Adding Fractions and Finding Fractions of Numbers

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What this lesson covers

  • To add fractions with the same bottom number, add the tops and keep the bottom.
  • Subtracting fractions takes away pieces of the same size.
  • To find 1/3 of a number, divide it by 3.
  • If you know one part, multiply to find the whole.
Key idea

Adding pieces of the same size

  • 1/8 + 2/8 is one eighth plus two eighths.
  • That makes 3 eighths: 3/8.
  • The bottom number stays the same. Only the number of pieces changes.
SumAnswer
1/8 + 2/83/8
1/8 + 2/8 + 3/86/8
1/5 + 3/54/5
2/6 + 3/65/6
Key idea

Try it: add the pieces

Key idea

Taking pieces away

  • You have 5/6 of a cake. Your family eats 2/6.
  • 5 sixths take away 2 sixths leaves 3 sixths: 3/6.
  • The pieces are still sixths.
SumAnswer
5/6 − 2/63/6
7/10 − 4/103/10
3/4 − 1/42/4
Key idea

Try it: take pieces away

Key idea

A fraction of a number is division

  • 1/3 of 15 means cut 15 into 3 equal groups.
  • 15 ÷ 3 = 5, so 1/3 of 15 is 5.
FindDivideAnswer
1/2 of 1616 ÷ 28
1/3 of 1515 ÷ 35
1/4 of 2020 ÷ 45
1/5 of 3030 ÷ 56
1/10 of 4040 ÷ 104
Key idea

Try it: divide to find a fraction

Key idea

Find the whole from one part

  • 1/4 of a bag of mandarins is 3 mandarins.
  • The whole bag is 4 quarters, so it is 4 lots of 3.
  • 4 × 3 = 12 mandarins.
  • Check: 12 ÷ 4 = 3.
Key idea

Part and whole: times, not plus

  • If 1/4 is 3, the whole is not 3 + 4 = 7.
  • The whole is 4 times as big as one quarter: 4 × 3 = 12.
  • If 1/2 of a number is 6, the number is 2 × 6 = 12.

Common mistakes

  • 1/8 + 2/8 = 3/16.
    Add the tops only. Eighths plus eighths are still eighths: 3/8.
  • 1/3 of 15 is 15 − 3 = 12.
    Find 1/3 by dividing: 15 ÷ 3 = 5.
  • If 1/4 of a set is 3, the whole set is 3 + 4 = 7.
    There are 4 quarters, so the whole set is 4 × 3 = 12.
  • 5/6 − 2/6 = 3/0.
    Keep the bottom number: 5/6 − 2/6 = 3/6.

Your turn

1

2/7 + 3/7

2

9/10 − 4/10

3

What is 1/4 of 24?

4

1/3 of the pencils in a tin is 8 pencils. How many pencils are in the whole tin?

5

1/8 + 2/8 + 4/8

Show answer

1. 5/7 2. 5/10 3. 6 (24 ÷ 4 = 6) 4. 24 (3 × 8 = 24) 5. 7/8

Summary

What to take away

  • Same bottom number: add or take away the tops, keep the bottom.
  • A unit fraction of a number: divide.
  • The whole from one part: multiply.
Report a mistake

More in Number

Numbers to 1,000: Hundreds, Tens and OnesNotesCounting in Groups, Rounding and EstimatingNotesSkip Counting, Odd and Even NumbersNotesAdding and Subtracting up to 1,000NotesMultiplying and Dividing with GroupsNotesUnit Fractions: One Equal PartNotesComparing Fractions and Finding Equal OnesNotesAdding Fractions and Finding Fractions of NumbersNotesDollars, Cents and Giving ChangeNotes

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