a, rút gọn
24/32 ; 14/35; 30/25 ;63/36
b, quy đồng mẫu số các phân số
3/5 và 4/7 2/3 và 5/6 4/9 vaf1/6
rút gọn :
A=1+3+32+33+....+3100
B=1+12+24+...+2100
C=1-3+32-33+...+3100
A = 1 + 3 + 32 + 33 + ... + 3100
3A = 3 + 32 + 33 +34+ .... + 3101
3A - A = (3 + 32 + 34 + ... + 3101) - (1 + 3 + 32 + 33 + ... + 3100)
2A = 3 + 32 + 34 + ... + 3101 - 1 - 3 - 32 - 33 - ... - 3100
2A = (3 - 3) + (32 - 32) + ... + (3100 - 3100) + (3101 - 1)
2A = 3101 - 1
A = \(\dfrac{3^{101}-1}{2}\)
Rút gọn rồi tính
A.4/5+3/15 B.2/3+32/24 C.5/6+15/18
a) \(\dfrac{4}{5}+\dfrac{3}{15}=\dfrac{4}{5}+\dfrac{1}{5}=\dfrac{5}{5}=1\)
b) \(\dfrac{2}{3}+\dfrac{32}{24}=\dfrac{2}{3}+\dfrac{4}{3}=\dfrac{6}{3}=2\)
c) \(\dfrac{5}{6}+\dfrac{15}{18}=\dfrac{5}{6}+\dfrac{5}{6}=\dfrac{10}{6}=\dfrac{5}{3}\).
Rút gọn các phân số sau:\(\frac{{24}}{{108}};\,\,\frac{{80}}{{32}}\)
Ta có:
\(\begin{array}{l}\frac{{24}}{{108}} = \frac{{24:12}}{{108:12}} = \frac{2}{9};\\\frac{{80}}{{32}} = \frac{{80:16}}{{32:16}} = \frac{5}{2}\end{array}\)
Rút gọn các phân số sau:
24/32=....................=
75/100=................=
45/60=.....................=
27/63=.................=
\(\dfrac{24}{32}=\dfrac{24:8}{32:8}=\dfrac{3}{4}\)
\(\dfrac{75}{100}=\dfrac{75:25}{100:25}=\dfrac{3}{4}\)
\(\dfrac{45}{60}=\dfrac{45:15}{60:15}=\dfrac{3}{4}\)
\(\dfrac{27}{63}=\dfrac{27:9}{63:9}=\dfrac{3}{7}\)
Rút gọn các phân số sau:
24/32 45/60 75/100 27/63
\(\dfrac{24}{32}=\dfrac{24:8}{32:8}=\dfrac{3}{4}\)
\(\dfrac{45}{6}=\dfrac{45:3}{6:3}=\dfrac{15}{2}\)
\(\dfrac{75}{100}=\dfrac{75:25}{100:25}=\dfrac{3}{4}\)
\(\dfrac{27}{63}=\dfrac{27:9}{63:9}=\dfrac{3}{7}\)
Rút gọn các phân số
18/27; 24/32; 15/25.
Rút gọn rồi tính :
a) 4/5 + 3/15 b)2/3 + 32/24 c) 5/6 + 15/18
4/5 + 1/5 = 5/5=1
2/3 + 4/3 = 6/3 = 2
5/6 +5/6 = 10/6 = 5/3
Rút gọn psố: 2×4+2×4×8+4×8×16+8×18×32 phần 3×3+2×6×8+4×12×16+8×24×32
a)Rút gọn phân số : \(\dfrac{25^{28}+25^{24}+25^{20}+.....+25^4+1}{25^{30}+25^{28}+....+25^2+1}\)
b) Cho S = 1-3 + 32-33+.....+398-399
a) Ta có: \(\dfrac{25^{28}+25^{24}+25^{20}+...+25^4+1}{25^{30}+25^{28}+...+25^2+1}\)
\(=\dfrac{25^{24}\left(25^4+1\right)+25^{16}\left(25^4+1\right)+...+\left(25^4+1\right)}{25^{28}\left(25^2+1\right)+25^{24}\left(25^2+1\right)+...+\left(25^2+1\right)}\)
\(=\dfrac{\left(25^4+1\right)\left(25^{24}+25^{16}+25^8+1\right)}{\left(25^2+1\right)\left(25^{28}+25^{24}+...+1\right)}\)
\(=\dfrac{\left(25^4+1\right)\cdot\left[25^{16}\left(25^8+1\right)+\left(25^8+1\right)\right]}{\left(25^2+1\right)\left[25^{24}\left(25^4+1\right)+25^{16}\left(25^4+1\right)+25^8\left(25^4+1\right)+\left(25^4+1\right)\right]}\)
\(=\dfrac{\left(25^4+1\right)\left(25^8+1\right)\left(25^{16}+1\right)}{\left(25^2+1\right)\left(25^4+1\right)\left(25^{24}+25^{16}+25^8+1\right)}\)
\(=\dfrac{\left(25^8+1\right)\left(25^{16}+1\right)}{\left(25^2+1\right)\left[25^{16}\left(25^8+1\right)+\left(25^8+1\right)\right]}\)
\(=\dfrac{\left(25^8+1\right)\left(25^{16}+1\right)}{\left(25^2+1\right)\left(25^8+1\right)\left(25^{16}+1\right)}\)
\(=\dfrac{1}{25^2+1}=\dfrac{1}{626}\)
các bạn ơi giúp mình với 2 .rút gọn rồi tính a)4/5 +3/15 ;2/3 +32/24 ; 5/6+15/18 . Cảm ơn các bạn nha
4/5 + 3/15 = 1
2/3 + 32/24 = 2
5/6 + 15/18 = 5/3
k nhé:))
\(\frac{4}{5}+\frac{3}{15}=\frac{4}{5}+\frac{1}{5}=\frac{4+1}{5}=\frac{5}{5}=1\)
\(\frac{2}{3}+\frac{32}{24}=\frac{2}{3}+\frac{4}{3}=\frac{2+4}{3}=\frac{6}{3}=2\)
\(\frac{5}{6}+\frac{15}{18}=\frac{5}{6}+\frac{5}{6}=\frac{5+5}{6}=\frac{10}{6}\)
HT