Question

Explain how you can determine if 1/3 and 4/12 are equivalent fractions.

Answer 1

The expression $\dfrac{1}{3}$ is $\boxed{{\mathbf{equivalent}}}$ to the expression $\dfrac{4}{12}$.

Further explanation:  

The number ab is the product of $a\;\text{and}\;b$  and it is the multiple of $a$ where $b$ are the integers.

It can be written as,

$ab=a\times b$  

Given:

The given expressions are $\dfrac{1}{3}$ and $\dfrac{4}{12}$.

Step by step explanation:

Step 1:

The given expression is $\dfrac{4}{12}$.

The denominator and the numerator of the given expression is the multiple of $4$.

The denominator of the expression can be written in the multiple of 4 as,

$12=4\times3$  

Therefore, the number 12 is the multiple of $3\;\text{and}\;4$.

The numerator of the expression can be written in the multiple of 4 as,

$4=4\times1$  

Therefore, the number 4 is the multiple of $1\;\text{and}\;4$.

Step 2:

Now, divide the given expression $\dfrac{4}{12}$ by 4 to convert in the lowest form as,

$\begin{aligned}\frac{4}{12}&=\dfrac{4\div4}{12\div4}\\&=\dfrac{1}{3}\end{aligned}$  

It can be seen that the resultant answer is $\dfrac{1}{3}$.

Now, divide the given expression  $\dfrac{1}{3}$ by 1 as,

$\begin{aligned}\dfrac{1}{3}&=\dfrac{1\div1}{3\div1}\\&=\dfrac{1}{3}\end{aligned}$  

It can be seen that the resultant answer is $\dfrac{1}{3}$.

Thus, it can be seen that the expression $\dfrac{1}{3}$ is equivalent to the expression $\dfrac{4}{12}$.

Learn more:  

1. Learn more about the multiplicative identity property brainly.com/question/4238982
2. Learn more about distance between two pints on the number line brainly.com/question/6278187
3. Learn more about midpoint of the segment brainly.com/question/3269852

Answer details:

Grade: Junior school

Subject: Mathematics

Chapter: Fractions  

Keywords: Integers, expression, denominator, numerator, fractions, lowest form, product, multiple, equivalent, number, divide, multiply.

Answer 2

To determine if 1/3 and 4/12 are equivalent fractions, you can either simplify 4/12 or raise 1/3. I'm going to explain with an example. So we have 1/8 and 3/24. I usually make the denominators (The lower number of the fraction) the same. To do that i multiply 8 by which ever number i think will calculate to 24. So 8 times 3 is 24. So i would change the number 8 to the number 24. But what you do to the bottom you HAVE to do to the top. So i multiplied the number 8 by 3 to get 24. No i am going to multiply the top of 1/8 (which is 1, or the numerator) by 3. And 1 times 3 is 3. And that gives me 3/24. It equals the second fraction, so 1/8 and 3/24 is equivalent.

So taking your fractions, 1/3 and 4/12, we just see how many times 3 goes into 12. Or what times 3 equals 12. That is 4. So what we do to the bottom we MUST do to the top, right? So we multiply 1 by 4. That gives us 4. So 1/3 changed into 4/12. So our first fraction is now 4/12 and our second fraction is also 4/12. So they are equivalent! Hope this helped <span />