Question

1. use a standard inch ruler to answer each question. then, write a multiplication equation and a division equation that answer the question.

a. how many \\(\frac{1}{4}\\)s are in 6?

b. how many \\(\frac{3}{16}\\)s are in \\(2\frac{1}{4}\\)?

c. how many \\(\frac{8}{9}\\)s are in 10?

Explanation:

Step1: Solve part a: Count 1/2s in 8

To find how many $\frac{1}{2}$ are in 8, divide 8 by $\frac{1}{2}$.
Division equation: $8 \div \frac{1}{2} = 8 \times 2 = 16$
Multiplication equation: $16 \times \frac{1}{2} = 8$

Step2: Solve part b: Count 3/16s in 2 1/4

First convert $2\frac{1}{4}$ to improper fraction: $2\frac{1}{4} = \frac{9}{4} = \frac{36}{16}$
Divide by $\frac{3}{16}$: $\frac{36}{16} \div \frac{3}{16} = \frac{36}{16} \times \frac{16}{3} = 12$
Multiplication equation: $12 \times \frac{3}{16} = \frac{36}{16} = 2\frac{1}{4}$

Step3: Solve part c: Count 5/6s in 10

Divide 10 by $\frac{5}{6}$: $10 \div \frac{5}{6} = 10 \times \frac{6}{5} = 12$
Multiplication equation: $12 \times \frac{5}{6} = 10$

Answer:

a. Division: $8 \div \frac{1}{2} = 16$; Multiplication: $16 \times \frac{1}{2} = 8$; Number of $\frac{1}{2}$s: 16
b. Division: $2\frac{1}{4} \div \frac{3}{16} = 12$; Multiplication: $12 \times \frac{3}{16} = 2\frac{1}{4}$; Number of $\frac{3}{16}$s: 12
c. Division: $10 \div \frac{5}{6} = 12$; Multiplication: $12 \times \frac{5}{6} = 10$; Number of $\frac{5}{6}$s: 12