Add or subtract the fractions, then simplify the answer if needed. You can leave your answer as an improper fraction where needed.
1) [tex]$\frac{5}{4}+\frac{3}{4}=\frac{8}{4}$[/tex]
2) [tex]$\frac{9}{3}-\frac{5}{3}=\frac{4}{3}$[/tex]
3) [tex]$\frac{23}{6}-\frac{7}{6}=[/tex]
4) [tex]$\frac{9}{8}+\frac{12}{8}=[/tex]
5) [tex]$\frac{16}{9}+\frac{8}{9}=[/tex]
6) [tex]$\frac{23}{10}-\frac{11}{10}=[/tex]
7) [tex]$\frac{20}{7}-\frac{5}{7}=[/tex]
8) [tex]$\frac{19}{12}+\frac{5}{12}=[/tex]
9) [tex]$\frac{22}{15}-\frac{17}{15}=[/tex]
10) [tex]$\frac{15}{13}+\frac{8}{13}=[/tex]
11) [tex]$\frac{13}{11}+\frac{14}{11}=[/tex]
12) [tex]$\frac{21}{8}-\frac{7}{8}=[/tex]
13) [tex]$\frac{9}{14}+\frac{15}{14}=[/tex]
14) [tex]$\frac{31}{8}-\frac{11}{8}=[/tex]
15) [tex]$\frac{23}{4}-\frac{11}{4}=[/tex]
16) [tex]$\frac{17}{5}+\frac{9}{5}=[/tex]
17) [tex]$\frac{11}{6}+\frac{13}{6}=[/tex]
18) [tex]$\frac{23}{10}-\frac{7}{10}=[/tex]
Answer (2)
Subtract the numerators of fractions with like denominators: 6 23 − 6 7 = 6 16 = 3 8 .
Add the numerators of fractions with like denominators: 8 9 + 8 12 = 8 21 .
Simplify the resulting fractions to their simplest form, resulting in the answers: 3 8 , 8 21 , 3 8 , 5 6 , 7 15 , 2 , 3 1 , 13 23 , 11 27 , 4 7 , 7 12 , 2 5 , 3 , 5 26 , 4 , 5 8 .
The answers to the calculations are: 3 8 , 8 21 , 3 8 , 5 6 , 7 15 , 2 , 3 1 , 13 23 , 11 27 , 4 7 , 7 12 , 2 5 , 3 , 5 26 , 4 , 5 8 .
Explanation
Understanding the problem We are asked to add or subtract improper fractions with like denominators and simplify the answer if needed. We can leave the answer as an improper fraction where needed.
Solving problem 3
6 23 − 6 7 = 6 23 − 7 = 6 16 = 3 8
Solving problem 4
8 9 + 8 12 = 8 9 + 12 = 8 21
Solving problem 5
9 16 + 9 8 = 9 16 + 8 = 9 24 = 3 8
Solving problem 6
10 23 − 10 11 = 10 23 − 11 = 10 12 = 5 6
Solving problem 7
7 20 − 7 5 = 7 20 − 5 = 7 15
Solving problem 8
12 19 + 12 5 = 12 19 + 5 = 12 24 = 2
Solving problem 9
15 22 − 15 17 = 15 22 − 17 = 15 5 = 3 1
Solving problem 10
13 15 + 13 8 = 13 15 + 8 = 13 23
Solving problem 11
11 13 + 11 14 = 11 13 + 14 = 11 27
Solving problem 12
8 21 − 8 7 = 8 21 − 7 = 8 14 = 4 7
Solving problem 13
14 9 + 14 15 = 14 9 + 15 = 14 24 = 7 12
Solving problem 14
8 31 − 8 11 = 8 31 − 11 = 8 20 = 2 5
Solving problem 15
4 23 − 4 11 = 4 23 − 11 = 4 12 = 3
Solving problem 16
5 17 + 5 9 = 5 17 + 9 = 5 26
Solving problem 17
6 11 + 6 13 = 6 11 + 13 = 6 24 = 4
Solving problem 18
10 23 − 10 7 = 10 23 − 7 = 10 16 = 5 8
Examples
Understanding fractions is crucial in everyday situations, such as cooking, where you might need to halve or double a recipe. For instance, if a recipe calls for 3 2 cup of flour and you want to make half the recipe, you need to calculate half of 3 2 , which is 3 1 . Similarly, when splitting a pizza with friends, you're dealing with fractions to ensure everyone gets a fair share. Knowing how to add, subtract, multiply, and divide fractions allows you to accurately measure ingredients, divide quantities, and manage your resources effectively.
To add or subtract fractions with the same denominators, keep the denominator and simply add or subtract the numerators. The results for the given problems can be calculated as demonstrated, covering both addition and subtraction of fractions. The answers have been provided for all problems along with simplifications where applicable.
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