Operations With Fractions

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Adding & Subtracting Fractions

Find the lowest common denominator (LCD) of the fractions.
Rewrite each fraction as an equivalent fraction with the LCD.
Add or subtract the numerators only; keep the denominator the same.
Simplify the result by cancelling common factors.
If a fraction is a mixed number, convert it to an improper fraction first.
After calculation, convert back to a mixed number if required.

Multiplying Fractions

Cancel any common factors between numerators and denominators before multiplying.
Multiply the numerators together and the denominators together.
If a fraction is a mixed number, convert it to an improper fraction first.
Simplify the final fraction by cancelling any remaining common factors.
Convert improper fractions back to mixed numbers if needed.

Dividing Fractions

Flip the second fraction (find its reciprocal) and change ÷ to ×.
This is often remembered as 'flip and times'.
Cancel common factors before multiplying.
Multiply the numerators together and the denominators together.
If a fraction is a mixed number, convert it to an improper fraction first.
Simplify and convert back to a mixed number if required.

Working with Mixed Numbers

Convert mixed numbers to improper fractions: multiply the whole part by the denominator, add the numerator, write over the denominator.
Perform the operation (add, subtract, multiply, divide) using the improper fractions.
Convert the final answer back to a mixed number if the question asks for it or if it's an improper fraction.

Simplifying Fractions

Always give your final answer in simplest form.
Cancel common factors by dividing numerator and denominator by the same number.
Check for common factors at every step to keep numbers small.
A fraction is in simplest form when the numerator and denominator have no common factors other than 1.

Common Mistakes to Avoid

Do not add or subtract denominators; only numerators.
Always find a common denominator before adding or subtracting.
Remember to convert mixed numbers before performing operations.
When dividing, flip only the second fraction, not the first.

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1.Work out \frac{5}{6} + \frac{2}{3}. Give your answer as a mixed number in its simplest form.
Medium
- A1\frac{1}{2}
- B1\frac{1}{3}
- C\frac{7}{9}
- D1\frac{1}{6}
2.Giulio's reaction times are \frac{1}{3} second and \frac{1}{8} second. Find the difference between the two reaction times.
Medium
- A\frac{5}{24} seconds
- B\frac{11}{24} seconds
- C\frac{1}{5} seconds
- D\frac{1}{24} seconds
3.Work out \frac{12}{35} \times \frac{7}{9}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{4}{15}
- B\frac{84}{315}
- C\frac{12}{45}
- D\frac{4}{45}
4.Write down a fraction that completes \frac{13}{11} \times \ldots = 1.
Easy
- A\frac{11}{13}
- B\frac{13}{11}
- C\frac{1}{11}
- D\frac{1}{13}
5.Work out \frac{7}{8} + \frac{1}{6}. Give your answer as a mixed number in its simplest form.
Medium
- A1\frac{1}{24}
- B\frac{25}{24}
- C1\frac{1}{12}
- D\frac{8}{14}
6.Work out 1\frac{3}{4} - \frac{11}{12}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{5}{6}
- B\frac{7}{12}
- C\frac{1}{2}
- D\frac{11}{12}
7.Work out \frac{15}{28} \div \frac{4}{7}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{15}{16}
- B\frac{105}{112}
- C\frac{15}{49}
- D\frac{60}{28}
8.Work out 1\frac{7}{12} + \frac{13}{20}. Give your answer as a mixed number in its simplest form.
Hard
- A2\frac{7}{30}
- B2\frac{1}{15}
- C1\frac{59}{60}
- D2\frac{1}{2}

Mehr Fragen

9.Work out \frac{5}{16} \times 1\frac{1}{7}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{5}{14}
- B\frac{5}{112}
- C\frac{5}{7}
- D\frac{40}{112}
10.Work out 2\frac{1}{3} + \frac{4}{5}. Give your answer as a mixed number in its simplest form.
Medium
- A3\frac{2}{15}
- B3\frac{1}{2}
- C2\frac{17}{15}
- D3\frac{1}{15}
11.Work out 2\frac{1}{4} \div \frac{3}{7}. Give your answer as a mixed number in its simplest form.
Medium
- A5\frac{1}{4}
- B\frac{21}{12}
- C1\frac{3}{4}
- D5\frac{1}{2}
12.Work out 2\frac{2}{3} \times 2\frac{3}{4}. Give your answer as a mixed number in its simplest form.
Hard
- A7\frac{1}{3}
- B7\frac{1}{2}
- C6\frac{1}{2}
- D7
13.Work out \frac{5}{6} \div 1\frac{1}{3}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{5}{8}
- B\frac{5}{9}
- C\frac{15}{24}
- D\frac{2}{3}
14.Work out 1\frac{1}{7} \times 2\frac{1}{10}. Give your answer as a mixed number in its simplest form.
Medium
- A2\frac{2}{5}
- B2\frac{1}{35}
- C2\frac{1}{5}
- D2\frac{3}{10}
15.Work out \left(2\frac{1}{3} - \frac{7}{8}\right) \times \frac{6}{25}. Give your answer as a fraction in its simplest form.
Hard
- A\frac{1}{4}
- B\frac{1}{5}
- C\frac{7}{20}
- D\frac{3}{10}
16.Work out 3\frac{1}{4} - 2\frac{2}{3}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{7}{12}
- B\frac{11}{12}
- C\frac{5}{12}
- D\frac{1}{2}
17.Work out \frac{1}{4} + \frac{3}{8}. Give your answer as a fraction in its simplest form.
Easy
- A\frac{5}{8}
- B\frac{4}{12}
- C\frac{1}{2}
- D\frac{7}{8}
18.Work out \frac{7}{10} - \frac{2}{5}. Give your answer as a fraction in its simplest form.
Easy
- A\frac{5}{5}
- B\frac{3}{10}
- C\frac{1}{2}
- D\frac{9}{10}
19.Work out \frac{2}{3} \times \frac{3}{4}. Give your answer as a fraction in its simplest form.
Easy
- A\frac{6}{12}
- B\frac{1}{2}
- C\frac{5}{7}
- D\frac{2}{4}
20.Work out \frac{5}{8} \div \frac{1}{4}. Give your answer as a mixed number in its simplest form.
Medium
- A\frac{5}{32}
- B2\frac{1}{2}
- C\frac{5}{2}
- D\frac{5}{12}
21.Work out 1\frac{2}{5} + \frac{3}{10}. Give your answer as a mixed number in its simplest form.
Medium
- A1\frac{5}{15}
- B1\frac{7}{10}
- C1\frac{1}{2}
- D1\frac{5}{10}
22.Work out 2\frac{1}{3} - 1\frac{1}{2}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{5}{6}
- B\frac{1}{6}
- C\frac{11}{6}
- D\frac{7}{6}
23.Work out \frac{3}{8} \times 2\frac{2}{5}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{9}{10}
- B\frac{36}{40}
- C\frac{6}{13}
- D\frac{3}{20}
24.Work out \frac{7}{12} \div \frac{5}{6}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{35}{72}
- B\frac{7}{10}
- C\frac{42}{60}
- D\frac{5}{14}
25.Work out 1\frac{3}{5} + \frac{7}{10}. Give your answer as a mixed number in its simplest form.
Medium
- A2\frac{3}{10}
- B1\frac{10}{15}
- C2\frac{1}{2}
- D1\frac{13}{10}
26.Work out 2\frac{1}{4} - \frac{5}{6}. Give your answer as a mixed number in its simplest form.
Medium
- A1\frac{5}{12}
- B1\frac{1}{2}
- C1\frac{7}{12}
- D1\frac{5}{6}
27.Work out \frac{4}{9} \times 2\frac{1}{4}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{8}{36}
- B1
- C\frac{9}{9}
- D\frac{4}{9}
28.Work out 1\frac{5}{6} \div \frac{7}{12}. Give your answer as a mixed number in its simplest form.
Medium
- A3\frac{1}{7}
- B\frac{22}{7}
- C3\frac{1}{2}
- D\frac{7}{22}
29.Work out 2\frac{2}{3} - 1\frac{5}{6}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{5}{6}
- B\frac{1}{2}
- C\frac{4}{6}
- D\frac{7}{6}
30.Work out \frac{9}{14} \times \frac{7}{15}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{63}{210}
- B\frac{3}{10}
- C\frac{9}{30}
- D\frac{7}{14}
31.Work out 3\frac{1}{8} \div 1\frac{2}{3}. Give your answer as a mixed number in its simplest form.
Medium
- A1\frac{7}{8}
- B\frac{15}{8}
- C2\frac{1}{8}
- D1\frac{5}{8}
32.Work out \left(1\frac{1}{2} + \frac{3}{4}\right) \times \frac{2}{9}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{1}{2}
- B\frac{5}{18}
- C\frac{2}{9}
- D\frac{1}{3}
33.A recipe requires \frac{3}{4} cup of sugar for one batch. To make 2\frac{1}{2} batches, how many cups of sugar are needed?
Medium
- A1\frac{7}{8}
- B1\frac{1}{2}
- C2\frac{1}{8}
- D2\frac{1}{4}
34.A rectangular garden has length \frac{5}{6} m and width \frac{3}{10} m. What is the area of the garden?
Medium
- A\frac{1}{4} m²
- B\frac{15}{60} m²
- C\frac{8}{16} m²
- D\frac{25}{30} m²
35.Work out \frac{2}{9} + \frac{1}{3}.
Easy
- A\frac{5}{9}
- B\frac{3}{12}
- C\frac{1}{3}
- D\frac{1}{2}
36.A jug contains 1\frac{3}{4} litres of water. After pouring out \frac{5}{8} litre, how much water remains?
Medium
- A1\frac{1}{8} litres
- B\frac{9}{8} litres
- C\frac{11}{8} litres
- D1\frac{3}{8} litres
37.Work out \left(1\frac{1}{2} - \frac{2}{3}\right) \div \frac{5}{12}.
Hard
- A2
- B1\frac{1}{5}
- C1\frac{7}{10}
- D\frac{5}{6}
38.Write \frac{3}{4} \times \frac{2}{5} as a fraction in its simplest form.
Easy
- A\frac{3}{10}
- B\frac{6}{20}
- C\frac{5}{9}
- D\frac{1}{2}
39.A piece of string 2\frac{1}{2} m long is cut into pieces each \frac{5}{8} m long. How many pieces are there?
Medium
- A4
- B3
- C5
- D2
40.In a school, \frac{3}{8} of the students are boys. If there are 120 girls, how many students are there in total?
Hard
- A192
- B320
- C200
- D150
41.What is the first step when adding two fractions?
Easy
- AFind the lowest common denominator
- BAdd the numerators
- CMultiply the denominators
- DConvert to decimals
42.When adding fractions, you add the denominators as well as the numerators.
Easy
True or false?
43.Which of the following is the reciprocal of \frac{3}{5}?
Easy
- A\frac{5}{3}
- B\frac{3}{5}
- C-\frac{3}{5}
- D\frac{1}{5}
44.Work out \frac{2}{3} + \frac{1}{4}.
Medium
- A\frac{11}{12}
- B\frac{3}{7}
- C\frac{8}{12}
- D\frac{5}{12}
45.Work out \frac{3}{8} \times \frac{4}{9}.
Medium
- A\frac{1}{6}
- B\frac{12}{72}
- C\frac{7}{17}
- D\frac{3}{18}
46.Work out 1\frac{1}{2} + \frac{3}{4}. Give your answer as a mixed number.
Medium
- A2\frac{1}{4}
- B1\frac{5}{4}
- C2\frac{3}{4}
- D1\frac{1}{4}
47.Work out 2\frac{2}{3} \times 1\frac{1}{2}. Give your answer as a mixed number.
Medium
- A4
- B3\frac{1}{3}
- C3\frac{2}{3}
- D4\frac{1}{3}
48.Match each operation with the correct first step.
Medium
- Adding fractions
- Subtracting fractions
- Multiplying fractions
- Dividing fractions
- Find a common denominator, then add the numerators
- Find a common denominator, then subtract the numerators
- Cancel common factors
- Flip the second fraction and multiply
49.Put the following steps in the correct order to work out \frac{2}{3} + \frac{1}{4}.
Medium
- Find the lowest common denominator of 3 and 4
- Write each fraction as an equivalent fraction over 12
- Add the numerators: 8 + 3 = 11
- Write the answer as \frac{11}{12}
50.When dividing fractions, you multiply the first fraction by the reciprocal of the second fraction.
Easy
True or false?
51.Complete the sentence.
Easy
To divide by a fraction, you multiply by its ____.
52.Work out \frac{5}{6} - \frac{1}{3}. Give your answer as a decimal.
Medium
53.Work out \frac{2}{5} \div \frac{3}{10}. Give your answer as a decimal, to 3 decimal places.
Medium
54.Work out 1\frac{3}{4} \div \frac{5}{8}. Give your answer as a decimal.
Medium
55.A recipe uses \frac{2}{3} cup of flour for one batch. To make 2\frac{1}{2} batches, how many cups of flour are needed?
Medium
56.Explain why you cannot add \frac{1}{3} and \frac{1}{4} by simply adding the numerators and denominators.
Hard
57.Work out \frac{5}{6} - \frac{1}{3}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{1}{2}
- B\frac{5}{18}
- C\frac{2}{3}
- D\frac{1}{3}
58.Work out \frac{2}{5} \div \frac{3}{10}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{4}{3}
- B\frac{3}{4}
- C\frac{3}{25}
- D\frac{20}{15}
59.Work out 1\frac{3}{4} \div \frac{5}{8}. Give your answer as a mixed number.
Medium
- A2\frac{4}{5}
- B1\frac{4}{5}
- C2\frac{1}{5}
- D3\frac{1}{5}
60.A recipe uses \frac{2}{3} cup of flour for one batch. To make 2\frac{1}{2} batches, how many cups of flour are needed?
Medium
- A2\frac{1}{3} cups
- B1\frac{2}{3} cups
- C1\frac{1}{3} cups
- D2 cups

Lernnotizen

## Operations with Fractions ### Adding & Subtracting Fractions - Find the **lowest common denominator** (LCD). - Write each fraction as an equivalent fraction over the LCD. - Add or subtract the numerators; keep the denominator the same. - Simplify by cancelling common factors. - If mixed numbers: convert to improper fractions first, then convert back at the end. **Example:** \(\frac{2}{3} + \frac{1}{5} = \frac{10}{15} + \frac{3}{15} = \frac{13}{15}\) **Example:** \(3\frac{3}{4} - \frac{5}{8} = \frac{15}{4} - \frac{5}{8} = \frac{30}{8} - \frac{5}{8} = \frac{25}{8} = 3\frac{1}{8}\) ### Multiplying Fractions - Cancel any common factors between numerators and denominators (cross-cancel). - Multiply numerators together, multiply denominators together. - Simplify if possible. - For mixed numbers: convert to improper fractions first. **Example:** \(\frac{4}{15} \times \frac{25}{11} = \frac{4}{3} \times \frac{5}{11} = \frac{20}{33}\) ### Dividing Fractions - **Flip the second fraction** (find its reciprocal) and change ÷ to ×. - Then follow multiplication steps. - Remember: “flip’n’times”. **Example:** \(3\frac{1}{4} \div \frac{3}{8} = \frac{13}{4} \times \frac{8}{3} = \frac{13}{1} \times \frac{2}{3} = \frac{26}{3} = 8\frac{2}{3}\) ### Key Tips - Always show working. - Simplify answers to simplest form. - For mixed number answers, ensure the fraction part is proper. - No calculators allowed in exam.

Lowest common denominator (LCD): The smallest number that is a multiple of both denominators; used to write fractions with a common denominator for addition/subtraction.
Improper fraction: A fraction where the numerator is greater than or equal to the denominator, e.g., 13/4.
Mixed number: A number consisting of an integer part and a proper fraction part, e.g., 3 1/4.
Reciprocal: The flipped version of a fraction; the reciprocal of a/b is b/a. Used in division: dividing by a fraction is multiplying by its reciprocal.
Simplify: Cancel common factors from numerator and denominator to write the fraction in its simplest form.

Karteikarten

How do you add or subtract fractions?

Find the lowest common denominator, write each fraction as an equivalent fraction over this denominator, then add or subtract the numerators. Do not add the denominators. Simplify if possible.

What should you do if any fractions are mixed numbers when adding or subtracting?

Convert any mixed numbers into improper fractions first, then add or subtract as usual. Convert the answer back to a mixed number if required.

How do you multiply two fractions?

Cancel any common factors between numerators and denominators, then multiply the numerators together and the denominators together. Simplify if possible.

What should you do if a fraction is a mixed number when multiplying?

Convert the mixed number into an improper fraction before multiplying. Convert the answer back to a mixed number if required.

How do you divide two fractions?

Flip the second fraction (find its reciprocal) and change ÷ to ×. Cancel any common factors, then multiply the fractions. Simplify if possible.

What should you do if a fraction is a mixed number when dividing?

Convert the mixed number into an improper fraction before dividing. Convert the answer back to a mixed number if required.

Find the lowest common denominator of 3 and 5.

Convert 3 3/4 to an improper fraction.

15/4

Convert 3 1/4 to an improper fraction.

13/4

What is the reciprocal of 4/5?

5/4

Simplify: 2/3 + 1/5

13/15

Simplify: 3 3/4 - 5/8 (answer as mixed number)

3 1/8

Simplify: 4/15 × 25/11

20/33

Simplify: 3 1/4 ÷ 3/8 (answer as mixed number)

8 2/3

Without a calculator, work out 5/6 + 2/3. Give your answer as a mixed number in simplest form.

1 1/2

Find the difference between 1/3 and 1/8.

5/24

Without a calculator, work out 12/35 × 7/9. Give your answer as a fraction in simplest form.

4/15

Find a fraction that completes 13/11 × ? = 1.

11/13

Without a calculator, work out 7/8 + 1/6. Give your answer as a mixed number in simplest form.

1 1/24

Without a calculator, work out 1 3/4 - 11/12. Give your answer as a fraction in simplest form.

5/6

Without a calculator, work out 15/28 ÷ 4/7. Give your answer as a fraction in simplest form.

15/16

Without a calculator, work out 1 7/12 + 13/20. Give your answer as a mixed number in simplest form.

2 7/30

Without a calculator, work out 5/16 × 1 1/7. Give your answer as a fraction in simplest form.

5/14

Without a calculator, work out 2 1/3 + 4/5. Give your answer as a mixed number in simplest form.

3 2/15

Without a calculator, work out 2 1/4 ÷ 3/7. Give your answer as a mixed number in simplest form.

5 1/4

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