MATHEMATICS MIDDLE SCHOOL

mark has 312 books in his bookcases. He has 11 times as many fiction books as nonfiction books. How many fiction books does Mark have? please tell me how you got answer step by step? thank you

Answers

Answer 1
Answer:

Answer: 286


Step-by-step explanation:

Let the number of non fiction books be 'x'

Then the number of fiction books = 11x

Total books in Mark's bookcase= 312

According to the given situation the equation will be

x+11x=312\n\Rightarrow12x=312..............[\text{combine like terms}]\n\Rightarrow\ x=26.......[\text{divide 12 on both sides}]

Hence, the number of non fiction books=26

and the number of Fiction books =11*26=286
Answer 2
Answer: Let number of non/fraction books =x
Then number of fiction books=11x
So, we form the equation x+11x=312
12x=312 x=26 so mark has 26*11=286 fiction books

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A girl is half as old as her sister and is also two years younger than her brother. If the sum of the three children's ages is $34$ years, what is the product of their ages?
1/5(2x-15) + 3/5x = 4 1/4 x=?

X = 8, y = 20. Find y when x = 42

Answers

Create proportions to do this question
When x is 8, y is 20
when x is 42, y is ?

(8)/(20) = (42)/(?)

Do cross multiplication:

8 × ? = 20 × 42
8 × ? = 840

Divide by 8 to isolate the unknown

(8*?)/(8) = (840)/(8)
8 and 8 cancels out

? = 105

y is 105 when x is 42
8 / 20 = 42 / y;
Then, y = ( 42 × 20 ) / 8 ;
y = 840 / 8 ;
y = 105;

How do you subtract 9 2/6 - 6 5/6

Answers

The result of subtraction of 9 2/6 - 6 5/6 is: 2 1/2.

Here, we have,

To subtract mixed numbers like 9 2/6 and 6 5/6, you can follow these steps:

Step 1: Convert the mixed numbers into improper fractions.

9 2/6 can be written as 9 + 2/6 = 9 + 1/3 = 27/3 + 1/3 = 28/3.

6 5/6 can be written as 6 + 5/6 = 6 + 5/6 = 36/6 + 5/6 = 41/6.

Step 2: Subtract the two fractions.

28/3 - 41/6 = (28 * 2)/(3 * 2) - 41/6 = 56/6 - 41/6 = 15/6.

Step 3: Simplify the resulting fraction, if possible.

15/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 3.

15/6 = (15/3) / (6/3) = 5/2.

Therefore, 9 2/6 - 6 5/6 is equal to 5/2 or 2 1/2.

To learn more on subtraction click:

brainly.com/question/2346316

#SPJ6
Well, first you would multiply the full number ( 9 and 6) by the denominator of the fraction (9*6 and 6*6). you would get 54 and add it to the numerator of the fraction getting 56/6 and 41/6. You would then subtract the 2 numerators from each other getting 15/6. Finally you would simplify the number to get 2 and 1/2 (3/6)

what algorithm (rule) will produce the correct result for the sum "a+b" where a and b each represent any rational number.

Answers

Answer:

To find the sum of  a + b where a and b are rational number.

1. when a and b are natural numbers

just add them . for example a =3, b=8

then ,a + b = 11

2. When a and b  are whole numbers,

simply add them . for example a= 0, b=8

a+ b = 0 + 8= 8

3. When  a and b are integers

for example, a =-1 b=8,

a+ b= -1+ 8 =7,

a=-2, b= -8

a+ b= -2-8=-10

a= -6 , b=2

a+ b= -6 + 2= -4

a= 8, b= -2

a+ b= 8 +(-2) =6

I have written this because Rational number = [Integers{Whole number(Natural number)}]

now when a= Any fraction=(p)/(q) and b = Any fraction=(u)/(v)

now ,

(p)/(q) + (u)/(v)

Find L.C.M of q and v

= if q and v are Co-prime , just multiply them to find their  L.C.M.

For example 14,9. LCM=14×9=126

Otherwise, Find factors of q and v . Then take out common factors first and then multiply the remaining with with common factors.For example

q=12 and v=18

12 =2×2×3

18=2×3×3

common factor =2,3

non common=2,3

L.C.M= 2×2×3×3=36

Suppose LCM of q and v = r

then ,(p)/(q) + (u)/(v)

=\frac{{(r)/(q)}* p+{(r)/(v)* u}}{r}\n

= {{(r)/(q)}* p+{(r)/(v)* u}} = k

then ,

a + b=(k)/(r)

What's the ratio in simplest form 20/60

Answers

Answer: 1/3 is the simplest form.

Step-by-step explanation:

All I did was see if 60 could be divided into 20, and it can.

60 divided by 20 = 3

Now I have to do the same with the 20.

20 divided by 20 = 1

Now I have 1/3.

Thats how I solved it.

Hope that helps!
1/3 is the answer or in decimal it is 0.3

The year is 1714. You are in a dark Spanish prison. You wake up to find yourself tied to a table with ropes. In the darkness you hear a rhythmic swishing sound-something going back and forth, back and forth. Eventually your eyes get accustomed to the dark and see that the source of the sound is a sharp bade at the end of a long pendulum that’s swinging back and forth over your body. With each sweep it gets a little lower-and a little closer to your chest. You note how long it takes between those swishes: exactly 7 seconds. And with each swish, the blade drops 1 inch lower. The last passing was only 15 inches above your chest. It won’t be much longer before the blade slices right through you. Should you scream for help? That would probably just summon a guard, who would run through with a sword then and there. But wait! You see a rat by your arms and he’s gnawing at the rope that binds you to the table. In fact, he has only 1 minute to go before he gnaws through it all the way. When he does that, you can get free! Will the rat chew through the rope before or after the blade has slashed through your chest? How much time do you have exactly?

Answers

If the rat will chew through the rope in 60 seconds you will be free.
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In 70 seconds it will be 5 inches
In 77 seconds it will be 4 inches
In 84 seconds it will be 3 inches
In 91 seconds it will be 2 inches
In 98 seconds it will be 1 inch
You have 6 seconds before it swings again and cuts you so you have 104 seconds exactly but lucky for you the rat chewed through the rope 44 seconds ago.

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Word Bank:

Answers

Answer:

                                            Circumcenter          Incenter              Centroid

Formed by intersection of   Perp. Bisectors    Angle bisectors     Medians

Type of circle                        Circumscribed      Inscribed               No circle

Special property              Equidistant from Equidistant from  Center of mass

                                                      vertices              Sides
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