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Subtracting Rational Numbers

• To subtract fractions with different denominators, write equivalent fractions for each fraction so that have the same denominator. Then subtract the numerators and keep the denominators the same. Remember to always check if you can simplify the fraction as your last step.
• Any common denominator can be used. If you are having trouble finding a common denominator you can multiply the denominators of the fractions with each other. However, using the Lowest Common Denominator may save steps and make simplifying the difference a lot easier.
• To subtract rational numbers that are in different forms, either make all the numbers fractions or make all the numbers decimals.

Subtracting Rational Numbers

[7/9] − [3/5] =
• [35/45] − [27/45] =
[8/45]
[6/7] − [1/3] =
• [18/21] − [7/21] =
[11/21]
− [8/15] − [1/6] =
• − [16/30] − [5/30] =
• − [21/30] =
− [7/10]
[34/8] − 2.2 =
• 4[2/8] − 2[2/10] =
• 4[10/40] − 2[8/40] =
• 2[2/40] =
2[1/20]
9.55 − 5[1/4] =
• 9[55/100] − 5[1/4] =
• 9[55/100] − 5[25/100] =
• 4[30/100] =
4[3/10]
[67/25] − 2.1 =
• 2[17/25] − 2[1/10] =
• 2[34/50] − 2[5/50] =
2[29/50]
5.09 − 2[3/8] =
• 5[9/100] − 2[3/8] =
• 5[18/200] − 2[75/200] =
• 4[218/200] − 2[75/200] =
2[143/200]
One watermelon weighs 10.4 pounds. Another watermelon weighs 10[7/9] pounds. How much more does the heavier watermelon weigh?
• 10.4 = 10[4/10] = 10[36/90]
• 10[7/9] = 10[70/90]
• 10[70/90] − 10[36/90] =
[34/90] pounds
A plant was 5[1/12] inches tall last year. Now, the plant is 17.29 inches tall. How much did the plant grow in the past year?
• Let g = inches the plant grew in the last year
• 5[1/12] + g = 17.29
• g = 17.29 − 5[1/12]
• 17[29/100] − 5[1/12] =
• 17[348/1200] − 5[100/1200] =
• 12[248/1200] =
12[31/150] inches

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Subtracting Rational Numbers

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What You'll Learn and Why 0:06
• Topics Overview
• Vocabulary 0:19
• Least Common Denominator (LCD)
• Subtracting with Unlike Denominators 0:41
• Example: 5/9 - 3/5
• Example: 3/4 - 7/8
• Subtracting Rational Numbers 1:59
• Example: 23/4 - 3.5
• Example: 11.7 - 3/4
• Subtracting Rational Numbers in Word Problems 4:37
• Puppy's Weight
• Extra Example 1: Subtracting with Unlike Denominators 6:48
• Extra Example 2: Subtracting Rational Numbers 7:27
• Extra Example 3: Rainfall 10:32
• Extra Example 4: Decorating Your House 12:06