Adding and Subtracting Fractions · Adding and Subtracting Fractions with Different Denominators...
Transcript of Adding and Subtracting Fractions · Adding and Subtracting Fractions with Different Denominators...
Adding and Subtracting Fractions
• To add and subtract fractions with the same denominator.
• To add and subtract fractions with different denominators.
• To add and subtract mixed number fractions.
• To add and subtract fractions.
Learning Objective
Success Criteria
Find the lowest common multiple for each pair of numbers.
Starter: Lowest Common Multiple
3 and 41
5 and 62
3 and 63
4 and 84
5 and 105
12
30
6
8
10
ExtensionFind the missing numbers for each fraction.
1. – = —
2. – = —
3. – = —
25
?20
58
?40
56
25?
Find the lowest common multiple for each pair of numbers.
Starter: Lowest Common Multiple
3 and 41
5 and 62
3 and 63
4 and 84
5 and 105
12
30
6
8
10
ExtensionFind the missing numbers for each fraction.
1. – = —
2. – = —
3. – = —
25
820
58
2540
56
2530
To add fractions which have the same denominator, you must add only the numerators together.
Adding and Subtracting Fractions with the Same Denominator
— + — = —210
510
710
Practice QuestionProve that – + – is –2
626
23
=
2 chairs + 3 chairs = 5 chairs
Adding and Subtracting Fractions with Different Denominators
What would 2 chairs + 7 rulers be?
We can’t add them together because they aren’t the same object. We can only add them together when they are the same. This is the same for fractions.
7 rulers – 5 rulers = 2 rulers
Adding and Subtracting Fractions with Different Denominators
What could we do to the fractions so we can add them? Discuss this with the person next to you.
At the moment you can’t add these fractions together because they have different denominators.
2– + —3105
Remember, they must have the same denominator before you can add the fractions together.
Adding and Subtracting Fractions with Different Denominators
2– + —3105
We need to find the lowest common multiple for 5 and 10.1
This needs to be the denominator for both fractions. 2
Now that the denominators are the same, perform the addition.4
10
10
– + —
— + —5 10? 3
10
2 3
– = —25
410
— + — = —410
310
710
Now write the equivalent fraction for 3 –52
Adding and Subtracting Fractions with Different Denominators
5– - –148
We need to find the lowest common multiple for 8 and 4.1
This needs to be the denominator for both fractions. 2
Now that the denominators are the same, perform the subtraction.4
8
8
— - —
— - —8 45 ?
8
5 1
– = —14
28
— - — = —58
28
38
Now write the equivalent fraction for 3 –41
Adding and Subtracting Fractions with Different Denominators
1– + –274
We need to find the lowest common multiple for 4 and 7.1
This needs to be the denominator for both fractions. 2
Now that the denominators are the same, perform the subtraction.4
28
— + —4 71 2
— + — = —728
828
1528
Now write the equivalent fraction for 3 –41
28? ?— + —
28
4 71 2
28— + —
28— + — 7 8
Adding and Subtracting Fractions with Different Denominators
3– - –254
We need to find the lowest common multiple for 4 and 5.1
This needs to be the denominator for both fractions. 2
Now that the denominators are the same, perform the subtraction.4
20
— - —4 53 2
— - — = —1520
820
720
Now write the equivalent fractions.3
20? ?— - —
20
4 5
3 2
20
15 8
20— - — — - —
Adding and Subtracting Mixed Number Fractions
How could we calculate the following?
Discuss with the person next to you.
12 – + 3 –134
Adding and Subtracting Mixed Number Fractions
Convert your mixed number fractions to improper fractions.1
2 — + 3 —4 3
– + —9
4
10
3
1 1
Find the lowest common multiple for 4 and 3.2
12
This needs to be the denominator for both fractions. 3
– + —4 3
— + —?
12
?
12
9 10
Adding and Subtracting Mixed Number Fractions
Write the equivalent fractions. 4
Now that the denominators are the same, perform the addition.5
Don’t forget to write your answer as a mixed number fraction, if appropriate.
6
– + —4 3
— + —
9
12
10
1227 40
— + — = —2712
4012
6712
— = 5 —12 1267 7
Adding and Subtracting Mixed Number Fractions
Convert your mixed number fractions to improper fractions.1
Find the lowest common multiple for 5 and 4.2
This needs to be the denominator for both fractions. 3
— - —5 4
2 13 2
— - —5
17
4
9
20
— - —5
17
4
9
— - —20
? ?
20
Adding and Subtracting Mixed Number Fractions
Write the equivalent fractions. 4
Now that the denominators are the same, perform the subtraction.5
Don’t forget to write your answer as a mixed number fraction, if appropriate.6
— - —5 4
17 9
— - —20
68
20
45
— - — = —20
68
20
45
20
23
20
23— = 1 —20
3