Mixed numbers and improper fractions

The Maths Habit

Ben and Sam each have some cake. All the cakes are the same size. Who has more cake?

Ben4 halves and 1 half: 5 halves
Sam5 halves

The same. Each whole cake is 2 halves.

Mixed number
A whole number and a fraction together.
212
Improper fraction
A fraction with a top number bigger than its bottom number.
52
Denominator
The bottom number of a fraction. It tells you how many equal parts make one whole.
34

How many parts are there?

1 whole2 halves
2 wholes6 thirds
3 wholes12 quarters

wholes×bottom+top=all the parts
soall the partsbottom
  1. 1Cut each whole into parts.The bottom number tells you how many parts.
  2. 2Count all the parts.Wholes times parts in each whole, then add the parts left.
  3. 3Keep the bottom.The parts do not change size.

Write 213 as an improper fraction.

1Cut each whole into parts.
111/3
2Count all the parts.
2×3+1=7
3Keep the bottom.
so73

Write 134 as an improper fraction.

1Cut each whole into parts.
13/4
2Count all the parts.
1×4+3=7
3Keep the bottom.
so74

Write 213 as an improper fraction.

1Cut each whole into parts.
111/3
2Count all the parts.
2×3+1=7
3Keep the bottom.
so73
1Cut each whole into parts.2Count all the parts.3Keep the bottom.

Write 225 as an improper fraction.

1Cut each whole into parts.
112/5
2Count all the parts.
2×5+2=12
3Keep the bottom.
so125

Write 213 as an improper fraction.

1Cut each whole into parts.
111/3
2Count all the parts.
2×3+1=7
3Keep the bottom.
so73
1Cut each whole into parts.2Count all the parts.3Keep the bottom.

Write 312 as an improper fraction.

1Cut each whole into parts.
1111/2
2Count all the parts.
3×2+1=7
3Keep the bottom.
so72

Write 213 as an improper fraction.

1Cut each whole into parts.
111/3
2Count all the parts.
2×3+1=7
3Keep the bottom.
so73
1Cut each whole into parts.2Count all the parts.3Keep the bottom.

Write 145 as an improper fraction.

1Cut each whole into parts.
14/5
2Count all the parts.
1×5+4=9
3Keep the bottom.
so95

1Cut each whole into parts.2Count all the parts.3Keep the bottom.

1Write 112 as an improper fraction.

11/2
1×2+1=3
so32

2Write 215 as an improper fraction.

111/5
2×5+1=11
so115

3Write 113 as an improper fraction.

11/3
1×3+1=4
so43

4Write 334 as an improper fraction.

1113/4
3×4+3=15
so154

How many full wholes?

4
3
1

full wholesparts left
sofull wholesparts leftbottom
  1. 1Fill the wholes.Shade the parts one whole at a time.
  2. 2Count the full wholes and the parts left.A full bar is 1 whole.
  3. 3Keep the bottom.The parts left make the fraction.

Write 73 as a mixed number.

1Fill the wholes.
111/3
2Count the full wholes and the parts left.
2full wholes1parts left
3Keep the bottom.
so213

Write 113 as a mixed number.

1Fill the wholes.
1112/3
2Count the full wholes and the parts left.
3full wholes2parts left
3Keep the bottom.
so323

Write 73 as a mixed number.

1Fill the wholes.
111/3
2Count the full wholes and the parts left.
2full wholes1parts left
3Keep the bottom.
so213
1Fill the wholes.2Count the full wholes and the parts left.3Keep the bottom.

Write 94 as a mixed number.

1Fill the wholes.
111/4
2Count the full wholes and the parts left.
2full wholes1parts left
3Keep the bottom.
so214

Write 73 as a mixed number.

1Fill the wholes.
111/3
2Count the full wholes and the parts left.
2full wholes1parts left
3Keep the bottom.
so213
1Fill the wholes.2Count the full wholes and the parts left.3Keep the bottom.

Write 52 as a mixed number.

1Fill the wholes.
111/2
2Count the full wholes and the parts left.
2full wholes1parts left
3Keep the bottom.
so212

Write 73 as a mixed number.

1Fill the wholes.
111/3
2Count the full wholes and the parts left.
2full wholes1parts left
3Keep the bottom.
so213
1Fill the wholes.2Count the full wholes and the parts left.3Keep the bottom.

Write 143 as a mixed number.

1Fill the wholes.
11112/3
2Count the full wholes and the parts left.
4full wholes2parts left
3Keep the bottom.
so423

Mixed numbers and improper fractions worksheet, page 1

Mixed numbers and improper fractions worksheet, page 2

Answer sheet

Is it right?
Thumbs up: right. Thumbs down: wrong.

  1. 123 = 53

    Right

  2. 214 = 214

    Wrong: it is 94

  3. 72 = 312

    Right

  4. 115 = 115

    Wrong: it is 215

  5. 315 = 85

    Wrong: it is 165

  1. Write 437 as an improper fraction.

    317

  2. Write 476 as a mixed number.

    756

  3. Write 212 as an improper fraction with a bottom number of 6.

    156

  1. Write 135 as an improper fraction.

    85
    1Cut each wholeinto parts.2Count allthe parts.×+=3Keep thebottom.so

  2. Write 74 as a mixed number.

    134
    1Fill the wholes.2Count the fullwholes and theparts left.full wholesparts left3Keep thebottom.so

  3. Write 413 as an improper fraction.

    133
Exit tickets to print