Plz solve using a bar model and will mark brainliest whoever’s correct with reasonable work

Mathematics

1 answer:

marishachu [46]4 years ago

4 0

You just need to do 12 1/5 ÷ 1 4/5.
To do this, first convert both fractions to improper fractions or topheavy fractions.

12 1/5 -
15 × 5 is 60, 60 + 1 is 61 so 12 1/5 = 61/5

1 4/5 -
1 × 5 is 5 and 5 + 4 is 9. 1 4/5 = 9/5

To divide fractions, you do keep, chang, flip (keep the 1st fraction, change the ÷ to ×, and flip the 2nd fraction)

the question starts as 61/5 ÷ 9/5 and becomes 61/5 × 5/9

multiplication in fractions is literally just numerator × numerator / denominator × denominator.

61 × 5 is 305. 5 × 9 is 45. the fraction is 305/45.

however, we need a whole number. 305/45 converted into a decimal is 6.7777778 (6.7 recurring). obviously you can't put a fraction of a book onto a shelt, so you round it down to the nearest whole number, which is 6.

final answer: 6

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Find the SUm of the infinite series.

givi [52]

I'll do problem 13 to get you started.

The expression $4\left(\frac{2^n}{7^n}\right)$ is the same as $4\left(\frac{2}{7}\right)^n$

Then we can do a bit of algebra like so to change that n into n-1

$4\left(\frac{2}{7}\right)^n\\\\4\left(\frac{2}{7}\right)^n*1\\\\4\left(\frac{2}{7}\right)^n*\left(\frac{2}{7}\right)^{0}\\\\4\left(\frac{2}{7}\right)^n*\left(\frac{2}{7}\right)^{1-1}\\\\4\left(\frac{2}{7}\right)^n*\left(\frac{2}{7}\right)^{1}*\left(\frac{2}{7}\right)^{-1}\\\\4*\left(\frac{2}{7}\right)^{1}\left(\frac{2}{7}\right)^n*\left(\frac{2}{7}\right)^{-1}\\\\\frac{8}{7}\left(\frac{2}{7}\right)^{n-1}\\\\$

This is so we can get the expression in a(r)^(n-1) form

a = 8/7 is the first term of the geometric sequence
r = 2/7 is the common ratio

Note that -1 < 2/7 < 1, which satisfies the condition that -1 < r < 1. This means the infinite sum converges to some single finite value (rather than diverge to positive or negative infinity).

We'll plug those a and r values into the infinite geometric sum formula below

S = a/(1-r)

S = (8/7)/(1 - 2/7)

S = (8/7)/(5/7)

S = (8/7)*(7/5)

S = 8/5

S = 1.6

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Answer in fraction form = 8/5

Answer in decimal form = 1.6

7 0

3 years ago