Which fractions are equivalent to 6/8?
The Correct Answer and Explanation is:
Correct Answer:
The fractions that are equivalent to 6/8 include:
- 3/4
- 12/16
- 18/24
- 30/40
Explanation:
To find fractions equivalent to 6/8, we use the concept of equivalent fractions. Equivalent fractions represent the same part of a whole, even if they use different numbers. These fractions are obtained by multiplying or dividing both the numerator (top number) and denominator (bottom number) of a fraction by the same nonzero number.
Let’s start by simplifying 6/8:
We look for the greatest common factor (GCF) of 6 and 8, which is 2.6÷28÷2=34\frac{6 ÷ 2}{8 ÷ 2} = \frac{3}{4}8÷26÷2=43
So, 3/4 is the simplified form of 6/8, and thus it is equivalent.
Now let’s create more equivalent fractions by multiplying both the numerator and denominator of 6/8 by the same number:
- Multiply both by 2: 6×28×2=1216\frac{6×2}{8×2} = \frac{12}{16}8×26×2=1612
- Multiply both by 3: 6×38×3=1824\frac{6×3}{8×3} = \frac{18}{24}8×36×3=2418
- Multiply both by 5: 6×58×5=3040\frac{6×5}{8×5} = \frac{30}{40}8×56×5=4030
Each of these fractions has the same value as 6/8 when simplified. They represent the same proportion of a whole.
To confirm, you can divide the numerator by the denominator using a calculator:
- 6 ÷ 8 = 0.75
- 3 ÷ 4 = 0.75
- 12 ÷ 16 = 0.75
- 18 ÷ 24 = 0.75
- 30 ÷ 40 = 0.75
Because they all equal 0.75, these fractions are equivalent to 6/8. This shows how equivalent fractions can have different numbers but represent the same value.
