Finding equivalent fractions is a fundamental concept in mathematics, crucial for understanding fractions, decimals, and ratios. This guide will clearly explain how to determine how many twelfths are equal to one-third (1/3). We'll break down the process step-by-step, making it easy to understand and apply to similar problems.
Understanding Equivalent Fractions
Equivalent fractions represent the same portion of a whole, even though they look different. Think of cutting a pizza: one-half (1/2) is the same as two-quarters (2/4), or four-eighths (4/8). They all represent half the pizza. The key is that the ratio between the numerator (top number) and the denominator (bottom number) remains constant.
Finding the Equivalent Fraction
To find how many twelfths are equivalent to 1/3, we need to find a fraction with a denominator of 12 that represents the same value as 1/3. Here's how:
1. Identify the target denominator: We want a denominator of 12.
2. Determine the multiplication factor: Ask yourself: "What number, when multiplied by the denominator of 1/3 (which is 3), will give us 12?" The answer is 4 (because 3 x 4 = 12).
3. Apply the multiplication factor: Since we multiplied the denominator by 4, we must also multiply the numerator by the same number to maintain the equivalent fraction. So, we multiply the numerator of 1/3 (which is 1) by 4: 1 x 4 = 4.
4. The equivalent fraction: This gives us the equivalent fraction 4/12.
Therefore, there are four twelfths (4/12) equivalent to one-third (1/3).
Visual Representation
Imagine a circle divided into 12 equal slices (twelfths). If you shade in 4 of those slices, you've shaded in exactly one-third of the circle. This visually demonstrates the equivalence.
Practice Makes Perfect
Try finding equivalent fractions for other fractions! For example:
- How many sixths are equivalent to 1/2?
- How many fifteenths are equivalent to 1/3?
By following the steps outlined above, you'll quickly master the skill of finding equivalent fractions. This is a crucial skill for success in various mathematical concepts.
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