Respuesta :
Answer:
a. 3⁄10 + 6⁄10 = 9/10
b. 1⁄3 + 1⁄4 + 1⁄6 = 3/4
c. 5⁄6 – 3⁄6 = 1/3
d. 2⁄3 – 6⁄10 = 1/15
e. 4⁄10 × 3⁄7 = 6/35
f. 1⁄6 × 6⁄15 = 1/15
g. 1⁄8 ÷ 4⁄9 = 9/32
h. 1⁄5 ÷ 3⁄4 = 4/15
Step-by-step explanation:
a. 3⁄10 + 6⁄10
= 3*1 + 6*1 / 10
= 3+6/10
= 9/10
b. 1⁄3 + 1⁄4 + 1⁄6
since denominators are different we take LCM of 3,4,6 which is 12
= 1*4 + 1*3 + 1*2 / 12
= 4+3+2/12
= 9 ÷ 3 / 12 ÷ 3
= 3 / 4
c. 5⁄6 – 3⁄6
= 5 - 3 / 6
= 2 ÷ 2 / 6 ÷ 2 = 1/3
d. 2⁄3 – 6⁄10
LCM of 3 and 10 is 30
= 2 * 10 - 6 * 3 / 30
= 20 - 18 / 30
= 2 ÷ 2 / 30 ÷ 2 = 1/15
e. 4⁄10 × 3⁄7
= 12 ÷ 2 / 70 ÷ 2 = 6/35
f. 1⁄6 × 6⁄15
= 6 ÷ 6/90 ÷ 6 = 1/15
g. 1⁄8 ÷ 4⁄9
= 1/ 8 * 9/4
=9/32
h. 1⁄5 ÷ 3⁄4
=1/5 * 4/3
= 4/15
Answer:
a)
[tex]\dfrac{9}{10}[/tex]
b)
[tex]\dfrac{3}{4}[/tex]
c)
[tex]\dfrac{1}{3}[/tex]
d)
[tex]\dfrac{1}{15}[/tex]
e)
[tex]\dfrac{6}{35}[/tex]
f)
[tex]\dfrac{1}{15}[/tex]
g)
[tex]\dfrac{9}{32}[/tex]
h)
[tex]\dfrac{4}{15}[/tex]
Step-by-step explanation:
a)
[tex]\dfrac{3}{10}+\dfrac{6}{10}[/tex]
Now, this expression could also be given by:
[tex]=\dfrac{6+3}{10}\\\\=\dfrac{9}{10}[/tex]
b)
[tex]\dfrac{1}{3}+\dfrac{1}{4}+\dfrac{1}{6}[/tex]
On taking the least common multiple of the denominator we have:
[tex]L.C.M\{3,4,6\}=12[/tex]
Hence, we have:
[tex]=\dfrac{1\times 4+1\times 3+1\times 2}{12}\\\\=\dfrac{4+3+2}{12}\\\\=\dfrac{9}{12}\\\\=\dfrac{3\times 3}{3\times 4}\\\\=\dfrac{3}{4}[/tex]
c)
[tex]\dfrac{5}{6}-\dfrac{3}{6}[/tex]
Now, this expression could also be given by:
[tex]=\dfrac{5-3}{6}\\\\=\dfrac{2}{6}[/tex]
which on reducing to the lowest terms is given by:
[tex]=\dfrac{1}{3}[/tex]
d)
[tex]\dfrac{2}{3}-\dfrac{6}{10}[/tex]
on reducing the second term we have:
[tex]=\dfrac{2}{3}-\dfrac{3}{5}[/tex]
Now on simplifying the expression we have:
[tex]=\dfrac{2\times 5-3\times 3}{15}\\\\=\dfrac{10-9}{15}\\\\=\dfrac{1}{15}[/tex]
e)
[tex]\dfrac{4}{10}\times \dfrac{3}{7}[/tex]
We know that:
[tex]\dfrac{4}{10}=\dfrac{2}{5}[/tex]
Hence, we have:
[tex]=\dfrac{2}{5}\times \dfrac{3}{7}\\\\=\dfrac{6}{35}[/tex]
f)
[tex]\dfrac{1}{6}\times \dfrac{6}{15}[/tex]
which on simplifying gives:
[tex]=\dfrac{1}{15}[/tex]
g)
[tex]\dfrac{\dfrac{1}{8}}{\dfrac{4}{9}}[/tex]
which is further written as:
[tex]=\dfrac{1\times 9}{4\times 8}\\\\=\dfrac{9}{32}[/tex]
h)
[tex]\dfrac{\dfrac{1}{5}}{\dfrac{3}{4}}[/tex]
which is given by:
[tex]=\dfrac{1\times 4}{3\times 5}\\\\=\dfrac{4}{15}[/tex]
