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\(\dfrac{9}{5}+\dfrac{5}{8}=\dfrac{72}{40}+\dfrac{25}{40}=\dfrac{97}{40}\)
\(\dfrac{3}{5}+\dfrac{13}{9}=\dfrac{27}{45}+\dfrac{65}{45}=\dfrac{82}{45}\)
\(\dfrac{2}{3}+\dfrac{11}{2}=\dfrac{4}{6}+\dfrac{33}{6}=\dfrac{37}{6}\)
\(\dfrac{9}{4}+\dfrac{17}{20}=\dfrac{45}{20}+\dfrac{17}{20}=\dfrac{62}{20}=\dfrac{31}{10}\)
\(\dfrac{43}{6}+\dfrac{45}{8}=\dfrac{172}{24}+\dfrac{135}{24}=\dfrac{307}{24}\)
\(\dfrac{5}{9}+\dfrac{7}{15}=\dfrac{25}{45}+\dfrac{21}{45}=\dfrac{46}{45}\)
\(\dfrac{9}{5}+\dfrac{5}{8}\\ =\dfrac{72}{40}+\dfrac{25}{40}\\ =\dfrac{97}{40}\\ ----------\\ \dfrac{3}{5}+\dfrac{13}{9}\\ =\dfrac{27}{45}+\dfrac{65}{45}\\ =\dfrac{92}{45}\\ --------\\ \dfrac{2}{3}+\dfrac{11}{2}\\ =\dfrac{4}{6}+\dfrac{33}{6}\\ =\dfrac{37}{6}\\ --------\\ \dfrac{9}{4}+\dfrac{17}{20}\\ =\dfrac{45}{20}+\dfrac{17}{20}\\ =\dfrac{62}{20}=\dfrac{31}{10}\\ ----------\\ \dfrac{43}{6}+\dfrac{45}{8}\\ =\dfrac{172}{24}+\dfrac{135}{24}\\ =\dfrac{307}{24}\)
\(-----------\\ \dfrac{5}{9}+\dfrac{7}{15}\\ =\dfrac{25}{45}+\dfrac{21}{45}\\ =\dfrac{46}{45}\)
\(\dfrac{x^3-3x^2y+3xy^2-y^3}{x-y}=\dfrac{\left(x-y\right)\left(x^2+xy+y^2\right)-3xy\left(x-y\right)}{x-y}\)
\(=\dfrac{\left(x-y\right)\left(x^2-2xy+y^2\right)}{x-y}=\left(x-y\right)^2\)
\(\dfrac{8}{3}+\dfrac{10}{7}=\dfrac{56}{21}+\dfrac{30}{21}\\ =\dfrac{56+30}{21}=\dfrac{86}{21}\)
\(\dfrac{8}{3}+\dfrac{10}{7}\)
\(=\dfrac{56}{21}+\dfrac{30}{21}\)
\(=\dfrac{56+30}{21}\)
\(=\dfrac{86}{21}\)
\(\dfrac{4}{5}+\dfrac{3}{4}=\dfrac{16}{20}+\dfrac{15}{20}\\ =\dfrac{16+15}{20}=\dfrac{31}{20}\)
\(\dfrac{4}{5}+\dfrac{3}{4}\)
\(=\dfrac{16}{20}+\dfrac{15}{20}\)
\(=\dfrac{16+15}{20}\)
\(=\dfrac{31}{20}\)
a: Trên tia Ox, ta có: OA<OB
nên A nằm giữa O và B
=>OA+AB=OB
=>AB+4=6
=>AB=2(cm)
b: C là trung điểm của OA
=>\(CO=CA=\dfrac{OA}{2}=2\left(cm\right)\)
Vì AO và AB là hai tia đối nhau
nên AC và AB là hai tia đối nhau
=>A nằm giữa hai điểm B và C
Ta có: A nằm giữa B và C
mà AB=AC(=2cm)
nên A là trung điểm của BC
d: Các góc đỉnh D trong hình vẽ là: \(\widehat{ODC};\widehat{ODA};\widehat{ODB};\widehat{CDA};\widehat{CDB};\widehat{ADB}\)
b: \(cos14=sin76;cos37=sin53\)
Vì 47<48<53<76 nên \(sin47< sin48< sin53< sin76\)
=>\(sin47< sin48< cos37< cos14\)
c: \(cot25=tan65;cot38=tan52\)
Vì 52<62<65<73
nên \(tan52< tan62< tan65< tan73\)
=>\(cot38< tan63< cot25< tan73\)
a: Vì 75>45
nên \(tan75>1\)
Vì 40<45
nên \(cot40>1\)
\(cot40=tan50;tan75=tan75\)
mà \(tan50< tan75\)
nên \(1< cot40< tan75\left(1\right)\)
\(cos56=sin34;sin50=sin50\)
mà 34<50
nên \(sin34< sin50< 1\)
=>\(cos56< sin50< 1\left(2\right)\)
Từ (1),(2) suy ra \(cos56< sin50< cot40< tan75\)
Bài 3:Điền dạng thích hợp của động từ trong ngoặc để hoàn thành các câu sau:
1.Did you enjoy(watch)__watching____the comedy last night?
2.Many people prefer(do)__doing____gardening after their retirement.
3.My cat dislikes(sleep)___sleeping_____on the floor.
4.My father doesn’t mind(work)____working__hard.
5.My cousin doesn’t like(study)___studying______Math and Chemistry.
6.They dislike(talk)_____talking_____with each other.
7.Jim and Jane don’t fancy(go)__going________out tomorrow.
8.Did you hate(eat)__eating____vegetables when you was small?
9.she didn’t prefer(tell)_____telling___him about her plan.
10.James'd like (have)___to have____dinner in a luxury restaurant.
11.I hope my mother will enjoy(spend)__spending_____time with her grandchildren.
12.Some people enjoy(take)___taking___a shower in the morning.
13.I think your brother won’t mind(lend)__lending______you a helping hand.
14.My boyfriend dislike(wait)_____waiting_______.
15.What do you detest(do)___doing_______the most?
Bài 4: Dựa vào các từ cho sẵn, viết thành câu hoàn chỉnh:
1.Peter/ enjoy / play/ computer games/ in his free time.
_____Peter enjoys playing computer games in his free time._________
2.You/ hate/ do/ the washing?
_____Do you hate doing the washing?____________________
3.My father/ enjoy/ play/ sports/ and/ read/ books.
_____My father enjoys playing sports and reading books. ___________
4.The teacher/ 'd like / help/ you/ with difficult exercises.
_____The teacher'd like to help you with difficult exercises.__________
5.Jane/ not fancy/ read/ science books.
______Jane does not fancy reading science books.__________________
6.Which kind of juice/ you/ dislike/ drink/ the most?
______Which kind of juice do you dislike drinking the most?__________________
7. Ann/ fancy/ do /DIY/ in her free time.
______Ann fancies doing DIY in her free time._________________
8. My father/ prefer/ not eat/ out.
________My father prefers not eating out._______________________
9.Mr.Smith/ love/ go/ shopping/ at weekend.
________Mr.Smith loves going shopping at weekend._____________________
10.Everyone/ adore/ receive/ presents/ on their birthday.
_________Everyone adores receiving presents on their birthday._____________
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
Bài 3:Điền dạng thích hợp của động từ trong ngoặc để hoàn thành các câu sau:
1.Did you enjoy(watch)___watching___the comedy last night?
2.Many people prefer(do)___doing___gardening after their retirement.
3.My cat dislikes(sleep)_____sleeping___on the floor.
4.My father doesn’t mind(work)__working____hard.
5.My cousin doesn’t like(study)_____studying____Math and Chemistry.
a) \(\dfrac{-3}{21}+\dfrac{-2}{7}+\dfrac{1}{3}=\dfrac{-3}{21}+\dfrac{-6}{21}+\dfrac{7}{21}=-\dfrac{2}{21}\)
b) \(\dfrac{-13}{15}+\dfrac{5}{-18}+\dfrac{4}{9}=\dfrac{-78}{90}+\dfrac{-25}{90}+\dfrac{40}{90}=\dfrac{63}{90}=\dfrac{7}{10}\)
c) \(\dfrac{-2}{5}-\left(\dfrac{-3}{11}\right)=\dfrac{-2}{5}+\dfrac{3}{11}=\dfrac{-22}{55}+\dfrac{15}{55}=\dfrac{-7}{55}\)
d) \(\left(-4\right)-\left(\dfrac{-4}{5}\right)-\dfrac{2}{3}=\left(-4\right)+\dfrac{4}{5}-\dfrac{2}{3}=\dfrac{-60}{15}+\dfrac{12}{15}-\dfrac{10}{15}=\dfrac{-58}{15}\)
e) \(\dfrac{3}{5}+\left(\dfrac{-4}{3}\right)-\dfrac{-3}{4}=\dfrac{3}{5}+\left(\dfrac{-4}{3}\right)+\dfrac{3}{4}=\dfrac{36}{60}+\dfrac{-80}{60}+\dfrac{45}{60}=\dfrac{1}{60}\)
g) \(\dfrac{5}{8}-\left(-\dfrac{2}{5}\right)-\dfrac{3}{10}=\dfrac{5}{8}+\dfrac{2}{5}-\dfrac{3}{10}=\dfrac{25}{40}+\dfrac{16}{40}-\dfrac{12}{40}=\dfrac{29}{40}\)
h) \(\dfrac{3}{4}-\left(-\dfrac{5}{3}\right)+\left(\dfrac{1}{12}+\dfrac{2}{9}\right)=\dfrac{3}{4}+\dfrac{5}{3}+\left(\dfrac{3}{36}+\dfrac{8}{36}\right)=\dfrac{27}{36}+\dfrac{60}{36}+\dfrac{11}{36}=\dfrac{98}{36}=\dfrac{49}{18}\)
a) \(\dfrac{-3}{21}+\dfrac{-2}{7}+\dfrac{1}{3}=\dfrac{-3}{21}-\dfrac{6}{21}+\dfrac{7}{21}\\ =\dfrac{-3-6+7}{21}=-\dfrac{2}{21}\)
b) \(\dfrac{-13}{15}+\dfrac{5}{-18}+\dfrac{4}{9}=\dfrac{-78}{90}-\dfrac{25}{90}+\dfrac{40}{90}\\ =\dfrac{-78-25+40}{90}=\dfrac{-63}{90}=-\dfrac{7}{10}\)
c) \(\dfrac{-2}{5}-\left(\dfrac{-3}{11}\right)=-\dfrac{2}{5}+\dfrac{3}{11}\\ =-\dfrac{22}{55}+\dfrac{15}{55}=-\dfrac{7}{55}\)