Perform the indicated operations and express your answer simplest form 16/24-6/12
The Correct Answer and Explanation is:
Let’s break down the problem step by step:
We are tasked with solving:1624−612\frac{16}{24} – \frac{6}{12}2416−126
Step 1: Simplify Each Fraction
We will first simplify the fractions.
Simplify 1624\frac{16}{24}2416:
To simplify a fraction, we find the greatest common divisor (GCD) of the numerator and the denominator and divide both by that GCD. The GCD of 16 and 24 is 8.1624=16÷824÷8=23\frac{16}{24} = \frac{16 \div 8}{24 \div 8} = \frac{2}{3}2416=24÷816÷8=32
Simplify 612\frac{6}{12}126:
Similarly, the GCD of 6 and 12 is 6.612=6÷612÷6=12\frac{6}{12} = \frac{6 \div 6}{12 \div 6} = \frac{1}{2}126=12÷66÷6=21
Step 2: Find a Common Denominator
Now that we have simplified the fractions to 23\frac{2}{3}32 and 12\frac{1}{2}21, we need to perform the subtraction. However, we can’t subtract fractions with different denominators directly, so we need to find a common denominator.
The least common denominator (LCD) of 3 and 2 is 6.
Step 3: Convert the Fractions to the Common Denominator
Now, we convert both fractions to have the denominator of 6.
- For 23\frac{2}{3}32, we multiply both the numerator and denominator by 2:
23=2×23×2=46\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}32=3×22×2=64
- For 12\frac{1}{2}21, we multiply both the numerator and denominator by 3:
12=1×32×3=36\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}21=2×31×3=63
Step 4: Perform the Subtraction
Now, we subtract the two fractions:46−36=4−36=16\frac{4}{6} – \frac{3}{6} = \frac{4 – 3}{6} = \frac{1}{6}64−63=64−3=61
Final Answer:
16\frac{1}{6}61
Explanation:
In this problem, we first simplified the individual fractions and then converted them to a common denominator to perform the subtraction. The key steps involved:
- Simplifying the fractions.
- Finding a common denominator (6 in this case).
- Converting each fraction to have the same denominator.
- Subtracting the numerators and placing the result over the common denominator.
This process ensures that we handle fractions correctly and get the result in its simplest form, 16\frac{1}{6}61.
