Questions: Use what you here learned to complete problem 4. Parts The shaded part of each rectangle models a fraction. Draw lines to match the fraction model on the left with an equivalent fraction on the right. Fraction Models Fractions 1/6 3 10 6 1/4 6/10 Part B Choose one of the fraction models in Part A. Explain how to use multiplication or division to check the equivalent fraction. Why does this work? Explain why 3/4 is equivalent to 9/12

$Use what you here learned to complete problem 4. Parts The shaded part of each rectangle models a fraction. Draw lines to match the fraction model on the left with an equivalent fraction on the right. Fraction Models Fractions 1/6 3 10 6 1/4 6/10 Part B Choose one of the fraction models in Part A. Explain how to use multiplication or division to check the equivalent fraction. Why does this work? Explain why 3/4 is equivalent to 9/12$

Transcript text: Use what you here learned to complete problem 4. Parts The shaded part of each rectangle models a fraction. Draw lines to match the fraction model on the left with an equivalent fraction on the right. Fraction Models Fractions $\frac{1}{6}$ 3 10 6 $\frac{1}{4}$ $\frac{6}{10}$ Part B Choose one of the fraction models in Part A. Explain how to use multiplication or division to check the equivalent fraction. Why does this work? Explain why $\frac{3}{4}$ is equivalent to $\frac{9}{12}$

Solution

Step 1: Matching the fraction models to their equivalent fractions

a. The model shows 1/2 shaded. The equivalent fraction is 3/6.
b. The model shows 1/2 shaded. The equivalent fraction is 2/4.
c. The model shows 2/4 shaded. The equivalent fraction is 1/2.
d. The model shows 3/6 shaded. The equivalent fraction is 1/2.

Step 2: Choosing a model and explaining the multiplication/division

We can choose model a, which represents 1/2 and its equivalent fraction 3/6. To check the equivalency through multiplication, multiply both the numerator and denominator of 1/2 by 3: (1 * 3)/(2 * 3) = 3/6.

To demonstrate equivalency through division, divide both the numerator and denominator of 3/6 by 3: (3 / 3)/(6 / 3) = 1/2

Step 3: Explaining why multiplication/division works

This works because multiplying or dividing both the numerator and the denominator by the same non-zero number is the same as multiplying or dividing by 1, which doesn't change the fraction's value but simply expresses it in a different form. It changes the size of the pieces represented while keeping the same overall proportion shaded.

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