Question

reflection & practice
(text above the image: )
7-5.
i can make a diagram to model division of whole numbers.
draw a diagram and write a division number sentence for how a team of four students would share five glasses of licorice.
7-6.
i can write a division problem as a fraction such as, 3 ÷ 2 is \\(\frac{3}{2}\\).
write the following division number sentences as fractions. then compute the quotient of each division number sentence. the first one has been done for you.
a. \\(5 \div 2 = \frac{5}{2} = 2\frac{1}{2}\\)
b. \\(7 \div 6 = \underline{quad} = \underline{quad}\\)
c. \\(10 \div 2 = \underline{quad} = \underline{quad}\\)
d. \\(11 \div 2 = \underline{quad} = \underline{quad}\\)
7-7. (from lesson 6.2.2)
malachi looked at his team and said, “84 is a common multiple of 2, 3, and 7, right?”
rosanna replied, “yes, and 84 is a common multiple of 4 and 12 too!”
if they want a complete list, what other factors of 84 do they still need to list?

Explanation:

7-6.b

Step1: Recall division to fraction rule

A division \(a\div b\) can be written as the fraction \(\frac{a}{b}\). So for \(7\div6\), the fraction is \(\frac{7}{6}\).

Step2: Convert improper fraction to mixed number

To convert \(\frac{7}{6}\) to a mixed number, divide 7 by 6. \(6\times1 = 6\), and \(7 - 6=1\). So \(\frac{7}{6}=1\frac{1}{6}\).

Step1: Apply division to fraction rule

For \(10\div2\), using \(a\div b=\frac{a}{b}\), we get \(\frac{10}{2}\).

Step2: Simplify the fraction

\(\frac{10}{2}=5\) (since \(10\div2 = 5\)).

Step1: Use division to fraction rule

For \(11\div2\), the fraction is \(\frac{11}{2}\).

Step2: Convert to mixed number

Divide 11 by 2. \(2\times5 = 10\), \(11 - 10 = 1\). So \(\frac{11}{2}=5\frac{1}{2}\).

Answer:

\(\frac{7}{6}\), \(1\frac{1}{6}\)

7-6.c