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$The fraction six-fifths$

⁶⁄₅ is an improper fraction, equal to the mixed fraction 1 ¹⁄₅.

Fractions 2 (Difficult)

Fractions are full of clever patterns. Learn to spot relationships between numbers and see how equal parts can look very different in 11 Plus Maths.

Explore the Topic →

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Fascinating Fact:

One half is equal to three sixths and four eighths, but if you add all three together you get one and one eighth. Fractions love to hide neat patterns.

In 11 Plus Maths, pupils develop confidence by exploring how fractions can be simplified, compared, and combined. This understanding supports future learning in percentages, ratios, and algebraic reasoning.

Key Terms

Equivalent Fractions: Fractions that represent the same value even though they use different numbers.
Simplify: To reduce a fraction to its smallest form by dividing both numerator and denominator by the same number.
Improper Fraction: A fraction where the numerator is larger than the denominator, for example 9/5.

Parents can find example questions and practice materials in our guide to 11 Plus sample questions.

Frequently Asked Questions (Click to see answers)

How do you know if two fractions are equivalent?

Two fractions are equivalent if you can multiply or divide both the numerator and denominator of one fraction to make the other. For example, 1/2 and 3/6 are equivalent.

How do you add fractions with different denominators?

Find a common denominator, convert each fraction to that base, then add the numerators. Finally, simplify the answer if needed.

Why do we simplify fractions?

Simplifying fractions makes them easier to understand and compare. It shows the same value using the smallest possible numbers.

Try These Related Quizzes

1 .

What is ²⁶⁄₆ as a mixed fraction in its simplest form?

4 ¹⁄₂

4 ¹⁄₃

4 ¹⁄₄

4 ¹⁄₆

To convert an improper fraction to a mixed fraction, follow these steps: 1. Divide the numerator by the denominator. 2. Note the whole number remainder. 3. Write the number from step 1 as the whole number in front of the fractional part AND write the fractional part with the remainder in the numerator and keep the original denominator. STEP 1: 26 ÷ 6 = 4. STEP 2: Remainder 2. STEP 3: 4 ²/₆. Divide the numerator and denominator by 2 to reduce the fraction to its simplest form: 4 ¹/₃

2 .

What is ⁵⁄₆ + ²⁄₃ + ⁶⁄₁₈ expressed as a mixed fraction?

1 ¹⁄₃

1 ²⁄₃

1 ⁵⁄₆

1 ¹⁷⁄₁₈

First, make all the fractions have the same denominator: ⁵/₆ + ²/₃ + ⁶/₁₈ = ⁵/₆ + ⁴/₆ + ²/₆. Here we see a shortcut: ⁴/₆ + ²/₆ = 1, so the answer is 1 ⁵/₆

3 .

If ⁵¹⁄₁₀₀ of the electorate voted for the government, how many people voted against the government?

24 people

49 people

²⁴⁄₅₀ of the electorate

⁴⁹⁄₁₀₀ of the electorate

⁵¹/₁₀₀ of the electorate voted for the government BUT fractions alone DO NOT tell you the actual number of people involved. If you had been told that there were 100 voters, then choice 2 would have been the best answer. Always be on the lookout for the BEST answer

4 .

What is ⁴²⁄₈ as a mixed fraction in its simplest form?

5 ²⁄₄

5 ¹⁄₂

5 ¹⁄₄

5 ¹⁄₈

To convert an improper fraction to a mixed fraction, follow these steps: 1. Divide the numerator by the denominator. 2. Note the whole number remainder. 3. Write the number from step 1 as the whole number in front of the fractional part AND write the fractional part with the remainder in the numerator and keep the original denominator. STEP 1: 42 ÷ 8 = 5. STEP 2: Remainder 2. STEP 3: 5 ²/₈. Simplify the fraction by dividing the numerator and denominator by the same number, in this case 2, to get your final answer, 5 ¹/₄.

5 .

There are 28 pupils in a class. If ⁴⁄₇ of them are girls, how many boys are in the class?

All you have to do is find ⁴/₇ of 28 and subtract it from 28: ⁴/₇ × 28 = (4 × 28) ÷ 7 = 112 ÷ 7 = 16. That's the number of girls. To find the number of boys, just subtract 16 from 28: 28 - 16 = 12

6 .

What is ³⁄₄ of ⁴⁄₁₅ in its simplest form?

¹⁄₅

¹⁄₄

¹⁄₃

¹⁄₆

The word OF means multiply: ³/₄ x ⁴/₁₅ = ¹²/₆₀. You multiply the numbers in the denominator together, and you multiply the numbers in the numerator together to form a single fraction. This fraction can then be reduced to its simplest form: sometimes you can reduce the fractions before you multiply them together

7 .

What is 14 ⁸⁄₁₀ as an improper fraction in its simplest form?

⁷⁴⁄₅

¹⁴⁸⁄₁₀

¹²⁰⁄₈

³¹⁄₂

To convert a mixed fraction to an improper fraction, follow these steps: 1. Multiply the whole number part by the denominator. 2. Add this result to the numerator. 3. Write the fraction with step 2 in the numerator and keep the original denominator. STEP 1: 14 × 10 = 140. STEP 2: 140 + 8 = 148. STEP 3: ¹⁴⁸/₁₀. Divide the numerator and denominator by 2 to reduce the fraction to its simplest form: ⁷⁴/₅

8 .

What is 5 ⁴⁄₁₆ as an improper fraction in its simplest form?

¹¹⁄₂

²¹⁄₄

⁴¹⁄₈

⁸⁴⁄₁₆

To convert a mixed fraction to an improper fraction, follow these steps: 1. Multiply the whole number part by the denominator. 2. Add this result to the numerator. 3. Write the fraction with step 2 in the numerator and keep the original denominator. STEP 1: 5 × 16 = 80. STEP 2: 80 + 4 = 84. STEP 3: ⁸⁴/₁₆. Divide the numerator and denominator by the same number, in this case 4, to reduce the fraction to its simplest form: ²¹/₄

9 .

A ¹⁄₁₂ x ¹⁄₁₂ is the same as what fraction of a sixth?

¹⁄₁₂

¹⁄₃₆

¹⁄₂₄

¹⁄₄₈

¹/₁₂ x ¹/₁₂ = ¹/₁₄₄. You now have to find a fraction which multiplied with ¹/₆ gives ¹/₁₄₄. Well, 144 ÷ 6 = 24, so the fraction (in its simplest form) must be ¹/₂₄

10 .

How many ⁴⁄₁₈ are there in ²⁄₃?

⁴/₁₈ can be reduced to ²/₉ (divide the numerator and the denominator by 2) and ²?₃ can be turned into ⁶/₉ (multiply the numerator and the denominator by 3) . Now you can see that ⁶/₉ is thrice as much as ²/₉

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)