Question

Cw 7.1 7.2 homework help

Answer 1

QUESTION 1

The given ratio is

$40:15$


Let us write the ratio in terms of prime factors to obtain,


$= {2}^{3} \times 5:3 \times 5$



We cancel out the common factor of

5 to get


$= {2}^{3}:3$

We simplify to get,

$= 8:3$

$\therefore 40:15 =8:3$


QUESTION 2

The given ratio is
$49 : 7$

We factor each term in the ratio, it will now be

$= 7 \times 7: 7$


If we cancel out the common factor of 7, the ratio will now be

$= 7 : 1$


QUESTION 3



We want to simplify 80 inches over 10 days, which is,

$\frac{80 \: inches}{10 \: days}$

We convert this into ratio to get,




$80 \:inches:10 \: days$


We factor the terms in the ratio to obtain,

$8 \times 10\:inches:10 \: days$

We cancel out common factors to obtain,


$8 \:inches:1\: days$


QUESTION 4


3 ounces costs $2.70.

We can write this as,


$\frac{3}{ 2.7 }$

We change the denominator to fraction,


$= \frac{3}{ \frac{27}{10} }$



We change the first bar to a normal division sign to get,

$= 3 \div \frac{27}{10}$



We now multiply by the reciprocal to get,

$= 3 \times \frac{10}{27}$


$= \frac{10}{9}$



We convert this back to ratio to get,

$3ounce: 2.7 \: dollars= 10 \: ounce: 9 \: dollars$


QUESTION 5

$10 \: ounce: 3.9 \: dollars$


We multiply each term in the ratio by 10, to get,


$10 \times 10 \: ounce: 3.9 \times 10 \: dollars$


$100\: ounce: 39 \: dollars$


QUESTION 6

$12 \: boxes: 96 \: books$

If we factor each term, the ratio

$= 12 \: boxes: 12 \times 8 \: books$

We cancel out the common factors and the ratio will be

$= 1 \: box: 8 \: books$



QUESTION 7

The ratio of the sides of the triangle is

$3:4:6$


The total ratio is
$= 3 + 4 + 6 = 13$



The shortest sides corresponds to the least ratio which is 3,


The shortest side is
$= \frac{3}{13} \times 104$
$= 24 \: units$


The length of the medium side is



$= \frac{4}{13} \times 104$

$= 32 \: units$


The length of the longest side,

$= \frac{6}{13} \times 104$

$= 48 \: units$



QUESTION 8.



The ratio of the sides of the triangle is


$7 : 9: 12$



The total ratio is

$7 + 9 + 12 = 28$

The shortest sides of the triangle corresponds to the least ratio which is 7,



The shortest side
$= \frac{7}{28} \times 84$
$= 21 \: units$


The length of the medium side is

$= \frac{9}{28} \times 84$

$= 27 \: units$


The length of the longest side is

$= \frac{12}{28} \times 84$
$= 36 \: units$



QUESTION 9.


The given ratio is

$6:7:9$


The total ratio is

$= 6 + 7 + 9 = 22$

The length of the shortest side is,


$= \frac{6}{22} \times 77$


$21 \: units$


The length of the medium side is

$= \frac{7}{22} \times 77$

$= 24.5 \: units$



The length of the shortest side is

$= \frac{9}{22} \times 77$

$= 31.5 \: units$


QUESTION 4

The given ratio is

$4:5:6$


The total ratio is
$= 4 + 5 + 6 = 15$
The sum of the interior angles of the triangle is 180°.


The measure of the smallest angle is
$= \frac{4}{15} \times 180 \degree$


$= 48 \degree$
The measure of the medium angle is,

$= \frac{5}{15} \times 180 \degree$

$= 60 \degree$


The measure of the biggest angle is

$= \frac{6}{15} \times 180 \degree$


$= 72 \degree$



We could have also gotten this angle by subtracting the measure of the sum of smallest and the medium angle from 180°,

$= 180 - (48 + 60)$


$= 180 -108$



$= 72 \degree$


QUESTION 11

The given ratio is

$5:7:8$


The sum of the total ratio is

$= 5 + 7 + 8 = 20$

The measure of the biggest angle corresponds to the biggest ratio which is 8.


The biggest angle is


$= \frac{8}{20} \times 180 \degree$


$= 72 \degree$



The measure of the smallest angle corresponds to 5,


$= \frac{5}{20} \times 180 \degree$


$= 45 \degree$

The measure of the third angle is
$= \frac{7}{20} \times 180 \degree$


$= 63 \degree$