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3 years ago

3 1⁄8 − 1 7⁄8 = ⁄8 (Write your answer as a mixed number.)

Mathematics

2 answers:

valentinak56 [21]3 years ago

5 0

Step-by-step explanation:

$\bold{METHOD\ 1}\\\\3\dfrac{1}{8}=2+1\dfrac{1}{8}=2+\dfrac{9}{8}=2\dfrac{9}{8}\\\\3\dfrac{1}{8}-1\dfrac{7}{8}=2\dfrac{9}{8}-1\dfrac{7}{8}=(2-1)+\dfrac{9-7}{8}=1+\dfrac{2}{8}=1\dfrac{2:2}{8:2}=1\dfrac{1}{4}$

$\bold{METHOD\ 2}\\\\3\dfrac{1}{8}-1\dfrac{7}{8}=(3-1)+\dfrac{1-7}{8}=2+\dfrac{-6}{8}=2-\dfrac{6}{8}=1\dfrac{8}{8}-\dfrac{6}{8}=1\dfrac{8-6}{8}=1\dfrac{2}{8}=1\dfrac{1}{4}$

$\bold{METHOD\ 3}\\\\\text{convert to the decimal:}\\\\3\dfrac{1}{8}=3+(1:8)=3+0.125=3.125\\\\1\dfrac{7}{8}=1+(7:8)=1+0.875=1.875\\\\3\dfrac{1}{8}-1\dfrac{7}{8}=3.125-1.875=1.25=1\dfrac{25}{100}=1\dfrac{25:25}{100:25}=1\dfrac{1}{4}$

kotegsom [21]3 years ago

3 0

I think the answer is 1 2/8

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To find the sixth term, substitute $n=6$ in $a_{n}=a_{1} \cdot r^{n-1}$

$\begin{aligned}a_{6} &=(48) \cdot\left(-\frac{1}{4}\right)^{6-1} \\&=(48) \cdot\left(-\frac{1}{4}\right)^{5} \\&=(48)\left(-\frac{1}{1024}\right) \\a_{5} &=-0.046875\end{aligned}$

To find the sum of the first six terms:

The general formula to find Sn for $|r|$ is $S_{n}=\frac{a\left(1-r^{n}\right)}{1-r}$

$\begin{aligned}S_{6} &=\frac{48\left(1-\left(-\frac{1}{4}\right)^{6}\right)}{1-\left(-\frac{1}{4}\right)} \\&=\frac{48\left(1-\frac{1}{4096}\right)}{1+\frac{1}{4096}} \\&=\frac{48(0.95)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{48(0.9998)}{5} \\&=\frac{47.9904}{5} \\&=38.39\end{aligned}$

Thus, the sum of first six terms is 38.39

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3 years ago