MATHEMATICSConverting between Mixed Numbers and Improper Fractions

Lesson Objectives

•The aim of this powerpoint is to help you…

• to convert mixed numbers to improper fractions

• to convert improper fractions to mixed numbers

RECAP: Types of Fractions…

• PROPER fractions have a smaller value on the top than the bottom. They are worth less than 1.

e.g.

• IMPROPER (or top-heavy) fractions have a bigger value on the top than the bottom. They are worth more than 1.

e.g.

• MIXED NUMBERS are whole numbers and proper fraction together.

e.g. 2

Fractions are divisions…• The line in a fraction represents division.• ¾ means 3 ÷ 4• Pictorially let’s share 3 squares equally between 4 people

• Each person gets one colour = ¾ of a square

Improper Fractions Mixed Numbers

• To convert an improper fraction to a mixed number…

• Divide the top number by the bottom number

• The answer becomes the whole number part

• Any remainder becomes the fractional part (and is written over the original bottom number)

Example 1

• Let’s convert to a mixed number• 21 ÷ 8 = 2 rem. 5 2

• Let’s check by shading in 21 of these ‘eighths’…

• You should see that 21 eighths = 2 whole ones + 5 eighths = 2

Example 2

• Let’s convert to a mixed number• 23 ÷ 5 = 4 rem. 3 4

• Let’s check by shading in 23 of these ‘fifths’…

• You should see that 23 fifths = 4 whole ones + 3 fifths

Quick Practice

• Convert each of the following improper fractions into mixed numbers.

A D

B E

C F

Work out the answers before moving on to the next slide.

Answers (and workings)

A 7 ÷ 2 = 3 r.1 3

B 15 ÷ 4 = 3 r.3 3

C 13 ÷ 3 = 4 r.1 4

D 25 ÷ 6 = 4 r.1 4

E 41 ÷ 7 = 5 r.6 5

F 39 ÷ 5 = 7 r.4 7

Whole Numbers and Fractions

• The bottom number of a fraction tells you the ‘type’ of fraction you have so whole numbers can be represented in a fraction over the number 1

• E.g. 8 =

• If you have the same number on the top and the bottom of the fraction, you have a whole one.

• E.g. = 1

E.g. 28 =

E.g. = 1

Whole Numbers and Fractions (cont’d)

• Remember that 5 fifths is equal to 1 whole one.• How many fifths are there in 2 whole ones?• i.e. 2 =

• Remember that 7 sevenths is equal to 1 (whole).• How many sevenths are there in 4?• E.g. 4 =

Ans. 2 =

Ans. 4 =

Mixed Numbers Improper Fractions

• To convert an improper fraction to a mixed number…

• Multiply the whole number by the bottom number of the fraction

• Add the top number of the fraction to your answer

• You now have the new numerator (top number) – the denominator (bottom number) stays the same!

Example

• Let’s convert 2 to an improper fraction• 2 (2 × 6) + 5 = 17

• 2 means 2 whole ones and 5 sixths

• You should be able to count the number of sixths in 2 = 17 sixths =

Quick Practice

• Convert each of the following mixed numbers into improper fractions.

A 1 D 3

B 5 E 2

C 2 F 4

Work out the answers before moving on to the next slide.

Answers (and workings)

A 1 (1 × 9) + 4 = 13

B 5 (5 × 2) + 1 = 11

C (2 × 8) + 7 = 23

D (3 × 5) + 3 = 18

E (2 × 11) + 9 = 31

F (4 × 12) + 7 = 55

What next?

• Print out the notes called Frac2a and Frac2b. Read them and make sure you answer any questions

• Work through all of the MyMaths lesson called Improper and Mixed Numbers found at: http://www.mymaths.co.uk/tasks/library/loadLesson.asp?title=fractions/improperFractions&taskID=1019

• If you need more practice, try the worksheet called MN-IF-S1.xlsx.

• Now move on to the Frac-3 powerpoint