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4 years ago

How to simplify fraction to its lowest terms

Mathematics

2 answers:

inna [77]4 years ago

8 0

To simplify a fraction you find the GCF (Greatest Common Factor) of the numerator and denominator.

To find the GCF find all the factors of both numbers and the factor that is highest is your GCF.

Example: 6/15

6: 1, 2, 3, 6
15: 1, 3, 5, 15

Three is the GCF in this example.

To simplify, divide the numerator and denominator by the GCF.

Example: 6/15

6/3 = 2
15/3 = 5

6/15 = 2/5

tatuchka [14]4 years ago

6 0

5/15 = 1/3
6/15 = 2/5
6/8 = 3/4
2/4 = 1/2

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After reading 7/9 of a book, 40 pages are left. Find the total number of pages in the book

dimaraw [331]

Answer:

180 pages

Step-by-step explanation:

let x be the number of pages in the book , then

$\frac{7}{9}$ x + 40 = x ( multiply through by 9 to clear the fraction )

7x + 360 = 9x ( subtract 7x from both sides )

360 = 2x ( divide both sides by 2 )

180 = x

The total number of pages in the book is 180

6 0

3 years ago

A circle with area \blue{25\pi}25πstart color #6495ed, 25, pi, end color #6495ed has a sector with a central angle of \purple{\d

vredina [299]

Answer:

Step-by-step explanation:

Given that

The area of circle is 25π square unit

Area = 25π square unit

The area of a circle can be calculated using

Area = πr²

Where r is radius of the circle

Then, let find the radius of the circle

Area = πr²

25π = πr²

Divided Both side by π

25π / π = πr² / π

25 = r²

Take square root of both sides

√25 = √r²

5 = r

Then, the radius of the circle is 5 unit

Then, given that the angle subtended by the sector is 9π/10 rad

θ = 9π/10 rad

Then, we want to find the area of the sector

Area of a sector is calculated using

Area of sector = (θ / 360) × πr²

Area of sector = θ × πr² / 360

The formula is in degree let convert to radian

360° = 2π rad.

Then,

Area of sector = θ × πr² / 2π rad

Then,

Area of sector = θ × r² / 2

Area of sector = ½ θ•r²

Then, Area of the sector is

A = ½ θ•r²

A = ½ × (9π / 10) × 5²

A = (9π × 5²) / (2 × 10)

A = 225π / 20

A = 45π / 4

A = 11.25π Square unit

A = 35.34 square unit

3 0

3 years ago

Check each equation whose graph is the line that

yanalaym [24]

Answer:

Points P ( 4 , - 7 ) and Q ( 1 , 5 ) belong to the equations:

1 ; 4 ; and 5

Step-by-step explanation:

Equations 1 ; 4 and 5 are the same equation

Equation 1 y = - 4*x + 9

Equation 4

y + 7 = - 4 * ( x - 4 ) ⇒ y + 7 = - 4*x + 16 ⇒ y = - 4*x - 7 + 16

y = -4*x + 9

Equation 5

4*x + y = 9 ⇒ y = - 4*x + 9

Now for the equation y = - 4*x + 9

P ( 4 , -7)

For x = 4 y = - 4*(4) + 9 ⇒ y = - 16 + 9 ⇒ y = - 7

Then point P is in the line y = - 4*x + 9

Point Q (1 , 5 )

For x = 1 y = - 4 * ( 1) + 9 ⇒ y = - 4 + 9 ⇒ y = 5

Point Q is in the line y = - 4*x + 9

Equation 2

y = - 4*x - 23

Point P ( 4 , - 7 )

For x = 4 y = 16 - 23 y = - 7

Point P is in the line

Point Q

For x = 1 y = - 4 *(1) - 23 ⇒ y = - 27

Then poin Q is not in the line

Equation 3

y - 1 = - 4 * ( x - 4 )

y - 1 = -4*x + 16 ⇒ y = - 4*x + 17

Point P ( 4 , - 7 )

For x = 4

y = - 16 + 17 ⇒ y = 1

Point P is not in the line

And Point Q ( 1 , 5 )

For x = 1

y = - 4* ( 1 ) + 17 ⇒ y = 13 Q is not in the line

3 0

3 years ago

Find the equation of a straight line passing throught the point listed and having the given gradient. Express your answer in the

Igoryamba

First let's try to find the equation in this form : y = mx + c

The gradient is given 3 . In a line's equation, x's coefficient represents the line's gradient.

So equation of a line with the gradient of 3, would look like this ;

 $y= 3x + c$

Now a point that the line passes through is given, (1, 2)

This point's x-coordinate is 1 and y-coordinate is 2.

So we'll plug its x-coordinate value in the equation and also y-coordinate value. So we can solve it.

As you know, $x=1$ and $y=2$

$y = 3x + c$

$2\quad =\quad 3\cdot 1+c\\ \\ 2\quad =\quad 3+c\\ \\ 2-3\quad =\quad c\\ \\ -1\quad =\quad c$

We found c = -1

Also in a line's equation, c is constant and it represents the line's y-intercept

So let's build the line's equation.

$m=3$ and $c=-1$

$y= mx + c$

$y= 3x -1$

We found the line's equation in this form, $y= mx + c$

Now let's turn it into this form, $ax + by + c = 0$

$y\quad =\quad 3x-1\\ \\ y-3x\quad =\quad -1\\ \\ y-3x+1\quad =\quad 0\\ \\ -3x+y+1\quad =\quad 0$

Final answers,

$\boxed { y\quad =\quad 3x-1 }$

and

$\boxed { -3x+y+1\quad =\quad 0 }$

I hope this was clear enough :)

5 0

4 years ago

Read 2 more answers

Which math expression means "44 more than an unknown number"?

worty [1.4K]

Answer: C. X + 44

Step-by-step explanation:

Let x be the unknown number.

Given statement : "44 more than an unknown number".

By using addition operation ,

Mathematical expression for "44 more than an unknown number" = 44 +x

Hence, the correct expression is x+44.

So, the correct option is C.

5 0

3 years ago