Simplify 10/16 to lowest terms and find an equivalent fraction that has a denominator of 32?
The Correct Answer and Explanation is:
To simplify the fraction 10/16 to its lowest terms and find an equivalent fraction with a denominator of 32, we need to follow these steps:
Step 1: Simplify the Fraction 10/16 to Lowest Terms
To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator (10) and the denominator (16). The GCD is the largest number that can divide both 10 and 16 without leaving a remainder.
Find the Factors of 10:
The factors of 10 are:
1, 2, 5, 10
Find the Factors of 16:
The factors of 16 are:
1, 2, 4, 8, 16
Find the Greatest Common Divisor (GCD):
The common factors of 10 and 16 are:
1, 2
The greatest common factor is 2.
Simplify the Fraction:
Now, divide both the numerator and the denominator by the GCD (which is 2):
[
\frac{10}{16} = \frac{10 \div 2}{16 \div 2} = \frac{5}{8}
]
So, 10/16 simplified to lowest terms is 5/8.
Step 2: Find an Equivalent Fraction with a Denominator of 32
Now, we want to express the simplified fraction 5/8 as an equivalent fraction with a denominator of 32.
To do this, we need to find the number by which we must multiply the denominator (8) to get 32.
[
8 \times 4 = 32
]
So, we multiply both the numerator and the denominator of 5/8 by 4:
[
\frac{5}{8} \times \frac{4}{4} = \frac{5 \times 4}{8 \times 4} = \frac{20}{32}
]
Thus, the equivalent fraction with a denominator of 32 is 20/32.
Final Answer:
- The simplified form of 10/16 is 5/8.
- An equivalent fraction with a denominator of 32 is 20/32.
Explanation:
The process of simplifying fractions involves finding the GCD of the numerator and denominator. Once the GCD is identified, dividing both the numerator and denominator by that number gives the fraction in its simplest form. To find an equivalent fraction with a specific denominator, we multiply both the numerator and denominator by the same factor so that the new denominator matches the target number. In this case, to convert 5/8 to a fraction with a denominator of 32, we multiplied both parts of the fraction by 4.