###### expression 1

$$1\frac{3}{4}-1\frac{11}{17}\times\frac{51}{56}$$

Compute

$$1\frac{3}{4}-1\frac{11}{17}\times\frac{51}{56}=\frac{7}{4}-\frac{28}{17}\times\frac{51}{56}=\frac{7}{4}-\frac{6}{4}=\frac{1}{4}=0,25$$

200 g of an alloy contained 80 g of copper, then how much copper did 300 g of alloy contain?

Compute

If 200 g of an alloy contained 80 g of cooper, then 300 g of an alloy contained X g of cooper. Then

$$\frac{200}{300}=\frac{80}{x}$$

$$x=\frac{300\times80}{200}=120$$ g

###### expression 3

$$(1,5+\frac{1}{4}):18\frac{1}{3}$$

Compute

$$(1,5+\frac{1}{4}):18\frac{1}{3}=(\frac{3}{4}+\frac{1}{4}):\frac{55}{3}=\frac{7}{4}\times\frac{3}{55}=\frac{21}{220}$$

###### expression 4

$$(\frac{5}{6}-\frac{1}{3})+(\frac{1}{2}+\frac{9}{10})$$

Compute

$$(\frac{5}{6}-\frac{1}{3})+(\frac{1}{2}+\frac{9}{10})=\frac{1}{2}+\frac{14}{10}=\frac{5+14}{10}=1,9$$

###### expression 5

$$2\frac{2}{3}:3\frac{17}{21}$$

Compute

$$2\frac{2}{3}:3\frac{17}{21}=\frac{8}{3}:\frac{80}{21}=\frac{8\times{21}}{3\times80}=\frac{7}{10}=0,7$$

The plan is 35 parts per day. The worker made 42 parts. For what percentage did he exceed the plan?

Compute

He made 42 parts. The plan was 35 parts. Then he exeeded the plan on $$\frac{42}{35}=1,2=120%$$%

Into the store they brought 14 tons of cabbage. 30% of the cabbage was sold. How many cabbage is left?

Compute

They sold 30% of the cabbage. The 70% is left.

$$14\times0,7=9,8$$ tons

For 5 tables you have to pay $120. How much do 7 tables cost? Compute 5 tables -$120

7 tables - \$X

$$\frac{5}{7}=\frac{120}{x}$$

$$x=\frac{7\times120}{5}=168$$

For sowing 8 hectares the farmer spent 560 kg of peas. How many kilograms of peas does it require to seed 11 hectares?

Compute

8 ha - 560 kg of peas

11 ha - x kg of peas.

Then $$\frac{8}{11}=\frac{560}{x}; x=\frac{11\times560}{8}=770$$ kg

The farmer planted 150 hectares with wheat and oats in a ratio of 4:2. For how many hectares more did he seed with wheat than oats?

Compute

If x - is wheat and y - oat, then

$$\frac{x}{y}=\frac{4}{2}$$ and $$x+y=150$$

Then $$x=2y$$ (from the first equation)

$$2y+y=150; 3y=150; y=50$$ ha

$$x=100$$ ha

Then he seed wheat on 50 ha more.

###### Ratio

Find the ratio of 4 km to 80 meters

Find the ratio of 4 km to 80 meters

4 km is 4000 m.

Then $$\frac{4000}{80}=50$$

###### Number 1

Find the number if 13% of it is 1,69?

Find the number if 13% of it is 1,69?

$$1,69:0,13=13$$

###### Number 2

Anna, increasing the number 145 by 60%, calculated 25% from the last number. What is the number calculated by Anna?

$$(145+145\times0,6)\times0,25=1,6\times145\times0,25=58$$

###### expresion 21

Compute $$x^3+x^2+x+1$$ when x=4

Compute

$$x^3+x^2+x+1=4^3+4^2+4+1=85$$

###### fraction

Get rid of irrationality in the denominator of the fraction $$\frac{10}{3\sqrt5}$$

$$\frac{10}{3\sqrt5}=\frac{10\sqrt5}{3\times5}=\frac{2\sqrt5}{3}$$

###### expression 29

$$\sqrt{9+4\sqrt5}$$

Compute

$$\sqrt{9+4\sqrt5}=\sqrt{4+4\sqrt5+5}=\sqrt{(2+\sqrt5)^2}=2+\sqrt5$$

###### Number 3

Find the minimal common multiple of 525 and 588

$$525=5^2\times3\times7$$

$$588=2^2\times7^2\times3$$

the minimal common multiple $$525\times7\times2^2=14700$$

###### test

At a test operation 18 people were rated good or excellent. Number of ratings excellent and good is proportional to the numbers 2 and 1. How much less good ratings than excellent?

x - excellent

y - good

x/y=2/1; x=2y

x+y=18; 3y=18; y=6

x=12

12-6=6

###### Number 4

Which figure can be put in place of * in 46 * three-digit number to the resulting number is divisible by 2, 3, 6, 9 at the same time?

The resulting number 46* must be divisible by only 2 and 9 (and then it will be divisible by 2,3,6,9).

Then 46* must be even (only 6 and 8 are fit, because 10 is not a figure).

To be divisible by 9, the sum 4+6+* must be divisible by 9.

4+6+*=10+*

* could be only 8, because 18 is divisible by 9.

###### proportion 2

$$15:2\frac{1}{2}=x:8\frac{1}{3}$$

Find x

$$\frac{15}{\frac{5}{2}}=\frac{x}{\frac{25}{3}}$$

$$\frac{30}{5}=\frac{3x}{25}$$

$$30\times25=3x\times5$$

x=50

###### expresion 22

5,6a+8,4a+186,4

Compute when a=3,5

$$5,6a+8,4a+186,4=14a+186,4=14\times3,5+186,4=235,4$$

###### expresion 25

(0,7*0,4+0,32)*5

Compute

(0,7*0,4+0,32)*5=(0,28+0,32)*5=0,6*5=0,3

###### Z

Find Z if 60% of Z is equal to 108.

108:0,6=180

###### expresion 37

$$(\sqrt2-\sqrt5)(\sqrt2+\sqrt5)$$

Compute

$$(\sqrt2-\sqrt5)(\sqrt2+\sqrt5)=(\sqrt2)^2-(\sqrt5)^2=2-5=-3$$

###### find x

Find x if 40% of x is equal to 52.

Find x if 40% of x is equal to 52.

0,4x=52

x=52:0,4

x=130

###### expression 38

$$\sqrt{3\frac17}\times\sqrt{\frac{7}{88}}$$

Compute

$$\sqrt{3\frac17}\times\sqrt{\frac{7}{88}}=\sqrt{\frac{22}{7}\times\frac{7}{88}}=\sqrt{\frac14}=\frac12=0,5$$

###### expression 38

Compute

$$(81108:27-125\times12):4$$

$$(81108:27-125\times12):4=(3004-1500):4=1504:4=376$$

###### Root

$$\sqrt[4]{\frac{0,0016a^4}{81b^8c^12}}$$

Compute when a=3; b=2; c=1

$$\sqrt[4]{\frac{0,0016a^4}{81b^8c^12}}=\frac{0,2a}{3b^2c^3}=\frac{0,2\times3}{3\times4\times1}=\frac{1}{20}$$

###### expression 44

$$(a^4)^{-\frac34}\times(b^{-\frac23})^{-6}$$

Simplify

$$(a^4)^{-\frac34}\times(b^{-\frac23})^{-6}=a^{4\times(-\frac34)}\times{b^{(-\frac23)\times(-6)}}=a^{-3}b^4=\frac{b^4}{a^3}$$

###### Number 5

Find 12% from 900

Find 12% from 900

900*0,12=108

###### Expression 47

$$1-0,15:(\frac{11}{12}-0,75)$$

Compute

$$1-0,15:(\frac{11}{12}-0,75)=1-\frac{15}{100}:(\frac{11}{12}-\frac{9}{12})=1-\frac{15}{100}\times6=1-0,9=0,1$$