Đề cương ôn tập cuối kì 2 Toán lớp 4 Cánh diều có đáp án - Phần II. Tự luận

a)

So sánh: 34 610 789 < 43 246 970 < 156 243 078 < 198 574 613 < 245 136 188

Vậy: Sắp xếp các số theo thứ tự từ bé đến lớn là:

34 610 789; 43 246 970; 156 243 078;  198 574 613; 245 136 188

b)

So sánh: 2 451 013 < 3 655 489 < 4 316 980 < 6 359 784 < 9 054 267

Vậy: Sắp xếp các số theo thứ tự từ bé đến lớn là:

2 451 013; 3 655 489; 4 316 980; 6 359 784; 9 054 267

c)

So sánh: 9 267 < 53 168 < 64 135 < 167 498 < 210 345

Vậy: Sắp xếp các số theo thứ tự từ bé đến lớn là:

9 267; 53 168; 64 135; 167 498; 210 345

d)

So sánh: 659 < 1 246 < 21 035 < 47 569 < 55 983

Vậy: Sắp xếp các số theo thứ tự từ bé đến lớn là:

659; 1 246; 21 035; 47 569; 55 983

e)

So sánh: 269 < 346 < 589 < 1 024 < 1 620

Vậy: Sắp xếp các số theo thứ tự từ bé đến lớn là:

269; 346; 589; 1 024; 1 620

a)

32 654 + 15 024 = 47 678

50 356 – 21 698 = 28 658

So sánh: 47 678 > 28 658

Vậy: 32 654 + 15 024 > 50 356 – 21 698

b)

2 458 × 4 = 9 832

26 457 + 16 987 = 43 444

So sánh: 9 832 < 43 444

Vậy: 2 458 × 4 < 26 457 + 16 987

c)

2 364 + 5 981 = 8 345

268 × 24 = 6 432

So sánh: 8 345 > 6 432

Vậy: 2 364 + 5 981 > 268 × 24

d)

359 486 + 168 794 = 528 280

846 100 – 369 415 = 476 685

So sánh: 528 280 > 476 685

Vậy: 359 486 + 168 794 > 846 100 – 369 415

e)

34 569 : 3 = 11 523

1 458 × 9 = 13 122

So sánh: 11 523 < 13 122

Vậy: 34 569 : 3 < 1 458 × 9

f)

12 645 × 23 = 290 835

346 701 + 246 997 = 593 698

So sánh: 290 835 < 593 698

Vậy: 12 645 × 23 < 346 701 + 246 997

a)

\[\frac{5}{7} - \frac{3}{{14}} = \frac{{10}}{{14}} - \frac{3}{{14}} = \frac{7}{{14}} = \frac{1}{2}\]

So sánh: \[\frac{1}{2} < 1\]

Vậy: \[\frac{5}{7} - \frac{3}{{14}}\,\, < \,\,1\]                                

b)

\[\frac{6}{5} - \frac{3}{{10}} = \frac{{12}}{{10}} - \frac{3}{{10}} = \frac{9}{{10}}\]

So sánh: \[\frac{9}{{10}} < 1\]

Vậy: \[\frac{6}{5} - \frac{3}{{10}}\,\, < \,\,1\]

c)

\[\frac{7}{6} + \frac{5}{3}\, = \frac{7}{6} + \frac{{10}}{6} = \frac{{17}}{6} = \frac{{34}}{{12}}\]

\[\frac{1}{2} + \frac{7}{{12}} = \frac{6}{{12}} + \frac{7}{{12}} = \frac{{13}}{{12}}\]

So sánh: \[\frac{{34}}{{12}} > \frac{{13}}{{12}}\]

Vậy: \[\frac{7}{6} + \frac{5}{3}\,\, > \,\,\frac{1}{2} + \frac{7}{{12}}\]              

d)

\[\frac{6}{5} + \frac{3}{4} = \frac{{24}}{{20}} + \frac{{15}}{{20}} = \frac{{39}}{{20}}\]

\[\frac{3}{2} + \frac{{17}}{{20}} = \frac{{30}}{{20}} + \frac{{17}}{{20}} = \frac{{47}}{{20}}\]

So sánh: \[\frac{{39}}{{20}} < \frac{{47}}{{20}}\]

Vậy: \[\frac{6}{5} + \frac{3}{4}\,\, < \,\,\frac{3}{2} + \frac{{17}}{{20}}\]

e)

\[\frac{9}{4} - \frac{1}{5} = \frac{{45}}{{20}} - \frac{4}{{20}} = \frac{{41}}{{20}}\]

\[\frac{3}{{10}} + \frac{{17}}{{20}} = \frac{6}{{20}} + \frac{{17}}{{20}} = \frac{{23}}{{20}}\]

So sánh: \[\frac{{41}}{{20}} > \frac{{23}}{{20}}\]

Vậy: \[\frac{9}{4} - \frac{1}{5}\,\, > \,\,\frac{3}{{10}} + \frac{{17}}{{20}}\]     

f)

\[\frac{5}{4} - \frac{1}{2} = \frac{5}{4} - \frac{2}{4} = \frac{3}{4} = \frac{9}{{12}}\]

\[\frac{2}{3} + \frac{5}{6} = \frac{4}{6} + \frac{5}{6} = \frac{9}{6} = \frac{{18}}{{12}}\]

So sánh: \[\frac{9}{{12}} < \frac{{18}}{{12}}\]

Vậy: \[\frac{5}{4} - \frac{1}{2}\,\, < \,\,\frac{2}{3} + \frac{5}{6}\]

a) \[\frac{5}{6} + \frac{3}{2} = \frac{5}{6} + \frac{9}{6} = \frac{{14}}{6} = \frac{7}{3}\]  b) \[\frac{9}{5} - \frac{3}{{10}} = \frac{{18}}{{10}} - \frac{3}{{10}} = \frac{{16}}{{10}} = \frac{8}{5}\]

c) \[\frac{5}{9} \times \frac{2}{7} = \frac{{10}}{{63}}\]             d) \[\frac{6}{{11}}:\frac{7}{2} = \frac{6}{{11}} \times \frac{2}{7} = \frac{{12}}{{77}}\]

e) \[\frac{8}{9} + \frac{2}{3} = \frac{8}{9} + \frac{6}{9} = \frac{{14}}{9}\]       f) \[\frac{9}{4} - \frac{5}{6} = \frac{{27}}{{12}} - \frac{{10}}{{12}} = \frac{{17}}{{12}}\]

g) \[\frac{6}{7} \times \frac{8}{9} = \frac{{48}}{{63}} = \frac{{16}}{{21}}\]           h) \[\frac{4}{9}:\frac{5}{7} = \frac{4}{9} \times \frac{7}{5} = \frac{{28}}{{45}}\]

a) \[\frac{5}{9} + \frac{5}{{11}} + \frac{1}{9} + \frac{4}{{11}} + \frac{1}{3} + \frac{2}{{11}}\]

\[ = \left( {\frac{5}{9} + \frac{1}{9} + \frac{1}{3}} \right) + \left( {\frac{5}{{11}} + \frac{4}{{11}} + \frac{2}{{11}}} \right)\]

\[ = \left( {\frac{5}{9} + \frac{1}{9} + \frac{3}{9}} \right) + \frac{{11}}{{11}}\]

\[ = \frac{9}{9} + \frac{{11}}{{11}}\]

= 1 + 1 = 2

b) \[\frac{6}{7} \times \frac{2}{7} + \frac{6}{7} \times \frac{{11}}{{14}} + \frac{6}{7}\]

\[\begin{array}{l} = \frac{6}{7} \times \left( {\frac{2}{7} + \frac{{11}}{{14}} + 1} \right)\\ = \frac{6}{7} \times \left( {\frac{4}{{14}} + \frac{{11}}{{14}} + \frac{{14}}{{14}}} \right)\\ = \frac{6}{7} \times \frac{{29}}{{14}}\\ = \frac{{174}}{{98}} = \frac{{87}}{{49}}\end{array}\]

c) \[\frac{2}{5} \times \frac{3}{8} + \frac{2}{5} \times \frac{1}{4} + \frac{2}{5} \times \frac{5}{6} + \frac{2}{5} \times \frac{1}{3}\]

\[ = \frac{2}{5} \times \left( {\frac{3}{8} + \frac{1}{4} + \frac{5}{6} + \frac{1}{3}} \right)\]

\[ = \frac{2}{5} \times \left( {\frac{9}{{24}} + \frac{6}{{24}} + \frac{{20}}{{24}} + \frac{8}{{24}}} \right)\]

\[ = \frac{2}{5} \times \frac{{43}}{{24}}\]

\[ = \frac{{43}}{{60}}\]

d) \[\frac{1}{7}:\frac{2}{5} + \frac{1}{7}:\frac{4}{3} + \frac{1}{7}:\frac{{12}}{7}\]

\[ = \frac{1}{7} \times \frac{5}{2} + \frac{1}{7} \times \frac{3}{4} + \frac{1}{7} \times \frac{7}{{12}}\]

\[ = \frac{1}{7} \times \left( {\frac{5}{2} + \frac{3}{4} + \frac{7}{{12}}} \right)\]

\[ = \frac{1}{7} \times \left( {\frac{{30}}{{12}} + \frac{9}{{12}} + \frac{7}{{12}}} \right)\]

\[ = \frac{1}{7} \times \frac{{46}}{{12}}\]

\[ = \frac{{46}}{{84}} = \frac{{23}}{{42}}\]