what are the equivalent fractions of 6/8 and 1/2
The Correct Answer and Explanation is:
Correct Answer:
Equivalent fractions of 6/8 include 3/4, 12/16, and 18/24.
Equivalent fractions of 1/2 include 2/4, 3/6, and 4/8.
Explanation:
Equivalent fractions are fractions that have different numerators and denominators but represent the same value or proportion of a whole. To find an equivalent fraction, you can either multiply or divide both the numerator and denominator of a given fraction by the same non-zero number. This does not change the value of the fraction.
Let us start with 6/8. To simplify it, we look for the greatest common factor (GCF) of 6 and 8, which is 2. Dividing both the numerator and denominator by 2 gives us: 6÷2=3and8÷2=46 ÷ 2 = 3 \quad \text{and} \quad 8 ÷ 2 = 46÷2=3and8÷2=4
So, 6/8 = 3/4, which means they are equivalent. You can also create other equivalent fractions by multiplying both the numerator and denominator of 6/8 by the same number. For example:
- 6×2=126 × 2 = 126×2=12 and 8×2=168 × 2 = 168×2=16, so 6/8=12/166/8 = 12/166/8=12/16
- 6×3=186 × 3 = 186×3=18 and 8×3=248 × 3 = 248×3=24, so 6/8=18/246/8 = 18/246/8=18/24
Now let us look at 1/2. This fraction is already in its simplest form, but you can find equivalent fractions by multiplying both parts:
- 1×2=21 × 2 = 21×2=2 and 2×2=42 × 2 = 42×2=4, so 1/2=2/41/2 = 2/41/2=2/4
- 1×3=31 × 3 = 31×3=3 and 2×3=62 × 3 = 62×3=6, so 1/2=3/61/2 = 3/61/2=3/6
- 1×4=41 × 4 = 41×4=4 and 2×4=82 × 4 = 82×4=8, so 1/2=4/81/2 = 4/81/2=4/8
By understanding how to multiply or divide both parts of a fraction, you can easily generate equivalent fractions that represent the same value.
