Question

sam od education, scholastic.com/math16/student/client/ SUCCESS ZONE Block e Tople 3 Strategies for Dividing Fractions In one year, the Perseid meteor shower had a meteor appear every 15 minutes 1 on average. That same year, the Leonid meteor shower had a meteor appear every a? minutes on average.

Answer 1

You have to determine how many more meteors were seen each minute in the Perseid meteor shower than in the Leonid meteor shower.

The Perseid meteor shower had a meteor appear every 1 1/5 minutes on average.

The Leonid meteor shower had a meteor appear every 4 2/3 minutes on average.

To make all calculations easy, the first step is to express both mixed numbers as fractions:

Perseid meteor shower

-To express the mixed number 1 1/5 as a fraction, the first step is to divide the whole number by 1, then add 1/5:

$1\frac{1}{5}=\frac{1}{1}+\frac{1}{5}$

-To add both fractions they must be expressed under the same denominator, in this case, the denominator must be 5. So multiply the first fraction (both, the numerator and denominator) by 5:

$\frac{1\cdot5}{1\cdot5}+\frac{1}{5}=\frac{5}{5}+\frac{1}{5}$

-And add them

$\frac{5}{5}+\frac{1}{5}=\frac{5+1}{5}=\frac{6}{5}$

For this meteor shower, there was 1 meteor every 6/5minutes.

Leonid meteor shower

To express the mixed number 4 2/3 as a fraction, the first step is to divide the whole number by one to write it as a fraction, then add 2/3:

$\frac{4}{1}+\frac{2}{3}$

-As before, to be able to add both fractions, first, you have to express them using the same denominator, which is 3, so you have to multiply the first fraction by 3:

$\frac{4\cdot3}{1\cdot3}+\frac{2}{3}=\frac{12}{3}+\frac{2}{3}$

-Next is to add them to determine the fraction equivalent to 4 2/3

$\frac{12}{3}+\frac{2}{3}=\frac{12+2}{3}=\frac{14}{3}$

For this meteor shower, there was one meteor every 14/3 minutes.

Once both ratios are expressed as fractions, using cross multiplication, you have to determine how many meteors were seen each minute:

Perseid meteor shower

6/5min______1meteor

1 min ________x meteors

Both relationships are at the same ratio so that:

$\begin{gathered} \frac{1}{\frac{6}{5}}=\frac{x}{1} \\ \frac{6}{5}=x \end{gathered}$

For the Perseid meteor shower, there were 6/5 meteors per minute.

Leonid meteor shower

14/3min_____1 meteor

1min_____x meteors

Both relationships are at the same ratio so that:

$\begin{gathered} \frac{1}{\frac{14}{3}}=\frac{x}{1} \\ \frac{3}{14}=x \end{gathered}$

For the Leonid meteor shower, there were 3/14meteors per minute

Finally, to determine how many more meteors were seen per minute on the Perseid shower than the Leonid shower, you have to divide both ratios, that is, divide the meteors per minute on the Perseid shower by the meteors per minute on the Leonid shower:

$\frac{6}{5}\div\frac{3}{14}$

To divide two fractions, you have to multiply the dividend fraction by the reciprocal fraction of the divisor, this means that you have to invert the second fraction and multiply it by the first one:

-Determine the reciprocal fraction of 3/14:

$\frac{3}{14}\to\frac{14}{3}$

-Multiply both fractions:

$\frac{6}{5}\cdot\frac{14}{3}=\frac{6\cdot14}{5\cdot3}=\frac{84}{15}$

Both 84 and 15 are divisible by 3, to simplify the result, divide both numbers by 3:

$\frac{84\div3}{15\div3}=\frac{28}{5}$

So, there were 28/5 times as many meteors in the Perseid shower as in the Leonid shower.

Next is to express the result as a mixed fraction, divide 28 by 5, to determine how many "whole numbers" are in the fraction:

$28\div5=5.6$

This means that there are 5 whole numbers on 28/5 and a remainder of 0.6.

To determine how many fifths corresponds to 0.6, multiply the decimal number by the denominator "5"

$0.6\cdot5=3$

This means that 0.6 is equal to 3 times 1/5 or, 3/5

So the result expressed as mixed numbers is:

$\frac{28}{5}=5\frac{3}{5}$

Each minute, there were 5 3/5 times as many meteors in the Perseid meteor shower as in the Leonid meteor shower.