Question

1. write \\(\frac{44}{5}\\) as a mixed number.

1. solve \\(\frac{7}{8} \times \frac{12}{21}\\)

1. find the gcf and lcm of 10 and 12.

1. how many hours are 420 minutes?

Explanation:

Step1: Divide numerator by denominator

$44 \div 5 = 8$ remainder $4$

Step2: Form the mixed number

$8 + \frac{4}{5}$

Step1: Simplify fractions first

$\frac{7}{8} \times \frac{12}{21} = \frac{1}{2} \times \frac{3}{3}$

Step2: Multiply simplified fractions

$\frac{1 \times 3}{2 \times 3} = \frac{1}{2}$

Step1: List factors of 10 and 12

Factors of 10: $1, 2, 5, 10$; Factors of 12: $1, 2, 3, 4, 6, 12$

Step2: Identify GCF

GCF = $2$

Step3: List multiples of 10 and 12

Multiples of 10: $10, 20, 30, 40, 50, 60...$; Multiples of 12: $12, 24, 36, 48, 60...$

Step4: Identify LCM

LCM = $60$

Step1: Use conversion factor (60 min = 1 hr)

$420 \div 60 = 7$

Answer:

1. $\boldsymbol{8\frac{4}{5}}$
2. $\boldsymbol{\frac{1}{2}}$
3. GCF = $\boldsymbol{2}$, LCM = $\boldsymbol{60}$
4. $\boldsymbol{7}$ hours