2/3 times what equals 1
The Correct Answer and Explanation is :
To solve the equation (2/3) × what = 1, we can set up a variable, say ( x ), to represent the unknown number:
[
\frac{2}{3} \times x = 1
]
To find ( x ), divide both sides of the equation by ( \frac{2}{3} ). Dividing by a fraction is the same as multiplying by its reciprocal (the reciprocal of a fraction is obtained by swapping its numerator and denominator):
[
x = 1 \times \frac{3}{2}
]
This simplifies to:
[
x = \frac{3}{2}
]
So, ( x = \frac{3}{2} ), or 1.5.
Explanation
Fractions represent parts of a whole, where the numerator (the top number) shows how many parts we have, and the denominator (the bottom number) shows how many equal parts make up a whole. The fraction ( \frac{2}{3} ) means two-thirds, or two parts out of three.
In the equation ( \frac{2}{3} \times x = 1 ), we are asked to find what number multiplied by ( \frac{2}{3} ) equals 1, which is the same as asking, “How many two-thirds make up 1?”
To isolate ( x ), we divide both sides by ( \frac{2}{3} ), which is like asking how many two-thirds fit into 1. Dividing by a fraction is equivalent to multiplying by its reciprocal. The reciprocal of ( \frac{2}{3} ) is ( \frac{3}{2} ). So, multiplying 1 by ( \frac{3}{2} ) gives us ( x = \frac{3}{2} ), or 1.5.
This means that ( \frac{3}{2} ) or 1.5 is the number which, when multiplied by ( \frac{2}{3} ), equals 1.