Welcome to Westonci.ca, where finding answers to your questions is made simple by our community of experts. Explore a wealth of knowledge from professionals across different disciplines on our comprehensive platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
To solve the problem of simplifying the fraction [tex]\(\frac{4}{16}\)[/tex] to its lowest terms and then finding an equivalent fraction with a denominator of 32, follow these steps:
### Step 1: Simplify the Fraction [tex]\(\frac{4}{16}\)[/tex] to Lowest Terms
1. Identify the numerator and the denominator:
[tex]\[ \text{Numerator} = 4, \quad \text{Denominator} = 16 \][/tex]
2. Find the Greatest Common Divisor (GCD) of the numerator and the denominator. The GCD of 4 and 16 is 4.
3. Divide both the numerator and the denominator by their GCD to simplify the fraction:
[tex]\[ \frac{4 \div 4}{16 \div 4} = \frac{1}{4} \][/tex]
So, the fraction [tex]\(\frac{4}{16}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex].
### Step 2: Find an Equivalent Fraction with a Denominator of 32
1. Identify the simplified fraction and the new required denominator:
[tex]\[ \text{Simplified fraction} = \frac{1}{4}, \quad \text{New denominator} = 32 \][/tex]
2. Determine the factor by which to multiply the denominator of the simplified fraction to achieve the new denominator. Since [tex]\(4\)[/tex] needs to be multiplied by [tex]\(8\)[/tex] to get [tex]\(32\)[/tex]:
[tex]\[ 4 \times 8 = 32 \][/tex]
3. Multiply both the numerator and the denominator of the simplified fraction by this factor:
[tex]\[ \frac{1 \times 8}{4 \times 8} = \frac{8}{32} \][/tex]
Thus, the equivalent fraction of [tex]\(\frac{1}{4}\)[/tex] with a denominator of 32 is [tex]\(\frac{8}{32}\)[/tex].
### Summary:
1. The fraction [tex]\(\frac{4}{16}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex].
2. An equivalent fraction with a denominator of 32 is [tex]\(\frac{8}{32}\)[/tex].
[tex]\[ \boxed{\frac{4}{16} = \frac{1}{4} = \frac{8}{32}} \][/tex]
### Step 1: Simplify the Fraction [tex]\(\frac{4}{16}\)[/tex] to Lowest Terms
1. Identify the numerator and the denominator:
[tex]\[ \text{Numerator} = 4, \quad \text{Denominator} = 16 \][/tex]
2. Find the Greatest Common Divisor (GCD) of the numerator and the denominator. The GCD of 4 and 16 is 4.
3. Divide both the numerator and the denominator by their GCD to simplify the fraction:
[tex]\[ \frac{4 \div 4}{16 \div 4} = \frac{1}{4} \][/tex]
So, the fraction [tex]\(\frac{4}{16}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex].
### Step 2: Find an Equivalent Fraction with a Denominator of 32
1. Identify the simplified fraction and the new required denominator:
[tex]\[ \text{Simplified fraction} = \frac{1}{4}, \quad \text{New denominator} = 32 \][/tex]
2. Determine the factor by which to multiply the denominator of the simplified fraction to achieve the new denominator. Since [tex]\(4\)[/tex] needs to be multiplied by [tex]\(8\)[/tex] to get [tex]\(32\)[/tex]:
[tex]\[ 4 \times 8 = 32 \][/tex]
3. Multiply both the numerator and the denominator of the simplified fraction by this factor:
[tex]\[ \frac{1 \times 8}{4 \times 8} = \frac{8}{32} \][/tex]
Thus, the equivalent fraction of [tex]\(\frac{1}{4}\)[/tex] with a denominator of 32 is [tex]\(\frac{8}{32}\)[/tex].
### Summary:
1. The fraction [tex]\(\frac{4}{16}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex].
2. An equivalent fraction with a denominator of 32 is [tex]\(\frac{8}{32}\)[/tex].
[tex]\[ \boxed{\frac{4}{16} = \frac{1}{4} = \frac{8}{32}} \][/tex]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. We appreciate your time. Please come back anytime for the latest information and answers to your questions. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.