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Solving Equations by Adding or Subtracting

  • You solve equations with fractions by using inverse operations, adding or subtracting, to isolate the variables.
  • Solving equations with fractions is similar to solving equations with integers and decimals; use the properties of equality to isolate the variable.
  • Remember to add and subtract fractions using the least common denominator. Create equivalent fractions with common denominators by multiplying both the numerator and denominator by the same number. Always write the answer in simplest form.

Solving Equations by Adding or Subtracting

Solve for x.
x + [3/4] = [7/9]
  • x = [7/9] − [3/4]
  • x = [28/36] − [27/36]
x = [1/36]
Solve for x.
[5/7] − x = [3/11]
  • − x = [3/11] − [5/7]
  • − x = [21/77] − [55/77]
  • − x = − [34/77]
x = [34/77]
Solve for x.
2[5/6] = [5/12] − x
  • 2[5/6] − [5/12] = − x
  • [17/6] − [5/12] = − x
  • [34/12] − [5/12] = − x
  • [29/12] = − x
  • x = − [29/12]
x = − 2[5/12]
Solve for x.
1[3/8] = x + 0.1
  • 1[3/8] − 0.1 = x
  • 1[3/8] − [1/10] = x
  • [11/8] − [1/10] = x
  • [55/40] − [4/40] = x
  • [51/40] = x
x = 1[11/40]
Solve for x.
− x + 3.5 = − [24/25]
  • − x = − [24/25] − 3.5
  • − x = − [24/25] − 3[5/10]
  • − x = − [24/25] − 3[1/2]
  • − x = − [24/25] − [7/2]
  • − x = − [48/50] − [175/50]
  • − x = − [223/50]
x = 4[23/50]
Solve for x.
11[3/4] + x = 12[11/12]
  • x = 12[11/12] − 11[3/4]
  • x = 12[11/12] − 11[9/12]
  • x = 1[2/12]
x = 1[1/6]
0.75 = x − [4/5]. Solve for x.
  • 0.75 + [4/5] = x
  • [75/100] + [4/5] = x
  • [3/4] + [4/5] = x
  • [15/20] + [16/20] = x
  • [31/20] = x
x = 1[11/20]
Eric's class is picking flowers for their mothers. If [1/4] of the class picks purple flowers, and [2/7] of the class picks red flowers, what fraction of the class picks flowers of another color?
  • Let f = the fraction of the class that chooses flowers of another color
  • [1/4] + [2/7] + f = 1
  • f = 1 − [1/4] − [2/7]
  • f = [28/28] − [7/28] − [8/28]
  • f = [21/28] − [8/28]
f = [13/28] of the class
A knitter has 4[2/9] yards of yarn. She uses 1[1/4] yards to make a scarf. How much yarn does the knitter have left?
  • Let y = amount of yarn the knitter has left
  • 1[1/4] + y = 4[2/9]
  • y = 4[2/9] − 1[1/4]
  • y = 4[8/36] − 1[9/36]
  • y = 3[44/36] − 1[9/36]
y = 2[35/36] yards
Sarah hammers a nail 3.5 inches long all the way through a board. On the other side, [3/4] inches of the nail pokes through. How thick is the board?
  • Let b = thickness of board.
  • b + [3/4] = 3.5
  • b + [3/4] = 3[5/10]
  • b + [3/4] = 3[1/2]
  • b + [3/4] = [7/2]
  • b = [7/2] − [3/4]
  • b = [14/4] − [3/4]
  • b = [11/4]
b = 2[3/4] inches thick

*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.

Answer

Solving Equations by Adding or Subtracting

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
  • What You'll Learn and Why 0:23
    • Isolate
  • Solving Equations with Fractions 0:41
    • Example: n + 1/2 = 11/12
    • Example: 3/5 - a = 13/20
  • Writing Equations with Fractions 3:08
    • Example: Thickness
  • Extra Example 1: Solving Equations 6:01
  • Extra Example 2: Solving Equations 6:58
  • Extra Example 3: School Lunches 8:23
  • Extra Example 4: Fashion Designer 10:44