Adding Fractions and Equivalent Ratios

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.