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Questions and Answers
What is the first step in adding fractions with different denominators?
How do you compare two fractions with different denominators?
What is the purpose of finding an equivalent ratio?
What is the result of adding 1/8 and 1/12?
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Which of the following is an equivalent ratio of 3/6?
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What is the result of comparing 2/3 and 3/4?
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What is the result of adding 2/5 and 3/10?
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Which of the following is NOT a step in adding fractions?
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Study Notes
Adding Fractions
- To add fractions, they must have the same denominator (bottom number).
- If the denominators are different, find the least common multiple (LCM) of the two denominators and convert both fractions to have the LCM as the denominator.
- Add the numerators (top numbers) and keep the denominator the same.
- Simplify the resulting fraction, if possible.
Example: Add 1/4 and 1/6 LCM of 4 and 6 is 12 Convert to 3/12 and 2/12 Add: 3/12 + 2/12 = 5/12
Equivalent Ratios
- Equivalent ratios are fractions that have the same value, but different numbers.
- To find an equivalent ratio, multiply or divide both the numerator and denominator by the same number.
- This does not change the value of the fraction.
- Equivalent ratios can be used to simplify fractions or to find a common denominator.
Example: Find an equivalent ratio of 2/4 Multiply both numbers by 2: 2/4 = 4/8 Multiply both numbers by 1/2: 2/4 = 1/2
Comparing Fractions
- To compare fractions, find a common denominator and convert both fractions to have the common denominator.
- Then, compare the numerators.
- The fraction with the larger numerator is the larger fraction.
- If the numerators are the same, the fraction with the smaller denominator is the larger fraction.
Example: Compare 1/4 and 2/6 Find a common denominator: 12 Convert to 3/12 and 4/12 Compare: 3/12 < 4/12, so 1/4 < 2/6
Adding Fractions
- Fractions must have the same denominator to be added.
- If denominators are different, find the least common multiple (LCM) and convert both fractions to have the LCM as the denominator.
- Add the numerators and keep the denominator the same.
- Simplify the resulting fraction, if possible.
Equivalent Ratios
- Equivalent ratios are fractions with the same value but different numbers.
- To find an equivalent ratio, multiply or divide both the numerator and denominator by the same number.
- This does not change the value of the fraction.
- Equivalent ratios can be used to simplify fractions or find a common denominator.
Comparing Fractions
- To compare fractions, find a common denominator and convert both fractions.
- Compare the numerators; the fraction with the larger numerator is larger.
- If numerators are the same, the fraction with the smaller denominator is larger.
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Description
Learn how to add fractions with different denominators and find equivalent ratios. Understand the concept of least common multiple (LCM) and simplify fractions.
