# Make the internet a better place to learn

2

## Is seven-nineths greater than two-thirds?

Siyang M.
Featured 2 weeks ago

Yes

#### Explanation:

If you divide seven by nine, you get a repeating decimal of 0.77777777.
However, when you divide two by three, you also get a repeating decimal but smaller. 0.66666666

2

## Is seven-nineths greater than two-thirds?

kate
Featured 2 weeks ago

Yes. If you change the fraction of 2/3 to something with the denominator of 9, you can compare the numerators easily and directly.

#### Explanation:

You would do this by multiplying 2/3 by 3/3 to make 6/9, which is smaller than 7/9.

3

## Does 10cm(squared) converted into millimetres(squared) equal this?

Ms. Worth
Featured 2 weeks ago

It is $\text{multiplication}$, not addition

It should be $1 \times {10}^{3}$

#### Explanation:

${\text{10 cm"^2 = "1000 mm}}^{2}$

In scientific notation, $1000 = {10}^{3}$

So $\text{1000 mm"^2 = 1xx10^3" mm"^2}$

3

## What fraction is equivalent to 1/3?

Sean
Featured 6 days ago

#### Explanation:

.

There are infinite number of fractions that are equal to $\frac{1}{3}$.

You can multiply the numerator and denominator of $\frac{1}{3}$ by any number and the resulting fraction would be equal to $\frac{1}{3}$ so long as you are multiplying both by the same number.

For example:

$\frac{1}{3} = \frac{1 \cdot 2}{3 \cdot 2} = \frac{2}{6}$

$\frac{1}{3} = \frac{1 \cdot 4000}{3 \cdot 4000} = \frac{4000}{12000}$

and so on and so forth.

3

## What are the prime factors of 1400?

Serena Ariella
Featured 1 week ago

$2 \times 2 \times 2 \times 5 \times 5 \times 7$

#### Explanation:

To find the prime factorization of $1400$, we need to break it down into prime factors.

Lets use these steps I found in here: https://www.wikihow.com/Find-Prime-Factorization Follow along!

Step 1: Understand factorization. Hopefully you do, but just in case I'll explain.

• Factorization: the process of breaking a larger number into smaller numbers (algebraic definition)

Step 2: Know prime numbers. They are basically numbers that can only be factored by 1 and itself. e.g. 5 ($5 \times 1$), 47 ($47 \times 1$)

Step 3: Start with the number, which is $1400$. It is always helpful to rewrite the problem, for it is easy to make mistakes if you don't.

Step 4: Start by factoring the number into any two factors.

• $1400$: $200 \times 7$

Step 5: If the factorization continues, start a factorization tree, so it is less vulnerable to mistakes.
- $1400$
-tttt^
- $200$ $7$

Step 6: Continue factorization.

• $1400$
• tttt^
• $200$ $7$
• ttt^
• $100$ $2$
• ttt^
• $50$ $2$
• ttt^
• $25$ $2$
• t^
• $5$ $5$

Step 7: Note any Prime numbers.

• $1400$
• tttt^
• $200$ $\textcolor{red}{7}$
• ttt^
• $100$ $\textcolor{red}{2}$
• ttt^
• $50$ $\textcolor{red}{2}$
• ttt^
• $25$ $\textcolor{red}{2}$
• t^
• $\textcolor{red}{5}$ $\textcolor{red}{5}$

Step 8: Finish factorization. I already did this in the $6 t h$ step, so...

Step 9: Finish by writing the line of prime factors neatly in increasing order.

• $\textcolor{b l u e}{1400 : 2 \times 2 \times 2 \times 5 \times 5 \times 7}$
1

## The HCF of two numbers is 12 and the LCM " is " 3780 The one number is 84. What is the other?

sjc
Featured 1 week ago

$540$

#### Explanation:

we have

$h c f \left(84 , b\right) = 12$

$\lcm \left(84 , b\right) = 3780$

to find $b$

we have the well known relationship

$a b = h c f \left(a , b\right) \times \lcm \left(a , b\right)$

$84 b = 12 \times 3780$

$b = \frac{\cancel{12} \times 3780}{\cancel{84}} ^ 7$

$b = \frac{3780}{7} = 540$

1

## The HCF of two numbers is 12 and the LCM " is " 3780 The one number is 84. What is the other?

EZ as pi
Featured 1 week ago

The other number is $540$

#### Explanation:

For any questions involving HCF and LCM,find each number as the product of the prime factors. That will tell you what you are working with.

$\text{ } 84 = \textcolor{b l u e}{2 \times 2 \times 3} \times \textcolor{red}{7}$
" "? = ul(color(blue)(?xx?xx?)xx?xx?xx?xx?)

$H C F = \textcolor{b l u e}{2 \times 2 \times 3} \textcolor{w h i t e}{w w w w w w w w w w w w w w} = 12$
$L C M = \textcolor{b l u e}{2 \times 2 \times 3} \times \textcolor{red}{7} \times \textcolor{p u r p \le}{3 \times 3 \times 5} \text{ } = 3780$

$3780 = \textcolor{b l u e}{H C F} \times \textcolor{red}{7} \times \text{ another number}$
$3780 = \text{ } \textcolor{b l u e}{12} \times \textcolor{red}{7} \times \textcolor{p u r p \le}{\left(3 \times 3 \times 5\right)}$
$3780 = \text{ } \textcolor{b l u e}{12} \times \textcolor{red}{7} \times \textcolor{p u r p \le}{45}$

The other number cannot have $7$ as a factor otherwise the $H C F$ would be $84$

The other number is therefore $12 \times 45 = 540$

1

## What are the prime factors of 1400?

EZ as pi
Featured 1 week ago

The prime factors of $1400 \text{ are } 2 , 5 , 7$

$1400 = 2 \times 2 \times 2 \times 5 \times 5 \times 7$

#### Explanation:

The intention of the question is not absolutely clear....

Is it asking which of the factors of $1400$ are prime numbers?

Or

Is it asking for $1400$ to be written as the product of its prime factors.

It will help to write $1400$ as the product of its prime factors anyway..

Divide $1400$ by prime numbers which are factors until you get $1$

$2 | \underline{\textcolor{w h i t e}{.} 1400}$
$2 | \underline{\text{ } 700}$
$2 | \underline{\text{ } 350}$
$5 | \underline{\text{ } 175}$
$5 | \underline{\text{ } 35}$
$7 | \underline{\text{ } 7}$
$\textcolor{w h i t e}{. . w w \ldots} 1$

The prime factors of $1400 \text{ are } 2 , 5 , 7$

As the product of its prime factors:

$1400 = 2 \times 2 \times 2 \times 5 \times 5 \times 7$

1

## What fraction is equivalent to 1/3?

EZ as pi
Featured 6 days ago

$\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \frac{5}{15} = \frac{9}{27} = \frac{14}{42} = \frac{17}{51} = \frac{50}{150} \ldots . .$

#### Explanation:

There are many fractions which are equivalent to $\frac{1}{3}$ but this is the simplest form.

To find an equivalent fraction, multiply $\frac{1}{3}$ by $1$, but with $1$ written as $\frac{2}{2} , \frac{3}{3} , \frac{4}{4}$ etc

Multiplying the numerator and denominator by the same number does not change the value of a fraction.

$\frac{1}{3} \times \frac{2}{2} = \frac{2}{6}$

$\frac{1}{3} \times \frac{7}{7} = \frac{7}{21}$

$\frac{1}{3} = \frac{2}{6} = \frac{3}{9} = \frac{4}{12} = \frac{5}{15} = \frac{9}{27} = \frac{14}{42} = \frac{17}{51} = \frac{50}{150}$ etc

2

## 3/5 ÷ 7 Find the quotient?

HighwireAct
Featured 3 days ago

$\frac{3}{35}$
When you divide $3 / 5$ by $7$, you can think of it as making that $3 / 5$ 7 times smaller.
If $1 / 5$ is what we get when we take a whole and chop it up into 5 equal pieces:
Then $1 / \left(5 \cdot 7\right)$ or $1 / 35$ is the value we get when we take $1 / 5$ and divide it into $7$ pieces:
And, of course, we have 3 of these divided pieces, giving us a total of $3 \cdot 1 / 35 = 3 / 35$.