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Fluency & PrecisionDivide Fractions by Integers 6
Lesson 15 – Divide Fractions by Integers
NC Objective:Divide proper fractions by whole numbers [for example [ for example ].
Resources needed:Differentiated SheetsTeaching Slides
Vocabulary:Fractions, numerator, denominator, division, multiple, integer, patterns, convert, improper fraction.
Children are introduced to dividing fractions by integers for the first time. They focus on dividing fractions where the numerator is a multiple of the integer they are dividing by. Encourage children to spot the pattern that the denominator stays the same and the numerator is divided by the integer Children link dividing fractions to multiplying by unit fractions. Use the diagrams children drew for multiplying fractions to discuss how and why the calculations are similar.
Key Questions:How could you represent this fraction? Is the numerator divisible by the integer?Why doesn’t the denominator change?What pattern can you see when dividing elevenths?How can we use the pattern to help us to calculate a mixed number by an integer? Can you convert it to an improper fraction?
Children will have completed diagrams to help them divide fractions.
Children will have blank diagrams which they will shade to help them divide fractions.
Children will create their own diagrams before completing the questions.
Children will use a range of harder fractions to multiply and divide. They match 4 fractions.
Reasoning & Problem Solving
Working Towards Working Within Greater Depth
12
÷ = 14
2
Children will use a range of fractions. They match 4 fractions.
Children will use fractions with a denominator of multiples of 5. They match 3 fractions and use tenths.
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Fluency & Precision
5 =35 ÷2 =2
3 ÷
6Divide Fractions by Integers
Malachi has of a chocolate bar. He shares it with his friend.
What fraction of the chocolate bar do they each get?
47
Use the diagrams to help you calculate.
Calculate.
4 =46 ÷
2 =27 ÷5 =5
8 ÷3 =34 ÷
3 =39 ÷2 =2
9 ÷1 =19 ÷
2 =89 ÷2 =6
9 ÷2 =49 ÷
3 =39 ÷3 =6
9 ÷3 =310 ÷ 1
masterthecurriculum.co.uk
Fluency & Precision
3 =35 ÷2 =2
3 ÷
6AnswersDivide Fractions by Integers
Malachi has of a chocolate bar. He shares it with his friend.
What fraction of the chocolate bar do they each get?
Use the diagrams to help you calculate.
Calculate.
4 =46 ÷
16
13
15
2 =27 ÷5 =5
8 ÷3 =34 ÷
14
18
17
3 =39 ÷2 =2
9 ÷1 =19 ÷
19
19
19
2 =89 ÷2 =6
9 ÷2 =49 ÷
29
39
49
3 =39 ÷3 =6
9 ÷3 =310 ÷
110
29
491
27
47
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Fluency & Precision 6Divide Fractions by Integers
3 =910 ÷3 =6
7 ÷
Use the diagrams to help you calculate.
Calculate.
2 =89 ÷
2 =45 ÷4 =8
11 ÷5 =1013 ÷
2 =1415 ÷3 =15
16 ÷4 =1217 ÷
7 =2123 ÷8 =16
17 ÷3 =910 ÷
5 =2021 ÷9 =18
25 ÷5 =1522 ÷
6 =3647 ÷9 =36
41 ÷4 =835 ÷
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Fluency & Precision 6AnswersDivide Fractions by Integers
3 =910 ÷3 =6
7 ÷
Use the diagrams to help you calculate.
Calculate.
2 =89 ÷
49
27
310
2 =45 ÷4 =8
11 ÷5 =1013 ÷
213
211
25
2 =1415 ÷3 =15
16 ÷4 =1217 ÷
317
516
715
7 =2123 ÷8 =16
17 ÷3 =910 ÷
310
217
323
5 =2021 ÷9 =18
25 ÷5 =1522 ÷
322
225
421
6 =3647 ÷9 =36
41 ÷4 =835 ÷
235
441
647
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Fluency & Precision 6Divide Fractions by Integers
Mark has of a watermelon. He shares it with his two friends.
What fraction of the watermelon do they each get?
Use the diagrams to help you calculate.
Liza eats of a cookies over 6 days. She eats the same amount each day.
How many cookies does Rosie eat each day?
7 =2122 ÷4 =12
15 ÷4 =1617 ÷
Calculate.
6÷5 =1519 ÷ 16
158÷=12
15 ÷ 3÷9 =1821 ÷
932
3÷=2132 ÷ 9÷4 =16
23 ÷
4863
12÷ = 3263 ÷
3÷4 = 917÷ 5÷9 = 5
17÷
3÷4 = 3943÷
1822
3÷ = 1222 ÷
4241
7÷=3041 ÷
68
1216
116
11÷ = 1216 ÷2
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Fluency & Precision 6AnswersDivide Fractions by Integers
Mark has of a watermelon. He shares it with his two friends.
What fraction of the watermelon do they each get?
Use the diagrams to help you calculate.
14
18
7 =2122 ÷4 =12
15 ÷4 =1617 ÷
Calculate.
6÷5 =1519 ÷
5243
315
1615
8÷=1215 ÷ 3÷9 =18
21 ÷
932
3÷=2132 ÷ 9÷4 =16
23 ÷
4863
12÷ = 3263 ÷
3÷4 = 917÷ 5÷9 = 5
17÷
3÷4 = 3943÷
1822
3÷ = 1222 ÷
322
417
917
1819
6
5
621
7 3623
4241
7÷=3041 ÷
1217
2
84
68
116
11÷ = 1216 ÷2
Liza eats of a cookies over 6 days. She eats the same amount each day.
How many cookies does Rosie eat each day?
1216
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Reasoning & Problem Solving
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Reasoning & Problem Solving
6
6
Divide Fractions by Integers
Divide Fractions by Integers
Rosie walks for of an hour over 3 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree? Explain why.
Dividing by 2 is the sameas finding half of a numberso is the same as
69
12 ×
269 ÷
Match the equivalent calculations.
Complete the missing integers.
310
38
14 × 23
8 ÷
38
12 × 43
8 ÷
38
18 × 83
8 ÷
1825
÷ = 615
1625
÷ = 225
Rosie walks for of an hour over 3 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree? Explain why.
Dividing by 2 is the sameas finding half of a numberso is the same as
69
12 ×
269 ÷
Match the equivalent calculations.
Complete the missing integers.
310
38
14 × 23
8 ÷
38
12 × 43
8 ÷
38
18 × 83
8 ÷
1825
÷ = 615
1625
÷ = 225
masterthecurriculum.co.uk
Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem Solving
6
6
Divide Fractions by Integers
Divide Fractions by Integers
Rosie walks for of an hour over 3 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree? Explain why.
Dividing by 2 is the sameas finding half of a numberso is the same as
69
12 ×
269 ÷
Match the equivalent calculations.
Complete the missing integers. 310
Rosie walks for of an hour each day. She walks for 6 minutes each day.
110
38
14 × 23
8 ÷
38
12 × 43
8 ÷
38
18 × 83
8 ÷
1825
÷ = 625
1625
÷ = 225
Answers
Answers
Malachi is correct. It may help children to understand this by reinforcing that is the same as of .
12× 6
912
69
3
8
Rosie walks for of an hour over 3 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree? Explain why.
Dividing by 2 is the sameas finding half of a numberso is the same as
69
12 ×
269 ÷
Match the equivalent calculations.
Complete the missing integers. 310
Rosie walks for of an hour each day. She walks for 6 minutes each day.
110
38
14 × 23
8 ÷
38
12 × 43
8 ÷
38
18 × 83
8 ÷
1825
÷ = 615
1625
÷ = 225
Malachi is correct. It may help children to understand this by reinforcing that is the same as of .
12× 6
912
69
3
8
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Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem Solving
6
6
Divide Fractions by Integers
Divide Fractions by Integers
Rosie walks for of an hour over 4 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree? Explain why.
Dividing by 3 is the sameas finding half of a numberso is the same as
69
13 ×
369 ÷
Match the equivalent calculations.
Complete the missing integers.
61217 ÷
46
1217
14 ×
41217 ÷12
1712 ×
21217 ÷12
1713 ×
31217 ÷12
1716 ×
1415
÷ = 715
1415
÷ = 215
1619
÷ = 419
1619
÷ = 819
Rosie walks for of an hour over 4 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree? Explain why.
Dividing by 3 is the sameas finding half of a numberso is the same as
69
13 ×
369 ÷
Match the equivalent calculations.
Complete the missing integers.
61217 ÷
46
1217
14 ×
41217 ÷12
1712 ×
21217 ÷12
1713 ×
31217 ÷12
1716 ×
1415
÷ = 715
1415
÷ = 215
1619
÷ = 419
1619
÷ = 819
masterthecurriculum.co.uk
Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem Solving
6
6
Answers
Answers
Divide Fractions by Integers
Divide Fractions by Integers
Rosie walks for of an hour over 4 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree? Explain why.
Dividing by 3 is the sameas finding half of a numberso is the same as
69
13 ×
369 ÷
Malachi is correct. It may help children to understand this by reinforcing that is the same as of .
13× 6
913
69
Match the equivalent calculations.
Complete the missing integers.
61217 ÷
46
Rosie walks for of an hour each day. She walks for 10 minutes each day.
16
1217
14 ×
41217 ÷12
1712 ×
21217 ÷12
1713 ×
31217 ÷12
1716 ×
1415
÷ = 715
1415
÷ = 215
1619
÷ = 419
1619
÷ = 819
2 7
4 2
Rosie walks for of an hour over 4 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree? Explain why.
Dividing by 3 is the sameas finding half of a numberso is the same as
69
13 ×
369 ÷
Malachi is correct. It may help children to understand this by reinforcing that is the same as of .
13× 6
913
69
Match the equivalent calculations.
Complete the missing integers.
61217 ÷
46
Rosie walks for of an hour each day. She walks for 10 minutes each day.
16
1217
14 ×
41217 ÷12
1712 ×
21217 ÷12
1713 ×
31217 ÷12
1716 ×
1415
÷ = 715
1415
÷ = 215
1619
÷ = 419
1619
÷ = 819
2 7
4 2
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Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem Solving
6
6
Divide Fractions by Integers
Divide Fractions by Integers
Rosie walks for of an hour over 3 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree?
Dividing the fraction by an integer number n
is the sameas multiplying this fraction
by the fraction .1n
Match the equivalent calculations.
Complete the missing integers.
31217 ÷
1820
1217
14 ×
41617 ÷16
1714 ×
41217 ÷15
1713 ×
31517 ÷12
1713 ×
1027
÷ = 227
2555
÷ = 211
3263
÷ = 263
272
÷ = 3772
1
1
Rosie walks for of an hour over 3 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree?
Dividing the fraction by an integer number n
is the sameas multiplying this fraction
by the fraction .1n
Match the equivalent calculations.
Complete the missing integers.
31217 ÷
1820
1217
14 ×
41617 ÷16
1714 ×
41217 ÷15
1713 ×
31517 ÷12
1713 ×
1027
÷ = 227
2555
÷ = 211
3263
÷ = 263
272
÷ = 3772
1
1
masterthecurriculum.co.uk
Reasoning & Problem Solving
masterthecurriculum.co.uk
Reasoning & Problem Solving
6
6
Answers
Answers
Divide Fractions by Integers
Divide Fractions by Integers
Rosie walks for of an hour over 3 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree?
Dividing the fraction by an integer number n
is the sameas multiplying this fraction
by the fraction .1n
Malachi is correct.
Match the equivalent calculations.
Complete the missing integers.
31217 ÷
1820
Rosie walks for of an hour each day. She walks for 18 minutes each day.
310
1217
14 ×
41617 ÷16
1714 ×
41217 ÷15
1713 ×
31517 ÷12
1713 ×
1027
÷ = 227
2555
÷ = 211
3263
÷ = 263
272
÷ = 3772
5 8
16 21
1
Rosie walks for of an hour over 3 days.
She walks for the same amount of time each day.
How many minutes does Rosie walk each day?
Malachi says,
Do you agree?
Dividing the fraction by an integer number n
is the sameas multiplying this fraction
by the fraction .1n
Malachi is correct.
Match the equivalent calculations.
Complete the missing integers.
31217 ÷
1820
Rosie walks for of an hour each day. She walks for 18 minutes each day.
310
1217
14 ×
41617 ÷16
1714 ×
41217 ÷15
1713 ×
31517 ÷12
1713 ×
1027
÷ = 227
2555
÷ = 211
3263
÷ = 263
272
÷ = 3772
5 8
16 21
1
