Inspecting expression details
I'm looking at this expression, and the character after the dot could be "33" or "3.3." It’s important to examine the context carefully. I see it right beside the 4.395 row and under 4.394 with the expression: "д) (4/7 - 3/5) · 33." It looks like "33," but might actually be decimal "3.3." I really want to make sure I’m interpreting this correctly, as it seems to be a textbook exercise designed to utilize the distributive property.Calculating expressions
I see a 33; instead of 3,3, so it could just be 33 without a visible comma. Now, I need to be thorough and calculate each part carefully.
For a), I have: 0.9*(-0.4) - 0.7*(-0.4), which breaks down to -0.08.
For b), I get 4/130.6 - 0.6(-9/13), simplifying to 0.6.
In c), I find -8/115/6 + 5/63/11, which results in -25/66.Inspecting fractions in an image
I see the fraction 2 over 3, so let's take a closer look. The image at approximately x638 seems to depict something like 1 \frac{2}{3} · 2.8 - 2 \frac{2}{9} · (-6.2). The text description suggests that after the 1, the fraction has a top value of 2 and a bottom value of 3, not 13. I wonder if the user can zoom in on the image because I can analyze the raster details. The image might be cropped around x 600-900 and y 540, and it seems rotated 90 degrees, indicating a landscape orientation.Breaking down calculations
I’m tackling some calculations involving mixed numbers and decimals. I might have misread one fraction — it should be 1 2/3 rather than 1 2/13. If I calculate \( -2 \frac{2}{9} \times (-6.2) \), that gets messy. I notice they don’t have common factors, and I’m trying to see if the distributive property applies here. Ultimately, I find that the sum results in \( -82/9 \). It’s convoluted, but I think I’m getting there!Clarifying calculations
This looks much better! If the first mixed fraction is 1 2/3, then my first product \( 14/3 \) simplifies to \( 42/9 \), while the second gives me \( -124/9 \), totaling \( -82/9 \), which is also \( -9 1/9 \). But I’m questioning if the expression is meant to have a common denominator. Using \( 2.8 \) as \( 14/5 \) and \( 6.2 \) as \( -31/5 \) aligns somewhat, so my results still hold. It’s not super neat, but I think I’m on the right track!Revising calculations
I'm running through some calculations here with fractions and mixed numbers. I think I've got the expression right, but I need to double-check everything. There seems like maybe a typo in the second operation.
When I examine the components, I realize subtracting a negative could have led to incorrect conclusions. If I plug in the right values, I'm seeing an answer of 166/9 or 18 4/9, which might indicate I need to clarify the signs. I need to ensure I'm keeping things consistent!Clarifying expressions
I’m working through some mathematical expressions right now. The expression looks to be 1 2/3 · 2.8 - 2 2/9 · (-6.2), which deliberately plays with the idea of subtracting a negative. I’m getting an ugly number like 166/9, but it seems like it could simplify nicely to 18 4/9.
I think the choice of numbers might show a common scenario and it all ends up being reasonable, particularly with that mixed number answer! I'm feeling better about this calculation!Calculating values and simplification
I’m considering whether I can simplify things. I found that the greatest common divisor (gcd) of 25 and 66 is 1, so they are relatively prime.
Then I calculated g as 166 divided by 9, which gives me 18 and 4/9. It feels straightforward, but I wonder if there’s a simpler way to express these fractions or calculations. Overall, I'm working through it step-by-step to ensure clarity!
Ответ:
а) \(-0{,}08\);
б) \(0{,}6\);
в) \(-\dfrac{25}{66}\);
г) \(18\dfrac49\);
д) \(-\dfrac{33}{35}\);
е) \(-50\).
Решение
Используем распределительное свойство:
\[ ab-cb=(a-c)b,\qquad ab+cb=(a+c)b. \]
а)
\[ 0{,}9\cdot(-0{,}4)-0{,}7\cdot(-0{,}4) =(-0{,}4)(0{,}9-0{,}7) =-0{,}4\cdot0{,}2=-0{,}08. \]
Проверка:
\[ -0{,}36-(-0{,}28)=-0{,}08. \]
б)
\[ \frac4{13}\cdot0{,}6-0{,}6\cdot\left(-\frac9{13}\right) =0{,}6\left(\frac4{13}+\frac9{13}\right) =0{,}6\cdot1=0{,}6. \]
в)
\[ -\frac8{11}\cdot\frac56+\frac56\cdot\frac3{11} =\frac56\left(-\frac8{11}+\frac3{11}\right) =\frac56\cdot\left(-\frac5{11}\right) =-\frac{25}{66}. \]
г)
\[ 1\frac23=\frac53,\quad 2\frac29=\frac{20}{9}, \quad 2{,}8=\frac{14}{5},\quad -6{,}2=-\frac{31}{5}. \]
\[ \frac53\cdot\frac{14}{5} -\frac{20}{9}\cdot\left(-\frac{31}{5}\right) =\frac{14}{3}+\frac{124}{9} =\frac{42+124}{9} =\frac{166}{9}=18\frac49. \]
д)
\[ \left(\frac47-\frac35\right)\cdot33 =\left(\frac{20}{35}-\frac{21}{35}\right)\cdot33 =-\frac1{35}\cdot33=-\frac{33}{35}. \]
е)
\[ \left(-1\frac23-1\frac19\right)\cdot18 =\left(-\frac53-\frac{10}{9}\right)\cdot18 =\left(-\frac{15}{9}-\frac{10}{9}\right)\cdot18 =-\frac{25}{9}\cdot18=-50. \]
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