Explain how you can determine if 1/3 and 4/12 are equivalent fractions.
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:
Answer details:
Grade: Junior school
Subject: Mathematics
Chapter: Fractions
Keywords: Integers, expression, denominator, numerator, fractions, lowest form, product, multiple, equivalent, number, divide, multiply.