Today we will be learning how to add fractions with UNLIKE denominators. “Adding Apples to Oranges”
Let’s begin with some warm-ups! Fill in the missing numerator. • = 4. = • = 5. = • =
In our last lesson, we learned how to add and subtract fractions with like denominators. • We can easily add and subtract fractions with like denominators. (This is like adding apples to apples.) + • We simply add (or subtract) numerator, and place the answer on top of the common denominator. • Remember to always simplify fractions.
Sometimes the addition of fractions results in a sum that is greater than 1. This is usually written as an improper fraction. • In this case, we write the improper fraction, as a mixed number. • = 1 Write as a mixed number. • = 1 Simplify.
The tricky part comes with adding and subtracting with different denominators. This is like adding apples to oranges. The denominators are not the same. + Before we add fractions with different denominators, we must first find a way to make the denominators the same. (Either make them all apples, or all of them oranges!) Adding fractions with Different denominators
In order to make the denominator the same, you must first write an equivalent fraction with the same denominator. • First find the lowest common multiple (LCM) of both denominators. • Rewrite the fraction as equivalent fractions with the LCM as the denominator.
Let’s review a bit on finding the lowest common multiple. Go ahead and write the first 7 multiple of 3 and 5. 3: 5: Now, place a circle around the first multiple that is in both list.
The least common multiple is the smallest multiple that is common to both numbers. 3: 3, 6, 9, 12, 15, 18, 21 5: 5, 10, 15, 20, 25, 30, 35 15 is the LCM. Now we will write an equivalent fraction using 15 as a common denominator.
The LCD is 15. Write the fractions with the same denominator. Now that we have our least common denominator, we can make equivalent fractions by multiplying the numerator and denominator by the factors needed. (5 and 3)
Add the numerators. Now that we have fractions with the same denominators, we can add the numerators and keep the same denominator. Simplify if needed!
Some tricks of the trade. • The greater number of the denominators is often the lowest common denominator. • Check to see if the smaller denominator divides evenly into the larger denominator. • If it does, use the larger denominator for your LCD. + 2 will divide evenly into 4, so 4 is your LCD or LCM.
Let’s try this one together! • Add + • Since 3 divides into evenly into 9, 9 is our LCD. • Rewrite the fractions using 9 as your LCD, and then add the fractions. + ___________
Here’s another shortcut! If the denominators are one number apart, such as 3 and 4, the LCD will be the product of the denominator. Add + Since the denominator are one number apart, the LCD is the product of 3 and 4 12 You try this one. + ___________
Going Apples and Oranges! Solve the cryptogram!
ANSWER ADDING UNLIKE FRACTIONS IS LIKE ADDING APPLES TO ORANGES. BEFORE WE CAN ADD, WE MUST MAKE EVERYTHING ONE FRUIT!
Assessment • Larry is crazy about fruits. Larry decides to make a fruit medley consisting of 2/3 cups apples and 2/5 cups oranges. What is the process by which you can find the amount of fruits in the medley? 2. What is the lowest common denominator of the following? (a) and (b) and (c) and
Add + • Add + • Every Saturday, Sean gets up early in the morning and walks to various farmer’s market. He walks 2/3 miles to the Glenville’s Farmer’s market and buys fresh apples. He walks another ¼ mile to Roseville’s Farmer’s market for oranges. What is the total distance that Sean walks? (a) 3/12 mile (b) 3/7 mile (c) 11/12 mile (d) 1 mile
Easy Quick Fruit Salad ¾ cup fresh apples 2/5 cup fresh oranges 1/5 cup pineapples ½ cup bananas • Maria wants to make this quick and easy fruit salad. If she was to find the total amount of fruits in this salad: (a) What would be the least least common denominator that she would use? (b) What equivalent fractions would she use? (c) What is the total amount of fruits in the salad?
Let’s recap what we learned in this session! • First off, we learned that we can’t add apples to oranges. + • Or in mathematical language, we cannot add fractions with unlike denominators. • We first must make the denominators the same by finding the lowest common denominator.
In order to do so we must follow 2 steps • First find the lowest common multiple (LCM) of both denominators. • Rewrite the fraction as equivalent fractions with the LCM as the denominator. Once we have a common denominator we can add and write the sum in simplest form.
We also learned some ways to find the lowest common denominator. • We can list the multiples of the numbers. The least common multiple is the smallest multiple that is common to both numbers. 3: 3, 6, 9, 12, 15, 18, 21 5: 5, 10, 15, 20, 25, 30, 35 • The greater number of the denominators is often the lowest common denominator. Check to see if the smaller denominator divides evenly into the larger denominator. ½ and ¾ LCD is 4 • LCD can sometimes be the product of denominator. ¼ and 2/3 LCD is 12