5 Ways to Master Adding Fractions with 10 and 100

Understanding Fractions

Fractions are a way to represent part of a whole. They consist of two numbers: the numerator and the denominator. The numerator tells us how many equal parts we have, while the denominator tells us how many parts the whole is divided into. To master adding fractions, we need to understand the concept of equivalent ratios and how to find a common denominator.

Step 1: Understanding Equivalent Ratios

Equivalent ratios are fractions that have the same value, but different numbers. For example, ¹⁄₂ and ²⁄₄ are equivalent ratios because they both represent the same part of the whole. To find equivalent ratios, we can multiply or divide both the numerator and the denominator by the same number.

🤔 Note: When multiplying or dividing both the numerator and the denominator, the value of the fraction remains the same.

Step 2: Finding a Common Denominator

To add fractions, we need to have the same denominator. If the denominators are different, we need to find the least common multiple (LCM) of the two denominators. The LCM is the smallest number that both denominators can divide into evenly.

Example: Finding the LCM of 10 and 100

To find the LCM of 10 and 100, we can list the multiples of each number:

Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, 90, 100 Multiples of 100: 100, 200, 300, 400, 500

The first number that appears in both lists is 100, so the LCM of 10 and 100 is 100.

Step 3: Converting Fractions to Have a Common Denominator

Once we have found the LCM, we can convert both fractions to have the same denominator.

Example: Converting Fractions to Have a Common Denominator

Suppose we want to add ¹⁄₁₀ and ³⁄₁₀₀. To do this, we need to convert both fractions to have a denominator of 100.

¹⁄₁₀ = ¹⁰⁄₁₀₀ (multiply numerator and denominator by 10) ³⁄₁₀₀ = ³⁄₁₀₀ (no change needed)

Now we can add the fractions:

¹⁰⁄₁₀₀ + ³⁄₁₀₀ = ¹³⁄₁₀₀

Step 4: Adding Fractions with the Same Denominator

Now that we have the same denominator, we can add the fractions by adding the numerators.

Example: Adding Fractions with the Same Denominator

Suppose we want to add ¹³⁄₁₀₀ and ²⁵⁄₁₀₀.

¹³⁄₁₀₀ + ²⁵⁄₁₀₀ = ³⁸⁄₁₀₀

Step 5: Simplifying the Answer (Optional)

If the answer is not in simplest form, we can simplify it by dividing both the numerator and the denominator by the greatest common divisor (GCD).

Example: Simplifying the Answer

Suppose we want to simplify ³⁸⁄₁₀₀.

The GCD of 38 and 100 is 2. To simplify the fraction, we can divide both the numerator and the denominator by 2:

38 ÷ 2 = 19 100 ÷ 2 = 50

So the simplified answer is ¹⁹⁄₅₀.

In conclusion, mastering adding fractions with 10 and 100 requires understanding equivalent ratios, finding a common denominator, converting fractions, adding fractions with the same denominator, and simplifying the answer. By following these steps, you can become proficient in adding fractions with different denominators.