a) Ta có: `3/4=0,75` và `3/5=0,6` 

Ta cần viết các số hữu tỉ nhỏ hơn 0,75 và lớn hớn 0,6 

\(0,65=\dfrac{13}{20}\)

\(0,7=\dfrac{7}{10}\)

\(0,72=\dfrac{18}{25}\) 

b) Ta có: `2/3=0,66...` và `3/4=0,75`

Ta cần viết các số hữu tỉ nhỏ hơn 0,75 và lớn hơn 0,66... 

\(0,68=\dfrac{17}{25}\)

\(0,7=\dfrac{7}{10}\)

\(0,72=\dfrac{18}{25}\)

\(6\dfrac{2}{3}+7\dfrac{5}{8}+3\dfrac{1}{3}-4\dfrac{5}{8}=\left(6+\dfrac{2}{3}\right)+\left(7+\dfrac{5}{8}\right)+\left(3+\dfrac{1}{3}\right)-\left(4+\dfrac{5}{8}\right)\\ =\left(6+7+3-4\right)+\left(\dfrac{2}{3}+\dfrac{1}{3}\right)+\left(\dfrac{5}{8}-\dfrac{5}{8}\right)\\ =12+\dfrac{3}{3}+0\\ =12+1=13\)

____________________

\(\left(4\dfrac{2}{5}+2\dfrac{3}{7}\right)-\left(2\dfrac{2}{5}-1\dfrac{4}{7}\right)=\left(4+\dfrac{2}{5}+2+\dfrac{3}{7}\right)-\left(2+\dfrac{2}{5}-\dfrac{4}{7}-1\right)\\ =\left(4+2-2+1\right)+\left(\dfrac{2}{5}-\dfrac{2}{5}\right)+\left(\dfrac{3}{7}+\dfrac{4}{7}\right)\\ =5+0+\dfrac{7}{7}\\ =5+1=6\)

________________________

\(1\dfrac{4}{5}+\dfrac{1}{5}\times\dfrac{1}{5}+\dfrac{1}{5}\times\dfrac{4}{5}\\ =1+\dfrac{4}{5}+\dfrac{1}{5}\times\left(\dfrac{1}{5}+\dfrac{4}{5}\right)\\ =1+\dfrac{4}{5}+\dfrac{1}{5}\\ =1+\dfrac{5}{5}\\ 1+1=2\)

6 `2/3` + 7 `5/8 `+ 3 `1/3` - 4 `5/8`

` = 20/3 + 61/8 + 10/3 - 37/8`

` = (20/3 + 10/3) - (61/8 - 37/8)`

` = 10 - 3`

` = 7`

(4 `2/5` + 2 `3/7`) - (2 `2/5` - 1 `4/7`)

` = (22/5 + 17/7) - (12/5 - 11/7)`

` = 239/35 - 29/35`

` = 200/35 = 40/7`

1`4/5 + 1/5 × 1/5 + 1/5 × 4/5`

` = 9/5 + 1/5 × 1/5 + 1/5 × 4/5`

` = 9/5 + 1/5 × (1/5 + 4/5)`

` = 9/5 + 1/5 × 1`

` = 9/5 + 1/5`

` = 10/5 = 2`

I.BÀI TẬP BỔ SUNG.

Exercise 1. Choose the correct answer.

1. Anna (likes/ hates) doing homework. She is lazy.

2. Lily (likes/ dislikes) the idea of staying out too late. It’s too dangerous.

3. Most girls (detest/ like) cockroaches.

4. Tom (likes/ hates) making models. He never does it.

5. We (enjoy/ hate) spending time with John. He is very interesting.

Exercise 2. Complete the sentences with the verb + -ing.

do; go; play; climb; swim; watch

1. Susan loves _____doing___________ yoga

2. They enjoy ______watching___________ the sports on TV.

3. We really like ____climbing_____________ in the Hoang Lien Son in February.

4. Simon hates _____playing____________ badmintons but he loves football.

5. I don’t like _______swimming____________ in the pool at the sports centre.

6. Do you like _______going_________ running in the morning?

Exercise 3. Rewrite the sentence without changing its meaning

1. My father likes to do gardening at the weekend.

→ My father enjoys _doing gardening at the weekend.__________.

2. She loves to collect glass bottles in her free time.

→ She enjoys _collecting glass bottles in her free time._____________.

3. I enjoy playing soccer.

→ I like playing soccer.____________________.

4. Do you like seeing a water puppet show?

→ Do you ____enjoy seeing a water puppet show?________________.

5. Do you enjoy making models with your friends?

→ Do you _____like making models with your friends?___________.

Exercise 4. Choose the best answer.

1. My mother loves _______ food for my family.

A. preparing      B. to prepare          C. prepare    D. A&B are correct.

2. My grandmother ________ to plant flowers in the garden behind her house.

A. 'd like        B. enjoys      C. detests      D. adores

3. Coco fancies ________ TV. He watches TV whenever he can.

A. to watch        B. watched       C. watch      D. watching

4. My sister hates  _______ with the dolls. It’s weird.

A. playing      B. to play     C. to playing      D. A&B are correct.

5. I enjoy ______ with my dog. He’s so cute

A. play             B. to play              C. playing        D. played

6. Tom fancies _______ computer games when he’s at home.

A. playing       B. to play                 C. played       D. A&B are correct.

7. Mary _______ reading Conan comics. She spends her free time on reading some volumes.

A. hates        B. detests         C. dislikes       D. enjoys

8. Henry doesn’t mind ________ up early in the morning.

A. waking        B. to wake       C. wake         D. will wake

9. My grandparents love ________ very much. There are a lot of beautiful flowers.

A. doing garden             B. doing gardening         C. do gardening      D. to do garden

10. Nga likes ________ with her close friend on Saturday evenings.

A. window shop       B. window to shop     C. window shops     D. window shopping

11. Do you fancy _______ around the West Lake with me this Sunday morning?

A going            B having            C. staying               D. moving

12. I don't like ________ up early in the winter days. I love ________ in bed late.

A. getting/ stay             B. get/ stay      C. getting/ staying      D. get/ staying

13. My father is fond of ________ a lot of trees and vegetables.

A. growing     B. grow       C. grew             D. grows

14. Teenagers often prefer travelling with their friends ________ travelling with their parents.

A. from        B. than      C. as         D. to

15. His parents are keen on  ________ to rock music at night.

A. listening     B. listen    C. to listen        D. to listening

Exercise 1. Choose the correct answer.

1. Anna (likes/ hates) doing homework. She is lazy.

2. Lily (likes/ dislikes) the idea of staying out too late. It’s too dangerous.

3. Most girls (detest/ like) cockroaches.

4. Tom (likes/ hates) making models. He never does it.

5. We (enjoy/ hate) spending time with John. He is very interesting.

Số chẵn lớn nhất có 2 chữ số là: 98

Hay hiệu chúng là 98

Phân số lớn hơn 1 hay tử số lớn hơn mẫu số

Mẫu số là:

  (176 - 98) : 2 = 39

Tử số là:

  39 + 98 = 137

Theo đề có thể suy ra mẹ hơn con 26 tuổi

Do mỗi năm cả con và mẹ đều thêm 1 tuổi nên hiệu số tuổi hai mẹ con không đổi dù ở thời điểm nào

Khi mẹ gấp 3 lần tuổi con: Coi tuổi con 1 phần, tuổi mẹ 3 phần

Hiệu số phần bằng nhau:

  3 - 1 = 2 (phần)

Tuổi con khi đó là:

  26 : 2 = 13 (tuổi)

Tuổi mẹ khi đó là:

  13 x 3 = 39 (tuổi)

Đề cho con năm nay 4 tuổi có vẻ hơi thừa nên mình bổ sung thêm cho bạn một đề khác có thể hỏi nhé: Hỏi sau bao nhiêu năm thì tuổi mẹ gấp 3 lần tuổi con

Sau số năm thì tuổi mẹ gấp 3 lần tuổi con là:

  13 - 4 = 9 (năm)

a) 

\(\dfrac{267}{268}< 1\Rightarrow-\dfrac{267}{268}>-1\)

\(\dfrac{1347}{1343}>1\Rightarrow-\dfrac{1347}{1343}< -1\)

\(\Rightarrow-\dfrac{1347}{1343}< -\dfrac{267}{268}\)

b) \(\dfrac{2022\cdot2023-1}{2022\cdot2023}=\dfrac{2022\cdot2023}{2022\cdot2023}-\dfrac{1}{2022\cdot2023}=1-\dfrac{1}{2022\cdot2023}\)

\(\dfrac{2023\cdot2024-1}{2023\cdot2024}=\dfrac{2023\cdot2024}{2023\cdot2024}-\dfrac{1}{2023\cdot2024}=1-\dfrac{1}{2023\cdot2024}\)

Vì: \(2022\cdot2023< 2023\cdot2024\)

\(\Rightarrow\dfrac{1}{2022\cdot2023}>\dfrac{1}{2023\cdot2024}\)

\(\Rightarrow1-\dfrac{1}{2022\cdot2023}< 1-\dfrac{1}{2023\cdot2024}\)

Hay: `(2022*2023-1)/(2022*2023) < (2023*2024 - 1)/(2023*2024)` 

c) \(\dfrac{2022\cdot2023}{2022\cdot2023+1}=\dfrac{2023\cdot2023+1-1}{2022\cdot2023+1}=1-\dfrac{1}{2022\cdot2023+1}\)

\(\dfrac{2023\cdot2024}{2023\cdot2024+1}=\dfrac{2023\cdot2024+1-1}{2023\cdot2024+1}=1-\dfrac{1}{2023\cdot2024+1}\)
Vì: \(2022\cdot2023+1< 2023\cdot2024+1\)

\(\Rightarrow\dfrac{1}{2022\cdot2023+1}>\dfrac{1}{2023\cdot2024+1}\)

\(\Rightarrow1-\dfrac{1}{2022\cdot2023+1}< 1-\dfrac{1}{2023\cdot2024+1}\)

Hay: `(2022*2023)/(2022*2023+1)<(2023*2024)/(2023*2024+1)`

\(\dfrac{4}{7}+\dfrac{3}{4}+\dfrac{2}{7}\\ =\dfrac{6}{7}+\dfrac{3}{4}\\ =\dfrac{24}{28}+\dfrac{21}{28}=\dfrac{45}{28}\\ ------------\\ \dfrac{1}{6}+\dfrac{5}{24}+\dfrac{2}{3}\\ =\dfrac{4}{24}+\dfrac{5}{24}+\dfrac{16}{24}=\dfrac{25}{24}\\ ---------\\ \dfrac{1}{2}+\dfrac{5}{16}-\dfrac{1}{4}\\ =\dfrac{8}{16}+\dfrac{5}{16}-\dfrac{4}{16}=\dfrac{9}{16}\)

\(----------\\ 1-\left(\dfrac{1}{5}+\dfrac{1}{2}\right)\\ =\dfrac{10}{10}-\dfrac{2}{10}-\dfrac{5}{10}=\dfrac{3}{10}\\ ---------\\ \dfrac{2}{3}+\dfrac{1}{2}-\dfrac{5}{6}\\ =\dfrac{4}{6}+\dfrac{3}{6}-\dfrac{5}{6}=\dfrac{2}{6}=\dfrac{1.}{3}\\ --------\\ \dfrac{5}{12}+\dfrac{5}{6}-\dfrac{3}{4}\\ =\dfrac{5}{12}+\dfrac{10}{12}-\dfrac{9}{12}=\dfrac{6}{12}=\dfrac{1}{2}\\ ---------\)

\(\dfrac{7}{5}-\dfrac{4}{15}-\dfrac{2}{3}\\ =\dfrac{21}{15}-\dfrac{4}{15}-\dfrac{10}{15}=\dfrac{7}{15}\)

\(\dfrac{4}{7}+\dfrac{3}{4}+\dfrac{2}{7}=\left(\dfrac{4}{7}+\dfrac{2}{7}\right)+\dfrac{3}{4}=\dfrac{6}{7}+\dfrac{3}{4}=\dfrac{24}{28}+\dfrac{21}{28}=\dfrac{45}{28}\)

\(\dfrac{1}{6}+\dfrac{5}{24}+\dfrac{2}{3}=\dfrac{4}{24}+\dfrac{5}{24}+\dfrac{16}{24}=\dfrac{25}{24}\)

\(\dfrac{1}{2}+\dfrac{5}{16}-\dfrac{1}{4}=\dfrac{8}{16}+\dfrac{5}{16}-\dfrac{4}{16}=\dfrac{9}{16}\)

\(1-\left(\dfrac{1}{5}+\dfrac{1}{2}\right)=1-\left(\dfrac{2}{10}+\dfrac{5}{10}\right)=1-\dfrac{7}{10}=\dfrac{10}{10}-\dfrac{7}{10}=\dfrac{3}{10}\)

\(\dfrac{2}{3}+\dfrac{1}{2}-\dfrac{5}{6}=\dfrac{4}{6}+\dfrac{3}{6}-\dfrac{5}{6}=\dfrac{2}{6}=\dfrac{1}{3}\)

\(\dfrac{5}{12}+\dfrac{5}{6}-\dfrac{3}{4}=\dfrac{5}{12}+\dfrac{10}{12}-\dfrac{9}{12}=\dfrac{6}{12}=\dfrac{1}{2}\)

\(\dfrac{7}{5}-\dfrac{4}{15}-\dfrac{2}{3}=\dfrac{21}{15}-\dfrac{4}{15}-\dfrac{10}{15}=\dfrac{7}{15}\)

\(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}\)

\(=\dfrac{3}{6}+\dfrac{2}{6}+\dfrac{1}{6}\)

\(=\dfrac{3+2+1}{6}\)

\(=\dfrac{6}{6}\)

\(=1\)

\(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{6}=\dfrac{5}{6}+\dfrac{1}{6}=1\)

gọi x là số tem loại A; y là số tem loại B

tổng số tiền mà anh đã mua tem là:

10 000 - 200 = 9 800 (VNĐ)

theo đề ta có: 1300x + 700y = 9800

13x + 7y = 98

để thoả mãn đề bài thì các giá trị của x và y là số nguyên

13x + 7 × 1 = 98

13x + 7 = 98

13x = 91

x = 7

y = \(\dfrac{98-13\cdot7}{7}=1\)

tổng số tem đã mua là: 7 + 1 = 8 (tem)

vậy số tem đã mua là 8