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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