5.6.4

Adding & Subtracting Mixed Numbers

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Adding & Subtracting Mixed Numbers

You can add and subtract mixed numbers by working out the whole numbers and the fractions separately.

Example 1

Example 1

  • Example 1 will look at adding two mixed numbers together.
  • Start by adding the whole numbers:
    • 1 + 2 = 3
Example 1 cont.

Example 1 cont.

  • Then add the fractions:
    • 25\large\frac{2}{5} + 15\large\frac{1}{5} = 35\large\frac{3}{5}
Example 2

Example 2

  • Example 2 will look at adding two mixed numbers together.
  • Start by adding the whole numbers:
    • 4 + 2 = 6
Example 2 cont.

Example 2 cont.

  • Then add the fractions:
    • 57\large\frac{5}{7} + 47\large\frac{4}{7} = 97\large\frac{9}{7}
Example 2 cont.

Example 2 cont.

  • 97\large\frac{9}{7} is an improper fraction.
    • 97\large\frac{9}{7} is the same as 127\large\frac{2}{7}.
  • 697\large\frac{9}{7} is the same as 6 + 127\large\frac{2}{7} = 727\large\frac{2}{7}

Adding & Subtracting Mixed Numbers

You can add and subtract mixed numbers by working out the whole numbers and the fractions separately.

Example 3

Example 3

  • The denominators (bottom numbers) on the fractions need to be the same to add (or subtract) the fractions.
  • You need to find equivalent fractions to make the denominators the same so you can add (or subtract) mixed numbers.
    • 223\large\frac{2}{3} = 246\large\frac{4}{6}
Example 3 cont.

Example 3 cont.

  • You can add the mixed numbers once the denominators (bottom numbers) are the same.
    • 2 + 1 = 3
    • 46\large\frac{4}{6} + 16\large\frac{1}{6} = 56\large\frac{5}{6}
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1

Year 5 - Number

1.1

Number & Place Value

1.1.1The Value of Digits to Millions1.1.2Smallest & Biggest Numbers to Millions1.1.3Ordering Numbers to Millions1.1.4Counting in Powers of 101.1.5Counting in Negative Numbers1.1.6Rounding Numbers up to 1,000,0001.1.7Reading Roman Numerals
1.2

Addition & Subtraction

1.2.1Written Methods for Adding Large Numbers1.2.2Written Methods for Subtracting Large Numbers1.2.3Mental Addition & Subtraction1.2.4Rounding to Check Your Answer
1.3

Multiplication & Division

1.3.1Multiples1.3.2Factors1.3.3Prime Numbers1.3.4Prime Factors1.3.5Composite Numbers1.3.6Factor Trees1.3.7Multiplication by a 1 Digit Number1.3.8Long Multiplication Using Column Method1.3.9Times Tables1.3.10Division1.3.11Multiplying & Dividing by 10, 100 & 1,0001.3.12Square & Cube Numbers
1.4

Fractions & Decimals

1.4.1Compare & Order Fractions1.4.2Identifying Equivalent Fractions1.4.3Add & Subtract Fractions1.4.4Mixed Numbers & Improper Fractions1.4.5Multiplying Fractions by Whole Numbers1.4.6Converting Between Decimals & Fractions1.4.7Rounding Decimals1.4.8Ordering Decimals
2

Year 5 - Measurement

2.1

Measures

2.1.1Metric Measurements2.1.2Imperial Measurements
2.2

Perimeter & Area

2.2.1Perimeter2.2.2Area
2.3

Time

2.3.1Units of Time
3

Year 5 - Geometry

3.1

Properties of 3D Shapes

3.1.1Types of 3D Shapes3.1.2Faces, Edges & Vertices
3.2

Properties of 2D Shapes

3.2.1Polygons
3.3

Angles

3.3.1Angles in Degrees3.3.2Types of Angle3.3.3Finding Missing Angles
3.4

Position & Direction

3.4.1Reflection & Translation
4

Year 5 - Statistics

4.1

Graphs

4.1.1Line Graphs4.1.2Tables4.1.3Timetables
5

Year 6 - Number

5.1

Number & Place Value

5.1.1The Value of Digits to Ten Millions5.1.2Ordering Numbers to Millions5.1.3Rounding5.1.4Negative Numbers
5.2

Multiplication & Division

5.2.1Multiplication by a 2 Digit Number5.2.2Division5.2.3Multiples5.2.4Factors5.2.5Primes
5.3

Mental Maths

5.3.1Multiplying & Dividing by 10, 100 & 1,0005.3.2Addition & Subtraction5.3.3Adding & Subtracting 10, 100 & 1,0005.3.4Multiplication & Division
5.4

Order of Operations

5.4.1BIDMAS
5.5

Problem Solving

5.5.1Addition & Subtraction Multi-step Problems5.5.2Problem Solving with Proportion
5.6

Fractions & Decimals

5.6.1Simplifying Fractions Using Equivalents5.6.2Ordering Different Types of Fraction5.6.3Adding & Subtracting Fractions5.6.4Adding & Subtracting Mixed Numbers5.6.5Multiplying Fractions5.6.6Dividing Fractions by Whole Numbers5.6.7Converting Between Decimals & Fractions5.6.8Dividing Decimals
6

Year 6 - Ratio & Proportion

6.1

Ratio

6.1.1Using Ratios6.1.2Simplifying Ratios
6.2

Percentages

6.2.1Calculating Percentages
6.3

Scale

6.3.1Scale of 2D Shapes
7

Year 6 - Algebra

7.1

Sequences

7.1.1Describing Sequences7.1.2Finding Gaps in Sequences
7.2

Missing Number Problems

7.2.1Missing Number Problems
7.3

Equations

7.3.1Balancing Equations7.3.2Combining Two Variables
8

Year 6 - Measurement

8.1

Problem Solving

8.1.1Problem Solving with Measures
8.2

Unit Conversion

8.2.1Conversion Between Miles & Kilometres
8.3

Perimeter, Area & Volume

8.3.1Area8.3.2Volume8.3.3Nets8.3.4Faces, Edges & Vertices
8.4

Angles

8.4.1Types of Angle8.4.2Finding Missing Angles8.4.3Finding Missing Angles in Triangles8.4.4Vertically Opposite Angles
8.5

Circles

8.5.1Parts of a Circle
8.6

Coordinate Grids

8.6.1Positions on Coordinate Grids8.6.2Reflection & Translation
9

Year 6 - Statistics

9.1

Displaying Data

9.1.1Pie Charts9.1.2Line Graphs
9.2

Averages

9.2.1Mean

Practice questions on Adding & Subtracting Mixed Numbers

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    What is 4$$\large\frac{6}{7}$$ + 1$$\large\frac{2}{7}$$?Multiple choice
  2. 2
    What is 1$$\large\frac{1}{9}$$ + 6$$\large\frac{4}{9}$$?Multiple choice
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