Which phrase should be inserted on the line to make a true statement? Use the models to help.

Question

Two-thirds blank line StartFraction 8 Over 12 EndFraction

Two-thirds

A model has 2 shaded parts and 1 unshaded part.
StartFraction 8 Over 12 EndFraction
A model has 8 shaded parts and 4 unshaded parts.
is greater than
is less than
cannot be compared to
is equal to

Answer 1

To determine which phrase should be inserted in the blank line, we need to compare "Two-thirds" with the fraction \( \frac{8}{12} \).

First, let's simplify the fraction \( \frac{8}{12} \):

• Both the numerator (8) and the denominator (12) can be divided by 4.
• So, \( \frac{8 \div 4}{12 \div 4} = \frac{2}{3} \).

Now we see that:

• Two-thirds is equivalent to \( \frac{2}{3} \).
• The fraction \( \frac{8}{12} \) simplifies to \( \frac{2}{3} \), which means they are equal.

Thus, the correct phrase to fill in the blank is "is equal to".

So the completed statement is:

Two-thirds is equal to \( \frac{8}{12} \).