Fractions Toolkit

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Notes de leçon

Basic Fractions

A fraction is written as \frac{a}{b} where a (numerator) and b (denominator) are integers.
The denominator shows how many parts each whole is split into; the numerator shows how many parts you have.
A fraction is less than 1 if numerator < denominator; greater than 1 if numerator > denominator.
To find a fraction of an amount: divide by denominator, multiply by numerator (e.g., \frac{2}{5} of 60: 60 ÷ 5 = 12, 12 × 2 = 24).
Equivalent fractions represent the same amount; multiply top and bottom by the same number to find them.
Simplify a fraction by dividing numerator and denominator by a common factor (e.g., \frac{12}{18} = \frac{2}{3}).

Mixed Numbers & Improper Fractions

A mixed number has an integer part and a fraction part (e.g., 3\frac{3}{4}).
An improper fraction (top-heavy) has numerator ≥ denominator (e.g., \frac{15}{4}).
To convert a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, write over the denominator.
To convert an improper fraction to a mixed number: divide numerator by denominator; the quotient is the whole number, remainder over denominator is the fraction.
Always convert mixed numbers to improper fractions before adding, subtracting, multiplying, or dividing.

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; keep the denominator the same.
Simplify the result by cancelling common factors.
If mixed numbers are involved, convert them to improper fractions first, then add/subtract, and convert back if needed.

Multiplying Fractions

Cancel any common factors between numerators and denominators before multiplying.
Multiply the numerators together and the denominators together.
Simplify the resulting fraction if possible.
If a mixed number is involved, convert it to an improper fraction first.
Example: \frac{4}{15} \times \frac{25}{11} = \frac{4 \times 25}{15 \times 11} = \frac{100}{165} = \frac{20}{33} after cancelling.

Dividing Fractions

To divide, flip the second fraction (find its reciprocal) and change ÷ to ×.
Then follow the multiplication steps: cancel, multiply numerators, multiply denominators.
If a mixed number is involved, convert it to an improper fraction first.
Example: 3\frac{1}{4} \div \frac{3}{8} = \frac{13}{4} \times \frac{8}{3} = \frac{13 \times 8}{4 \times 3} = \frac{104}{12} = \frac{26}{3} = 8\frac{2}{3}.

Working with Fractions of Amounts

To find a fraction of an amount, multiply the amount by the fraction.
Write the amount as a fraction over 1 (e.g., 60 = \frac{60}{1}).
Then multiply the fractions as usual.
Alternatively, divide by denominator then multiply by numerator.

Simplifying Fractions

A fraction is in its simplest form when numerator and denominator have no common factors other than 1.
Divide both numerator and denominator by their highest common factor (HCF).
Your calculator can simplify fractions automatically, but show the factor you divided by if working is required.

Common Mistakes & Tips

When adding/subtracting, do not add denominators.
Always simplify final answers unless stated otherwise.
Convert mixed numbers to improper fractions before any operation.
Remember "flip'n'times" for division: flip the second fraction and multiply.

Diapos

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Questions d'entraînement

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1.What is a fraction?
Easy
- AA number written as a/b where a and b are integers
- BA number with a decimal point
- CA number less than 1
- DA number greater than 1
2.What is the numerator in the fraction 3/5?
Easy
- A3
- B5
- C8
- D2
3.Which of the following is an improper fraction?
Easy
- A7/4
- B3/5
- C2/3
- D1/2
4.Convert 5 2/7 into an improper fraction.
Easy
- A37/7
- B35/7
- C12/7
- D33/7
5.Convert 22/3 into a mixed number.
Easy
- A7 1/3
- B7 2/3
- C6 1/3
- D7 1/2
6.Simplify 12/18 to its lowest terms.
Easy
- A2/3
- B3/4
- C1/2
- D4/6
7.Work out 2/5 of 60.
Easy
- A24
- B12
- C30
- D150
8.Which fraction is equivalent to 3.875?
Medium
- A31/8
- B15/4
- C29/8
- D15/8

Plus de questions

9.Work out 3/5 + 5/8. Give your answer as a mixed number in simplest form.
Medium
- A1 9/40
- B1 1/2
- C49/40
- D8/13
10.One month, Gretal spent a total of $360 on presents. She spent 1/5 on parents, then 2/3 of the remaining on friends, and the rest on sisters. What percentage did she spend on sisters?
Hard
- A26.67%
- B20%
- C13.33%
- D40%
11.Work out 4 2/3 ÷ 1 3/4. Write your answer as a fraction in simplest form.
Medium
- A8/3
- B2 2/3
- C7/3
- D5/2
12.Work out 2 2/3 + 3 1/2. Give your answer as a mixed number in simplest form.
Medium
- A6 1/6
- B5 5/6
- C6 1/3
- D5 1/6
13.Work out (2 1/3 - 7/8) × 6/25. Give your answer as a fraction in simplest form.
Hard
- A7/20
- B1/2
- C11/20
- D3/10
14.Write $24.60 as a fraction of $2870 in its lowest terms.
Medium
- A\frac{123}{14350}
- B\frac{246}{28700}
- C\frac{3}{350}
- D\frac{123}{1435}
15.Work out \frac{7}{11} of 198 kg.
Easy
- A126 kg
- B128 kg
- C124 kg
- D130 kg
16.Work out \frac{15}{28} \div \frac{4}{7}. Give your answer as a fraction in simplest form.
Medium
- A\frac{15}{16}
- B\frac{105}{112}
- C\frac{7}{15}
- D\frac{16}{15}
17.Work out \frac{2}{3} + \frac{1}{4} \times \frac{2}{3}. Give your answer as a fraction in simplest form.
Medium
- A\frac{5}{6}
- B\frac{1}{2}
- C\frac{7}{12}
- D\frac{11}{12}
18.Lily's age is 2 years and 4 months. Hugo's age is 1 year and 8 months. Write Lily's age in months as a fraction of Hugo's age in months. Give your fraction in its simplest form.
Medium
- A\frac{7}{5}
- B\frac{5}{7}
- C\frac{28}{20}
- D\frac{4}{3}
19.Work out \frac{3}{4} + \frac{1}{6}. Give your answer in its simplest form.
Medium
- A\frac{11}{12}
- B\frac{5}{6}
- C\frac{7}{12}
- D\frac{13}{12}
20.Work out \frac{2}{15} \times \frac{15}{22}. Give your answer in its lowest terms.
Easy
- A\frac{1}{11}
- B\frac{2}{11}
- C\frac{30}{330}
- D\frac{1}{22}
21.Work out 3\frac{1}{8} \div \frac{5}{12}. Give your answer as a mixed number in its simplest form.
Medium
- A7\frac{1}{2}
- B6\frac{1}{2}
- C8\frac{1}{2}
- D7\frac{3}{4}
22.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}
- B4\frac{3}{4}
- C5\frac{3}{4}
- D4\frac{1}{4}
23.Collette has $136 and spends half of her money on clothes and \frac{1}{5} of her money on books. Calculate the amount she has left.
Medium
- A$40.80
- B$47.60
- C$54.40
- D$34.00
24.Work out \frac{1}{7} \times \frac{2}{3}.
Easy
- A\frac{2}{21}
- B\frac{3}{10}
- C\frac{2}{10}
- D\frac{1}{10}
25.Work out \frac{3}{5} - \frac{1}{3}.
Easy
- A\frac{4}{15}
- B\frac{2}{15}
- C\frac{1}{15}
- D\frac{7}{15}
26.Work out 1\frac{3}{4} \times \frac{6}{35}. Give your answer as a fraction in its simplest form.
Medium
- A\frac{3}{10}
- B\frac{1}{5}
- C\frac{2}{5}
- D\frac{9}{70}
27.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}
- C1\frac{2}{3}
- D1\frac{1}{6}
28.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}{12}
- C\frac{7}{16}
- D\frac{5}{8}
29.What is the numerator in the fraction 5/8?
Easy
- A5
- B8
- C3
- D13
30.Giulio's reaction times are \frac{1}{3} second and \frac{1}{8} second. Find the difference.
Medium
- A\frac{5}{24} s
- B\frac{11}{24} s
- C\frac{1}{5} s
- D\frac{5}{11} s
31.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{4}{9}
- D\frac{12}{45}
32.Work out \frac{1}{4} \div \frac{2}{3}. Give your answer as a fraction.
Easy
- A\frac{3}{8}
- B\frac{1}{6}
- C\frac{2}{3}
- D\frac{3}{2}
33.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}
34.Work out 2\frac{2}{3} \times 2\frac{3}{4}. Give your answer as a mixed number in its simplest form.
Medium
- A7\frac{1}{3}
- B7\frac{1}{4}
- C7\frac{2}{3}
- D7\frac{1}{2}
35.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}
36.Which of the following is an equivalent fraction to \frac{3}{5}?
Easy
- A\frac{6}{10}
- B\frac{6}{5}
- C\frac{3}{10}
- D\frac{9}{5}
37.The fraction \frac{7}{4} is less than 1.
Easy
True or false?
38.What is \frac{3}{8} of 64?
Easy
- A24
- B8
- C16
- D32
39.Convert 5\frac{2}{3} into an improper fraction.
Easy
- A\frac{17}{3}
- B\frac{15}{3}
- C\frac{13}{3}
- D\frac{10}{3}
40.Match each fraction on the left with its equivalent simplified fraction on the right.
Medium
- 8/12
- 15/25
- 10/16
- 6/8
- 3/5
- 5/8
- 2/3
- 3/4
41.Place the following fractions in ascending order (smallest to largest).
Medium
- 2/3
- 5/8
- 3/5
- 7/12
42.The fraction 5/4 is less than 1.
Easy
True or false?
43.Which of the following is the correct result of \frac{3}{4} \times \frac{8}{9}?
Medium
- A2/3
- B3/8
- C27/32
- D1/2
44.Work out \frac{5}{6} \div \frac{2}{3}. Give your answer as a mixed number.
Medium
- A1 1/4
- B5/9
- C1 1/2
- D5/4
45.What is \frac{3}{8} of 72?
Easy
- A27
- B24
- C9
- D28
46.Work out \frac{2}{3} + \frac{1}{4}. Give your answer as a fraction in its simplest form.
Medium
47.Work out \frac{5}{6} - \frac{1}{3}. Give your answer as a fraction in its simplest form.
Easy
48.Work out \frac{2}{5} \times \frac{15}{16}. Give your answer as a fraction in its simplest form.
Medium
49.Work out \frac{3}{4} \div \frac{2}{5}. Give your answer as a fraction in its simplest form.
Medium
50.Work out 2\frac{1}{3} + 1\frac{3}{4}. Give your answer as a mixed number in its simplest form.
Medium
51.Work out 1\frac{2}{5} \div \frac{7}{10}. Give your answer as a mixed number in its simplest form.
Medium
52.Work out 3/5 of 250.
Easy
53.Convert the mixed number to an improper fraction.
Easy
5 2/3 = ____
54.Simplify the fraction 24/36 completely.
Easy
55.Work out 3/5 of 250.
Easy
- A150
- B180
- C135
- D165
56.Work out \frac{2}{3} + \frac{1}{4}. Give your answer as a fraction in simplest form.
Medium
- A12 /12
- B10 /12
- C13 /12
- D11 /12

Notes de révision

## Fractions Toolkit - Quick Revision ### Basic Fractions - **Fraction**: numerator/denominator (e.g., 2/3). - **Finding a fraction of an amount**: Divide by denominator, multiply by numerator. E.g., 2/5 of 60 = 60÷5×2 = 24. - **Equivalent fractions**: Multiply top and bottom by same number. - **Simplifying**: Divide top and bottom by common factor. ### Mixed Numbers & Improper Fractions - **Mixed → Improper**: Multiply whole by denominator, add numerator. E.g., 5 2/7 = (5×7+2)/7 = 37/7. - **Improper → Mixed**: Divide numerator by denominator; whole part is quotient, remainder over denominator. E.g., 22/3 = 7 1/3. ### Adding & Subtracting Fractions - Find lowest common denominator. - Convert to equivalent fractions. - Add/subtract numerators only. - Simplify. - For mixed numbers, convert to improper first. ### Multiplying & Dividing Fractions - **Multiply**: Cancel common factors, then multiply numerators and denominators. - **Divide**: Flip the second fraction and multiply ("flip'n'times"). - For mixed numbers, convert to improper first. ### Key Tips - Use calculator to simplify, but show working if asked. - Always simplify final answer. - Convert answers to mixed numbers if required.

Fraction: A number written as a/b where a and b are integers; a is numerator, b is denominator.
Equivalent fractions: Fractions that represent the same amount, obtained by multiplying numerator and denominator by the same number.
Simplifying (cancelling) a fraction: Dividing numerator and denominator by a common factor to get the smallest possible integer values.
Mixed number: A number consisting of an integer part and a fraction part, e.g., 3 3/4.
Improper fraction: A fraction where the numerator is greater than the denominator, e.g., 15/4.
Lowest common denominator: The smallest number that can be divided by all denominators in a set of fractions.
Reciprocal: The flipped version of a fraction; used when dividing fractions.

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