac{{1999}}{{2003}} < \frac{9}{8}$

l)

Vì: $\frac{{12}}{{31}} < 1 < \frac{{22}}{{21}}$ Nên: $\frac{{12}}{{31}} < \frac{{22}}{{21}}$

m)

Vì: $\frac{{47}}{{52}} > \frac{{47}}{{58}} > \frac{{45}}{{58}}$ Nên: $\frac{{47}}{{52}} > \frac{{45}}{{58}}$

n)

$\frac{{2015}}{{2011}} - 1 = \frac{4}{{2011}}$

$\frac{{1996}}{{1992}} - 1 = \frac{4}{{1992}}$

Vì: $\frac{4}{{2011}} < \frac{4}{{1992}}$ Nên: $\frac{{2015}}{{2011}}\,\, < \frac{{1996}}{{1992}}$

o)

Vì: $\frac{{1998}}{{1995}} > 1 > \frac{{2015}}{{2016}}$ Nên: $\frac{{1998}}{{1995}} > \frac{{2015}}{{2016}}$

p)

Ta có:

$\frac{{222}}{{333}} = \frac{{222:111}}{{333:111}} = \frac{2}{3} = 1 - \frac{1}{3}$

$\frac{{333}}{{444}} = \frac{{333:111}}{{444:111}} = \frac{3}{4} = 1 - \frac{1}{4}$

Vì $\frac{1}{3} > \frac{1}{4}$ nên $\frac{2}{3} < \frac{3}{4}$ hay $\frac{{222}}{{333}} < \frac{{333}}{{444}}$

q)

Vì: $\frac{{1313}}{{1515}} < \frac{{1326}}{{1515}} < \frac{{1326}}{{1428}}$ nên $\frac{{1313}}{{1515}} < \frac{{1326}}{{1428}}$

r)

$\frac{{119}}{{120}} = 1 - \frac{1}{{120}}$

$\frac{{118}}{{119}} = 1 - \frac{1}{{119}}$

Vì: $\frac{1}{{120}} < \frac{1}{{119}}$ Nên: $\frac{{119}}{{120}} > \frac{{118}}{{119}}$

s)

$\frac{{222}}{{555}} = \frac{{222:111}}{{555:111}} = \frac{2}{5}$

$\frac{{333}}{{444}} = \frac{{333:111}}{{444:111}} = \frac{3}{4}$

Vì $\frac{2}{5} < \frac{3}{5} < \frac{3}{4}$ nên $\frac{2}{5} < \frac{3}{4}$ hay $\frac{{222}}{{555}} < \frac{{333}}{{444}}$

a)

Quy đồng mẫu số các phân số với mẫu số chung bằng 120

$\frac{2}{3} = \frac{{2 \times 40}}{{3 \times 40}} = \frac{{80}}{{120}}$; $\frac{5}{4} = \frac{{5 \times 30}}{{4 \times 30}} = \frac{{150}}{{120}}$; $\frac{3}{8} = \frac{{3 \times 15}}{{8 \times 15}} = \frac{{45}}{{120}}$;

$\frac{7}{5} = \frac{{7 \times 24}}{{5 \times 24}} = \frac{{168}}{{120}}$; $\frac{6}{5} = \frac{{6 \times 24}}{{5 \times 24}} = \frac{{144}}{{120}}$

So sánh: $\frac{{45}}{{120}} < \frac{{80}}{{120}} < \frac{{144}}{{120}} < \frac{{150}}{{120}} < \frac{{168}}{{120}}$

Vậy: Sắp xếp các phân số theo thứ tự tăng dần là: $\frac{3}{8};\frac{2}{3};\frac{6}{5};\frac{5}{4};\frac{7}{5}$

b)

Quy đồng mẫu số các phân số với mẫu số chung bằng 72

$\frac{3}{4} = \frac{{3 \times 18}}{{4 \times 18}} = \frac{{24}}{{72}}$; $\frac{{11}}{8} = \frac{{11 \times 9}}{{8 \times 9}} = \frac{{99}}{{72}}$; $\frac{5}{6} = \frac{{5 \times 12}}{{6 \times 12}} = \frac{{60}}{{72}}$; $\frac{2}{9} = \frac{{2 \times 8}}{{9 \times 8}} = \frac{{16}}{{72}}$; $\frac{8}{3} = \frac{{8 \times 24}}{{3 \times 24}} = \frac{{192}}{{72}}$

So sánh: $\frac{{16}}{{72}} < \frac{{24}}{{72}} < \frac{{60}}{{72}} < \frac{{99}}{{72}} < \frac{{192}}{{72}}$

Vậy: Sắp xếp các phân số theo thứ tự tăng dần là: $\frac{2}{9};\frac{3}{4};\frac{5}{6};\frac{{11}}{8};\frac{8}{3}$

c)

Nhận thấy: $1 < \frac{{26}}{{15}} < \frac{{26}}{{11}}$; $1 > \frac{{215}}{{253}} > \frac{{162}}{{253}}$

Do đó: $\frac{{26}}{{11}} > \frac{{26}}{{15}} > \frac{{18}}{{18}} > \frac{{215}}{{253}} > \frac{{162}}{{253}}$

Vậy: Sắp xếp các phân số theo thứ tự tăng dần là: $\frac{{162}}{{253}};\frac{{215}}{{253}};\frac{{18}}{{18}};\frac{{26}}{{15}};\frac{{26}}{{11}}$