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Solve Exercises Lesson 20. Percentage (Chapter 5 Math 7 Connect)
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Solve problem 6.1 page 7 Math textbook 7 Connecting knowledge volume 2 – KNTT
Replace the following ratio with the ratio of integers:
\(a)\dfrac{{10}}{{16}}:\dfrac{4}{{21}};b)1,3:2,75;c)\dfrac{{ – 2}}{5 }:0.25\)
Solution method
Step 1: Calculate the ratio
Step 2: Return to the simplest fraction form
Step 3: Write the ratio below and put the ratio between the integers
Detailed explanation
\(\begin{array}{l}a)\dfrac{{10}}{{16}}:\dfrac{4}{{21}} = \dfrac{{10}}{{16}}.\ dfrac{{21}}{4} = \dfrac{{105}}{{32}} = 105:32;\\b)1,3:2.75 = \dfrac{{1,3}}{{ 2.75}} = \dfrac{{130}}{{275}} = \dfrac{{26}}{{55}} = 26:55;\\c)\dfrac{{ – 2}}{5 }:0.25 = \dfrac{{ – 2}}{5}:\dfrac{1}{4} = \dfrac{{ – 2}}{5}.\dfrac{4}{1} = \dfrac {{ – 8}}{5} = ( – 8):5\end{array}\)
Solve lesson 6.2 on page 7 Math 7 textbook Connecting knowledge volume 2
Find the equal ratios of the following ratios and then make the ratio:
\(12:30;\dfrac{3}{7}:\dfrac{{18}}{{24}};2,5:6,25\)\(12:30;\dfrac{3}{7) }:\dfrac{{18}}{{24}};2,5:6,25\)
Solution method
Step 1: Calculate the ratios.
Step 2: Find 2 equal proportions
Step 3: Make a ratio
Detailed explanation
\(\begin{array}{l}12:30 = \dfrac{{12}}{{30}} = \dfrac{2}{5};\\\dfrac{3}{7}:\dfrac{ {18}}{{24}} = \dfrac{3}{7}.\dfrac{{24}}{{18}} = \dfrac{9}{{14}};\\2,5:6 ,25 = \dfrac{{2,5}}{{6,25}} = \dfrac{{250}}{{625}} = \dfrac{2}{5}\end{array}\)
Thus, the equal ratios are: 12:30 and 2.5 : 6.25.
We get the ratio: 12:30 = 2.5 : 6.25
Solve lesson 6.3, page 7 Math textbook 7 Connecting knowledge volume 2
Find x in the following proportions:
\(a)\dfrac{x}{6} = \dfrac{{ – 3}}{4};b)\dfrac{5}{x} = \dfrac{{15}}{{ – 20}}\ )
Solution method
Using the proportionality property: If \(\dfrac{a}{b} = \dfrac{c}{d}\) then ad =bc
Detailed explanation
\(\begin{array}{l}a)\dfrac{x}{6} = \dfrac{{ – 3}}{4}\\x = \dfrac{{( – 3).6}}{4 }\\x = \dfrac{{ – 9}}{2}\end{array}\)
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So \(x = \dfrac{{ – 9}}{2}\)
\(\begin{array}{l}b)\dfrac{5}{x} = \dfrac{{15}}{{ – 20}}\\x = \dfrac{{5.( – 20)}} {{15}}\\x = \dfrac{{ – 20}}{3}\end{array}\)
So \(x = \dfrac{{ – 20}}{3}\)
Solve problem 6.4, page 7 Math 7 Textbook Connecting knowledge volume 2
Make all possible proportions from Equation 14.(-15)= (-10).21
Solution method
If ad= bc (a,b,c,d \( \ne \) 0), we have the following proportions:
\(\dfrac{a}{b} = \dfrac{c}{d};\dfrac{a}{c} = \dfrac{b}{d};\dfrac{d}{b} = \dfrac{ c}{a};\dfrac{d}{c} = \dfrac{b}{a}\)
Detailed explanation
The possible ratios are:
\(\dfrac{{14}}{{ – 10}} = \dfrac{{21}}{{ – 15}};\dfrac{{14}}{{21}} = \dfrac{{ – 10} }{{ – 15}};\dfrac{{ – 15}}{{ – 10}} = \dfrac{{21}}{{14}};\dfrac{{ – 15}}{{21}} = \dfrac{{ – 10}}{{14}}\)
Solution 6.5 page 7 Math textbook 7 Connecting knowledge volume 2
To mix physiological saline, people need to mix in the right ratio. Know that for every 3 liters of pure water mixed with 27 g of salt. If there is 45 g of salt, how many liters of pure water should be mixed to get physiological saline?
Solution method
The ratio of the volume of pure water to the mass of salt to be mixed is constant
Detailed explanation
Call the number of liters of pure water to be mixed: x (liter) (x > 0)
We have the final scale: \(\dfrac{3}{{27}} = \dfrac{x}{{45}} \Rightarrow x = \dfrac{{3.45}}{{27}} = 5\)
So need 5 liters of water
Solve problem 6.6 page 7 Math textbook 7 Connecting knowledge volume 2
To plow a field in 14 days, 18 plows must be used. How many plows should be used to plow that field in 12 days? (Knowing the productivity of the plows is the same)?
Solution method
The product of the number of plows and the completion time remains constant
Detailed explanation
Let the number of plows needed to plow that field in 12 days is: x (machine) (x \( \in \) N)\( \in \)
Since the product of the number of plows and the time to complete is constant, then:
\(14.18 = 12.x \Rightarrow x = 21\)
So need 21 plows
