CBSE Class 6 Maths: Fractions Exercise 7.3 - Equivalent Fractions

What are Equivalent Fractions?

Equivalent fractions are fractions that look different but represent the exact same part of a whole. Think of it like this: if you have a chocolate bar and break it into two equal pieces, one piece is 1/2 of the bar. Now, if you take that same chocolate bar and break it into four equal pieces, then two of those pieces (2/4) would be the same amount as 1/2. Similarly, if you broke it into six equal pieces, three of those pieces (3/6) would also represent the same amount.

So, 1/2, 2/4, and 3/6 are all equivalent fractions. They all stand for the same quantity. The key idea is that the whole is divided into more parts, but you are taking proportionally more of those parts. This concept is incredibly useful when you need to compare fractions or add/subtract them, as it allows us to express them with a common denominator. Understanding equivalent fractions builds a strong foundation for all future fraction-related topics.

How to Find Equivalent Fractions

1. Method 1: Multiplication (Making larger parts) — To find an equivalent fraction, you can multiply both the numerator (top number) and the denominator (bottom number) by the same non-zero number. This is like dividing the existing parts into even smaller pieces. Example: Find an equivalent fraction for 2/3. 1. Choose a number, let's say 2. 2. Multiply the numerator by 2: 2 2 = 4. 3. Multiply the denominator by 2: 3 2 = 6. So, 2/3 is equivalent to 4/6. You can choose any whole number (except zero) to multiply, and you'll get a new equivalent fraction!
2. Method 2: Division (Simplifying to smaller parts) — If the numerator and denominator have a common factor (a number that can divide both exactly), you can divide both by that common factor to find an equivalent (and usually simpler) fraction. This is the process of simplifying a fraction. Example: Find an equivalent fraction for 6/8. 1. Find a common factor of 6 and 8. Both can be divided by 2. 2. Divide the numerator by 2: 6 / 2 = 3. 3. Divide the denominator by 2: 8 / 2 = 4. So, 6/8 is equivalent to 3/4. This method helps in reducing a fraction to its simplest form.

How to Check if Two Fractions are Equivalent

• Example 1: Using Simplification Are 4/10 and 2/5 equivalent? Step 1: Simplify 4/10. Both 4 and 10 are divisible by 2. 4 ÷ 2 = 2 10 ÷ 2 = 5 So, 4/10 simplifies to 2/5. Step 2: Compare the simplified form to the second fraction. Since 2/5 is equal to 2/5, the fractions 4/10 and 2/5 are equivalent.
• Example 2: Using Cross-Multiplication Are 3/4 and 9/12 equivalent? Step 1: Multiply the numerator of the first fraction by the denominator of the second fraction. 3 12 = 36 Step 2: Multiply the denominator of the first fraction by the numerator of the second fraction. 4 9 = 36 Step 3: Compare the products. Since 36 = 36, the products are equal, which means the fractions 3/4 and 9/12 are equivalent.

YoLearn's Exam Tip: Avoid Common Mistakes!

A common mistake students make is multiplying or dividing the numerator and denominator by different numbers. Remember, to maintain the value of the fraction, you must multiply or divide both the top and bottom by the exact same non-zero number. If you multiply the numerator by 2 and the denominator by 3, you are changing the actual value of the fraction, not just its appearance! Always double-check that you're applying the same operation to both parts of the fraction.

Practice Questions with Solutions

• Q: Find two equivalent fractions for 3/7.
• A: Step 1: Multiply numerator and denominator by 2. 3 2 = 6 7 2 = 14 So, 6/14 is an equivalent fraction. Step 2: Multiply numerator and denominator by 3. 3 3 = 9 7 3 = 21 So, 9/21 is another equivalent fraction. Final answer: 6/14 and 9/21 (other answers like 12/28 are also correct).
• Q: Are 8/12 and 2/3 equivalent fractions?
• A: Step 1: Simplify 8/12. Find a common factor for 8 and 12. Both are divisible by 4. 8 ÷ 4 = 2 12 ÷ 4 = 3 So, 8/12 simplifies to 2/3. Step 2: Compare the simplified fraction with 2/3. Since 2/3 is equal to 2/3, they are equivalent. Final answer: Yes, 8/12 and 2/3 are equivalent fractions.
• Q: Fill in the blank to make the fractions equivalent: 5/9 = ?/36
• A: Step 1: Determine what number 9 was multiplied by to get 36. 36 ÷ 9 = 4. So, the denominator was multiplied by 4. Step 2: Multiply the numerator by the same number, 4. 5 * 4 = 20. Final answer: 5/9 = 20/36.
• Q: Which of the following fractions is equivalent to 15/20? (a) 3/4 (b) 6/8 (c) 1/2 (d) Both (a) and (b)
• A: Step 1: Simplify 15/20 to its simplest form. Both 15 and 20 are divisible by 5. 15 ÷ 5 = 3 20 ÷ 5 = 4 So, 15/20 simplifies to 3/4. Step 2: Check option (a). 3/4 is the simplified form of 15/20, so 3/4 is equivalent. Step 3: Check option (b). Simplify 6/8. Both 6 and 8 are divisible by 2. 6 ÷ 2 = 3 8 ÷ 2 = 4 So, 6/8 also simplifies to 3/4, making it equivalent to 15/20. Step 4: Check option (c). 1/2 is not 3/4, so it's not equivalent. Step 5: Conclude based on findings. Since both (a) and (b) are equivalent to 15/20. Final answer: (d) Both (a) and (b).

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