Mathematics Middle School

## Answers

**Answer 1**

18/30, is reduced to 9/15 then 3/5.

9/15 first, because 18 and 30 are both divisible by 2.

18÷2=9 and 30÷2=15.

Then how I got 3/5, was because both 9 and 15 are divisible by 3.

9÷3=3 and 15÷3=5 so the final answer that you are looking for, is 3/5.

**Answer 2**

Answer: 3/5

Step-by-step explanation: In order to write the fraction 18/30 in lowest terms, we divide the numerator and the denominator by the greatest common factor of 18 and 30 which is 6.18 divided by 6 is 3 and 30 divided by 6 is 5 so 18/30 written in lowest terms is 3/5.

## Related Questions

45 is 20% of what number?

### Answers

What is 1/16 as a whole number

### Answers

I dont think there is a whole number, but i found a decimal! :) convert 1/16 to a decimal which is 0.0625

92% of what number is 115 ?

### Answers

What is 1/8 divided by 2

### Answers

Whendividing 1/8 by 2

we have to first take the reciprocal of 2

reciprocal is when the numerator and denominator are exchanged

2 when written as a fraction is

we need to find the reciprocal of which is

then

when 'of' function is used it means to multiply the 2 fractions

when multiplying fractions multiply the numerators by numerators and multiply denominators by denominators

is

answer is

What is 48/56 in simplest form

### Answers

6/7 because 48 divided by 8 is 6 and 56 divided by 8 is 7

48/56 can be simplified by dividing 48 by 8 and you get 6. Then, you divide 56 by 8 equals 7. So, 48/56 in simplest form is 6/7.

A $40 jacket is on sale for 30% off what is the sale price

### Answers

So 40=100%

find 100%-30%=70%

70% of 40

'of' can be translated to multiply

70% times 40

percent means parts out of 100 so

70%=70/100=7/10=0.7

so

.7 times 40=28

the sale price=$28

Directions: Drag each tile to the correct box. Order the following conditions in order from the largest number of possible triangles to the least number of possible triangles.

Condition A: a perimeter of 12 and even-numbered side lengths

Condition B: a side length of 4 inches, a side length of 5 inches, an included angle of 110º, and a perimeter of 11 inches

Condition C: a right triangle with an area less than 13 square inches and odd-numbered leg lengths greater than 1 inch

Condition D: an isosceles triangle with two angles that measure 50º

### Answers

D, C, A nad then B

Figure out the number of possible triangles that fitcondition A. There are 3 possible combinations of three even numbers that sum to 12.Of these three, there is only one where every length is less than the sum of the other two:4 inches,4 inches,4 inches.So, there is only one triangle that fitscondition A.Figure out the number of possible triangles that fitcondition B. Since the perimeter and two side lengths are given, subtract the two side lengths from the perimeter to get the length of the third side.Sketch a triangle with lengths of2 inches,4 inches,and5 inches.From the sketch, the angle between the4-inchlength and5-inchlength has to be the smallest angle. Since it has to be the smallest angle, it cannot be more than a right angle. So, there is zero triangles that fitcondition B.Figure out the number of possible triangles that fitcondition C. For the area to be less than13 square inches, the product of the legs must be less than26 square inches. The right triangles withodd-numberedlegs greater than1 inchwhose product is less than26 square inchesare shown below.So, three triangles fitcondition C.Figure out the number of possible triangles that fitcondition D. If two angles of an isosceles triangle measure 50º, the third can be found by subtraction both angle measures from 180º.So, the angle measures must be 50º, 50º, and 80º. There is no condition on the lengths, so there are an infinite number of triangles that fitcondition D.Therefore, the conditions in order of greatest possible triangles to least are shown below.condition D,condition C,condition A,condition B

HELP ME DO THIS

y=2x+4

-5x-5y=-5

### Answers

Y=2x+4

-5x-5y=-5

subsitute 2x+4 for y

-5x-5(2x+4)=-5

-5x-10x-20=-5

-15x-20=-5

add 20 to both sdies

-15x=15

divide by -15

x=-1

subsitute

y=2(-1)+4

y=-2+4

y=2

x=-1

y=2

A red string of lights blinks once every 3 seconds while a string of blue lights blink once every 4 seconds. How many times will both sets of lights blink at the same time in 60 seconds?

### Answers

The string of red lights will blink 20 times and the blue lights will be 15 60 divided by 4 is 15 and 60 divided by 3 is 20

Vicki puts 10 books on a shelf.The 10 books take up 28 centimeters.What is the mean (average) thickness of her books?= 2.8 cmThe shelf is 120 centimeters long.Vicki fills the shelf with a mixture of books like the first ten books.Estimate how many books she can get on the 120 cm shelf.Please show your working out.

### Answers

So each book is an average of 2.8 cm

so 120 divided by each book=number of books

120/2.8=42.85

round down since you can't fit .85 of a book on a shelf

the answer is 42 books

Explain how you can use a number line to show that 5/8 is greater than 3/8

### Answers

You can start by drawing a number line and labeling it with eighths. ( 1/8, 2/8, etc.) Then you can place a dot on 3/8 and 5/8. From there, it's clear to seethat 5/8 is greater than 3/8.

Draw a fraction number line and put a dot where each fraction from greatest to least is. Hope this helps

0___1/8___2/8____3/8___4/8___

Explain how you can use a number line to show that 5/8 is greater than 3/8

### Answers

You can have a number line showing eigths and place the 2 fractions on the number line in the correct place.

What is 3/4 divided by 1/24

### Answers

Dividing fractions is the same thing as multiplying by the reciprocal

3/4 x 24/1 = 18

3/4 divided by 1/24, must do the reciprocal (flip) of 1/24 which is 24/1, when do this you now multiply, 3/4x24/1=72/4=18

What is 151/24 simplified

### Answers

Well 151 divided by 24 is 6 remainder 7 so the mixed number would be 6 and 7/24

Every prime number greater than 10 has a digit in the ones place that is included in which set of numbers below?

### Answers

The numbers are all prime and odd numbers

11, 13,17,19,23,29,31,37,

so the numbers are 1,3,7,9

because

2 is even and if it ends in 2 then divisible by 2

this crosses out all the even numbers :2,4,6,8

if it ends with 5 then it is divisible by 5 cross 5 out

so the numbers are 1,3,7,9

if the number ends with these number that doesn't mean that it is always prime exg 21 is not prime, 49 is not prime

so the numbers 1,3,7,9

N^2+16n+60 over 36-n^2

### Answers

Factor

36-n^2 is difference of 2 perfect squares

a^2-b^2=(a-b)(a+b)

6^2-n^2=(6-n)(6+n)

factor

n^2+16n+60

find what 2 numbers multiply to 60 and add to 16

factors of 60=2,2,3,5

the numbers are 10 and 6

so factored out

(x+6)(x+10)

(x+6)=(6+x)

so the equation is

[(x+6)(x+10)]/[(6+x)(6-x)]=[(6+x)/(6+x)] times (x+10)/((6-x)=1 times (x+10)/(6-x)

the answer is (x+10)/(6-x)

Using the order of operations rule, solve the following: 12 ÷ 2 + 4 – 2 × 3 = ? A. 24 B. 36 C. 0 D. 4

### Answers

The answer is D, because you have to divide 12 by 2 so you get 6 then 2 times 3 to get 6, so now you should have 6+4-6 which will then become 10-6 which equals 4

Which one of the following groups of numbers includes all prime numbers? A. 7, 17, 63, 67 B. 3, 11, 23, 31 C. 1, 3, 11, 23 D. 2, 3, 5, 15

### Answers

The prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

A.

7 - is a prime number

17 - is a prime number

63 - is not a prime number because 63 = 3 × 21

B.

3 - is a prime number

11 - is a prime number

23 - is a prime number

31 - is a prime number

C.

1 - is not a prime number

D.

2 - is a prime number

3 - is a prime number

5 - is a prime number

15 - is not a prime number because 15 = 3 × 5

How much did a purse original cost if you bought it for $55.00 at 25% off

### Answers

So 55=100%-25%

55=75%

divide by 3

18.333=25%

multiply both sides by 4

$73.33= 100%

it cost $73.33

8x squared plus 2x minus 3

### Answers

8x^2+2x-3

factor

()()

find what 2 numbers multiply to get -3 and add to get 2

the answer is -1 and 3

then what 2 numbers multiply to get 8

(2x-1)(4x+3) is the factored form