Question

full credit: all problems completed and all work shown
half credit: half of the problems completed and only partial work shown
no credit: no problems completed or no work shown
a (hexagon labeled 1 whole), b (parallelogram), c (trapezoid), d (triangle)

1. if a hexagon represents 1 whole, what fraction does each of the following shapes represent? be prepared to show or explain your reasoning.
2. 1 triangle ______
3. 1 rhombus ______
4. 4 triangles ______
5. 3 rhombuses ______
6. 1 trapezoid ______
7. 2 hexagons ______

answer the following questions. if you get stuck, consider using pattern blocks.

1. how many \\(\frac{1}{2}\\) are in \\(3\frac{1}{2}\\)?

a. 6
b. 7
c. 3
d. 9
(sketches of hexagons)

1. how many \\(\frac{1}{3}\\) are in \\(2\frac{2}{3}\\)?

a. 2
b. 5
c. 8
d. 6
(sketches)

1. how many \\(\frac{1}{3}\\) are in \\(2\frac{1}{3}\\)?

a. 4
b. 2
c. 6
d. 7
(sketches)

1. how many \\(\frac{1}{6}\\) are in \\(1\frac{1}{3}\\)?

a. 3
b. 6
c. 4
d. 12

Explanation:

Step1: Convert mixed number to improper fraction

The mixed number \(3\frac{1}{2}\) can be converted to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(3\frac{1}{2}\), we have \(a = 3\), \(b = 1\), \(c = 2\). Then \(\frac{3\times2+ 1}{2}=\frac{6 + 1}{2}=\frac{7}{2}\).

Step2: Divide by the fraction \(\frac{1}{2}\)

To find how many \(\frac{1}{2}\) are in \(\frac{7}{2}\), we divide \(\frac{7}{2}\) by \(\frac{1}{2}\). When dividing by a fraction, we multiply by its reciprocal. So \(\frac{7}{2}\div\frac{1}{2}=\frac{7}{2}\times\frac{2}{1}\). The 2 in the numerator and denominator cancels out, leaving us with 7.

Answer:

B. 7